Terrorist attacks pose a serious threat to social stability and people's lives and property. By launching extreme violent attacks, terrorist organizations directly convey information about the strategic objectives and ideology of the organization to their members and potential supporters through actions, which stimulates the extreme level of their members' behavior and promotes the extreme level of their potential supporters' thoughts. The attack tactics of terrorist organizations reflect the goals of terrorist organizations, show the strength of terrorist organizations, and reflect the degree of violent extremism of terrorist organizations, which plays an important role in strengthening the organizational identity of terrorist organizations and promoting the evolution of the extremist process of their members. Therefore, studying the decision-making mechanism of terrorist organization's attack behavior is helpful for deeply understanding the problem of behavior extremism and mobilization at the organizational level, and is of great significance for realizing intelligent calculation, prediction and early warning of terrorist attacks and the formulation of anti-terrorist measures.
Aiming at the problem that the existing research can't fully understand the common mechanism of extreme behavior decision-making of terrorist organizations, firstly, based on the cost-benefit theory of social economics and the data analysis of “Global Terrorism Database” (GTD), the decision-making characteristics of extreme violent attacks of terrorist organizations are obtained.
This article selects the attack type, weapon information and attack target type data of “Taliban”, “Islamic State of Iraq and the Levant”, “Somali Al-Shabaab” and “Boko Haram” from the GTD for analysis. The analysis finds that there is an extreme phenomenon of terrorist attacks. The decision-making process of terrorist organization's attack activities is to minimize the cost of the activity and maximize the benefit of the attack, and follow the decision-making mechanism of “the most labor-saving and most effective”. Secondly, we consider the decision-making movement of terrorist organization's attack activities as a continuous process of the slider rising from the bottom of the slope. A physical model of the terrorist organization's attack activities is established. Then, the virtual mechanics system of the terrorist organization's attack process is constructed, which includes three types of forces: virtual endogenous driving force, virtual interaction force and virtual attack resistance. In the virtual mechanics system, the action amount that fuses the cost and benefit of the attack activity is determined, and the minimum action amount decision-making model aiming at the optimal comprehensive performance is proposed. Finally, the GTD data is used to calculate the attack speed of terrorist organizations according to the attack intensity judgment model. Through Wilcoxon rank sum test and comprehensive performance index analysis, the minimum and actual effects of the decision-making process of two terrorist organizations are calculated and tested. The experimental results verify the effectiveness of the model. Through this model, the simulation experiment of terrorist organization decision-making process under constrained resistance parameters is carried out, and the conclusions with practical guiding significance are obtained.
By analyzing the theoretical least action and actual action of Taliban and ISIL, no significant difference is observed between the theoretical least action and actual action of Taliban and ISIL. These results demonstrate that the decision-making mechanism of terrorist organizations follows the principle of least action. Based on the decision-making model of minimum action of terrorist attacks, the key factors affecting the decision-making of terrorist attacks are the degree of organizational extremism, the government's efforts to combat terrorism and the impact of the international terrorism situation. In the process of anti-terrorism decision-making: on the one hand, we need to take effective anti-terrorism measures to reduce the endogenous driving force of terrorist organizations; on the one hand, it is necessary to always adhere to the strike strategy, push up the attack cost of terrorist organizations and increase the restraint resistance of terrorist organizations. Moreover, it is necessary to scientifically optimize the implementation of the strike strategy, grasp the window of the strategic risk period and turning period of terrorist organizations, and give full play to the effect of the strike strategy. At the same time, the attack strategy helps to clarify the illegal status of terrorist organizations, create an environment and atmosphere to actively curb the spread of extremism in society, strengthen people's legal awareness and enhance people's sense of security. In addition, we must be alert to the sudden change of organizational behavior caused by the disturbance of international terrorism. It is necessary to effectively monitor and dynamically analyze the behavior characteristics of terrorist organizations, and timely introduce preventive and response measures for the new trends and trends of terrorists to avoid loopholes.

Grassroot police organ is the fundamental force for maintaining social harmony and stability. However, the problem of insufficient police resources has restricted a further improvement of policing effectiveness, coupled with the fact that police organs have limited methods to evaluate the efficiency of police resources allocation at the grassroot levels. Therefore, the ability to check the current situation of policing efficiency needs to be improved. At present, the quantitative research on police resources allocation is relatively rich, and various quantitative research methods have been appropriately applied in it, but there is a lack of a dynamic time comparison perspective. The DEA model is applicable to a wide range of objects, and can calculate the production efficiency of various units. The model has been relatively mature after years of development, and can further consider the external factors and the efficiency changes from the vertical perspective of time. Based on the above analysis, this study will employ a three-stage DEA-Malmquist model to analyze the dynamic evolution efficiency and external impact factors.
The specific steps of this study are as follows: At the first stage, the DEA-Malmquist model analysis of the original data is used to evaluate the initial static efficiency and dynamic efficiency of the grassroot police organs, and the slack variables of the police resources input will be obtained. At the second stage, SFA regression analysis will be used to eliminate the influence of environmental factors and random errors on the slack variables of police resources input in the first stage. At the third stage, the adjusted DEA-Malmquist model, according to the adjusted input value of police resources and the original police output value, will be used to calculate the real static efficiency and dynamic efficiency values of the grassroot police organs. Since the grassroot police station is the entity with the most extensive content of police activities, most of the police resources are prone to being allocated to the police station. In this study, we take the Police Bureau of District A as the sample unit. Considering the continuity of handling administrative cases, especially criminal cases, as well as the lag of daily data statistics, the data period selected for this study is 2017-2019.
By conducting a comprehensive evaluation of police resources allocation efficiency, we get the following empirical analysis results: (a)the police resources allocation among police stations is prone to scale inefficiency, with high overall pure technical efficiency and little gaps; (b)environmental factors can affect the efficiency of police resources allocation and widen the gap in efficiency values; (c)the technical change of police stations is mainly influenced by police policies; (d)compared with the scale efficiency, it is more difficult to achieve progress in pure technical efficiency of police stations; (e)the total factor productivity growth of police stations is mainly driven by the technical change; (f)the longitudinal indexes of urban police stations are more sensitive to the environmental impacts. According to the above research results, this study further proposes the following implementation suggestions to better improve the allocation efficiency of police resources. At the conceptual level, we should establish and strengthen the concept of scientific efficiency and technological innovation. At the resource allocation level, we should identify the scale and the structure of police resources allocation reasonably, improve the quality and motivation of police human resources, as well as optimize the safeguard and supervision mechanism of police funds. At the management level, we should improve the evaluation system of the efficiency of police resources allocation and exert the optimization effect of police policies on police resources allocation.

With the rise and popularization of the Internet, social media platforms such as Weibo have become more and more influential in human society. Government microblog is an official account opened by government departments on the microblog platform. It is an important part of the social media platform and an important channel for official communication and guidance of public opinion. It is usually used to publicize government information, respond to public opinion, and promote government achievements. The influence of government micro-blog is the most important measurement index for government departments to carry out policy propaganda and smooth communication between government and people, and selecting the appropriate method to evaluate the influence is the key work for the government to carry out the new media management of government affairs.
The existing work of microblog influence evaluation generally has three modes, based on the basic attributes of users, interactive behavior and social network structure. However, these algorithms usually have some problems such as incomplete index selection, static analysis mode, and single social network construction mode. Therefore, according to the reality of government microblog in social network platform, this paper carries out the influence evaluation of government microblog based on interaction behavior analysis and social network theory. Firstly, we use the Selenium module for the web reptile to obtain the basic information and interaction behavior information of 4492 government microblogs, and the Chinese government microblog data set is constructed. Then, by analyzing the main interactive behavior patterns of microblog (including the interaction between government microblogs, the interaction between government microblogs and ordinary users, and the user recommendation mechanism), the multi-dimensional social network system of government microblogs is constructed according to the mention, forwarding behavior and user recommendation relationship. Secondly, aiming at the defects of the traditional PageRank algorithm, this paper improves an influence evaluation algorithm GM-Rank which is more suitable to government microblog. GM-Rank takes the normalized number of fans and the number of microblogs as the initial PR value, and carries out unequal PR value propagation according to the correlation tightness of microblogs, and iteratively calculates the influence of government microblogs. Finally, the government microblog is ranked and the social network form and development situation of the domestic mainstream government new media are analyzed.
The experimental results show that, compared with the existing microblog influence evaluation algorithm, the GM-Rank method is practical and available, which can intuitively and effectively reflect the influence and development status of government microblog, and also provide a reliable reference for government departments to carry out the evaluation and management of government affairs new media.
Based on the experimental results, this paper analyzes the development status and characteristics of Chinese government microblog, and puts forward three policy suggestions: paying attention to the construction of internal matrix, improving the multi-level system of departments, and strengthening the cooperation and exchange between microblogs. In the next research, we will consider realizing the automation of the whole process through the encapsulation program, in order to serve the construction and development of government microblog more conveniently.

More than 200 rivers around the world are shared by different countries and much more rivers flow through various regions. On the one hand, inhabitants or firms along the river can utilize the water natural resources. On the other hand, they may also discharge household or industrial waste into the rivers, which has a substantial influence on ecological environment. Therefore, how to share the cost of controlling a polluted river becomes a more and more important issue.
NI and WANG (2007) introduced two allocation methods, namely the Local Responsibility Sharing (LRS for short) method and the Upstream Equal Sharing (UES for short) method, which are based on the principles of Local Responsibility (LR) and Downstream Responsibility (DR) respectively. The LR principle requires that a polluter should take the full responsibility for the cost of cleaning river pollutants in the segment where it locates. The DR principle states that an upstream polluter bears some responsibilities for its downstream segments. Most existing allocation rules are based on the DR principle, but there are also allocation demands that contradict the principle in practice. For example, the southeastern regions of China (such as the Yangtze Delta and the Pearl River Delta) have benefited from the policy of reform and opening up and have achieved significant development. With the industrial upgrading of the Chinese economy, a large number of high-energy-consuming and high-polluting industrial have been relocated to the central and western region (upstream and midstream areas). Considering the historical sacrifices made by the central and western regions (mainly in the economic aspect), it is necessary to discuss compensation from downstream to upstream regions. Although the DES method proposed by DONG et al. (2012) partially reflects this requirement, its essence is still based on the DR principle, which addresses the dual problem of cost-sharing in water pollution.
To embody the compensation demands of downstream regions from upstream regions, this paper proposes two new allocation methods: SLRS (Solidarity Local Responsibility Sharing) and SUES (Solidarity Upstream Equal Sharing) solidarity methods. Both adopt downstream compensation principles, but the methods differ. The SLRS rule achieves compensation by reducing the costs of upstream regions, while the SUES rule directly allocates upstream costs to downstream regions. Furthermore, the equivalence between the two allocation rules and the Solidarity value is revealed. It is worth noting that the LRS and UES method are the Shapley value of two corresponding games induced by the LR and DR principles respectively. The null player property of the Shapley value in cost games results in the fact that null players do not have to bear any costs. NOWAK and RADZIK (1994), based on the potential social or psychological factors in the game (often difficult to quantify), proposed the Solidarity value. Unlike the Shapley value, the Solidarity value provides a certain allocation to zero players. NOWAK and RADZIK (1996) pointed out that if there are friendly relationships among game participants that cannot be characterized by characteristic functions (possessing solidarity-related social attributes), the Solidarity value is more likely to be accepted by the participants. The two methods proposed in this paper are equivalent to the Solidarity value, and therefore SLRS and SUES are referred to as solidarity allocation methods.
To characterize the fairness of the two new allocation methods, we propose three properties. Nonzero dominance states that if a player is the only one with nonzero cost, then the withdraw of this player has a greater impact on other players. Most upstream nonzero dominance keeps the dominance of the unique nonzero cost player only when the players is located on the most upstream position. Zero balanced contribution implies that the withdrawal of zero cost players brings the same influence to other players if there exists a unique nonzero cost segment. To prove the uniqueness that the SLRS and SUES method satisfies certain properties respectively, we first consider a basis of original problem space and then decompose the problem into n sub-problems. By using mathematical inductions on the size of coalitions, we show the uniqueness on sub-problems. Together with additivity, we characterize the proposed allocation methods with different properties.
Further research can be conducted on the mechanism design method of allocation methods, by constructing non-cooperative game model and utilizing equilibrium solutions to achieve stable allocation methods for water pollution control cost allocation problems.

The metaverse born in the new era is the intersection of real life and the virtual world. In the real world, media devices are used to provide humans with a virtual binary world. In this binary world, there is no Riemannian space produced by the mass of celestial bodies in the real world, and there is no gravitation and gravity. However, when human consciousness exists in the metaverse, its overall development direction is random, and the information and digital wealth obtained by human consciousness in the metaverse are also common in the real world. Like the real world and the virtual world, the metaverse also has a chaotic effect, full of randomness and regularity. Different from the long evolution and development of the real universe, the construction of the metaverse will go through a process dominated by human awareness of artificial intelligence systems. In this process, the attributes of determinism, randomism, and chaos will accompany the entire life development cycle of the metaverse. In the specific analysis of the chaos of the metaverse, the K-entropy can be used as the characteristic quantity of the degree of unpredictability of the chaotic system. This paper attempts to use it to judge the degree of system chaos in the metaverse development process, and the feasibility of predicting the entire life cycle of the metaverse. Then, the K-entropy analysis of the metaverse's chaotic state verification is applied to the analysis of stock price fluctuation curves, and the specific demonstration is carried out in combination with Keynes' division of different stages of the economic cycle.
At the theoretical stage, this paper reconstructs the M-dimensional phase space of the development index time series during the development process of the metaverse, and conducts correlation calculations based on the distance formula between two points in Euclidean space to derive the maximum likelihood estimation of the metaverse development index K-entropy. At the experimental stage, leveraging Keynes' economic cycle theory, which divides the economic cycle into four stages—recession, depression, recovery, and prosperity—this paper analyzes the segmented characteristics of stock price curves of listed companies in the metaverse cultural media sector in 2021, using publicly available data on the highest and lowest stock price fluctuations. Based on daily stock price trends, the fluctuations in stock prices of listed companies in the metaverse cultural media sector can be roughly divided into four stages: during the prosperity stage, stock prices remain high overall, showing a fluctuating upward trend; during the recession stage, stock prices decline from their peak, exhibiting a fluctuating downward trend; during the depression stage, stock prices remain low overall, displaying a fluctuating downward trend; and during the recovery stage, stock prices rebound from their lowest point, showing a fluctuating upward trend. Simultaneously, K-entropy analysis is performed on the stock price fluctuations of listed companies in the metaverse cultural media sector in two-dimensional Euclidean space, with trading dates as the primary control variable and stock prices as the parameter variable, to obtain a complete “stock price-time” curve for nonlinear analysis. This enables the analysis of stage characteristics of typical stock price fluctuation curves, stage characteristics of atypical stock price fluctuation curves, and entropy analysis of stage characteristics of stock price fluctuation curves. The results show that typical stock price fluctuation curves can exhibit the curve states proposed by Keynes, while atypical stock price fluctuation curves display relatively chaotic states.
As a characteristic quantity for quantifying the unpredictability of chaotic systems, K-entropy reveals the intrinsic dynamical mechanisms of complex systems, demonstrating dual value in the analysis of the metaverse's evolution: it serves both as a quantitative measure of chaos and as a reflection of the interplay between order and disorder in the system. This ability to characterize nonlinear dynamical properties gives it significant advantages in predicting the developmental trajectory of the metaverse. Applying K-entropy to study the characteristics of stock price fluctuation curves, the research conclusions and analytical results mutually corroborate, providing scientific validation and a beneficial supplement to stock price fluctuation curve analysis methods. According to the stage characteristics of stock price fluctuation curves, the segmentation method based on entropy values is an effective approach for quantitative analysis. K-entropy analysis indicates that stock prices with higher K-entropy cannot exhibit clear stage characteristics, displaying disordered development states, while stock prices with lower K-entropy can show distinct stage characteristics, exhibiting relatively ordered development states. The developmental trends of stock price fluctuation curves are consistent with the level of K-entropy.

With the vigorous development of China's auto industry, by the first half of 2022, the quantity of the car in China had surpassed that in the United States and ranked first in the world, however, the market share of auto parts remanufacturing had been far lower than that in the United States. In order to promote the development of our remanufacturing industry, the government has adopted a series of incentive and subsidy policies related to remanufacturing, including both manufacturers' remanufacturing subsidies: consumers' “trading the old for the new” on the supply side and “trading the old for the remanufactured” subsidies on the demand side. In addition, with more and more consumer market segments in recent years, and the rapid development of personalized and diversified market segments, the organization of production on the supply side also needs to change. The existing literature on government subsidies considers the dual subsidies to manufacturers and consumers, but does not involve the dual subsidies that exist in both “trading the old for the new” and “trading the old for the remanufactured”, and there is a lack of research on how to implement the dual subsidies concretely. Based on the background of consumer segmentation and government dual subsidies policy, we divide government subsidy decision into subsidy ratio decision and subsidy total amount decision, and further study two different government subsidy policies and their corresponding impacts.
This paper constructs a Stackelberg game model dominated by the government, obtains the equilibrium solutions under the two kinds of subsidy decisions by a backward induction method, and explores which decision the government takes to ensure the maximization of social welfare, and how the manufacturer price their products under different government subsidy decisions to ensure their maximum profits. Then this paper studies the effects of acceptance degree of normal consumers to remanufactured products, government's attention to consumer surplus and manufacturer's profits on government subsidy decision, manufacturer pricing decision and manufacturer profits, consumer utility and social welfare by numerical analysis. The results can be summarized as follows. First, the government's subsidy ratio policy for recycling and remanufacturing of waste products is conducive to increasing social welfare and manufacturer's profits, and subsidies given to consumers for “trading the old for the new” should be at a higher rate than those for “trading the old for the remanufactured” to accelerate the recycling of products. Second, when the government implements the subsidy ratio policy, the subsidies given to the manufacturer for “trading the old for the remanufactured” are higher than those for “trading the old for the new”, which can reduce the remanufacturing cost of the manufacturer, encourage the manufacturer to carry out active remanufacturing production, and make the price advantage of remanufactured products significant, stimulating consumers to carry out green consumption, thus promoting the development of remanufacturing. Third, on the premise of effectively controlling subsidy expenditure, the government should attach importance to the share of consumer surplus and manufacturer profits in social welfare, encourage normal consumers to carry out green consumption, so that government subsidies can more effectively promote the continuation of product life cycle and the development of circular remanufacturing.
The management enlightenment is as follows: the government should focus on the implementation of the subsidy ratio policy to improve social welfare. In addition, the government should also pay attention to the share of consumer surplus and corporate profits in social welfare under the premise of effectively controlling the expenditure of subsidies. The manufacturer should adjust the prices of the two types of products according to the government's subsidy policy, so that the price advantage of remanufactured products is significant, and can promote the green behavior of consumers. Finally, normal consumers in the market should actively carry out green consumption, and cooperate with the government and the manufacturer to promote the continuation of product life cycle and the development of recycling and remanufacturing, so as to maximize social welfare. This paper only considers the remanufacturing supply chain model of the manufacturer's single-cycle direct selling. In reality, retail channels still occupy a large market share. In addition, the implementation cycle of government subsidy policies is long, so the decision considering multiple cycles is more practical. Therefore, retailers can be included in the supply chain in the future, and the government's optimal dual subsidy subdivision policy under the multi-cycle can be further studied.

The need for more funds has always been an important factor hindering the rapid development of many small and medium-sized manufacturers. The traditional source of corporate financing is mainly bank financing, but there are problems such as the need for adequate collateral, a slow loan approval process, and delayed payment time. Therefore, many retailers provide manufacturers or suppliers with tight financial resources and loan services. On the other hand, with the popularization and development of internet technology, even small and medium-sized manufacturers can directly communicate with consumers and sell products. However, compared to manufacturers who have just entered direct sales channels, especially small and medium-sized manufacturers with poor capital turnover, retailers with strong market dominance often have a dominant position in the supply chain, such as enjoying priority pricing rights. Although the development of financing tools has widened the financing channels of manufacturers, it has also led manufacturers to be more dominated by core enterprises and weakened their bargaining power. Therefore, it is necessary to explore the impact of different financing methods on manufacturers' dual channel pricing and financing strategy selection under the retailer-led supply chain from the perspective of manufacturers in a weak position.
This paper builds a model with the Game theory and analyzes the solution. As a branch of modern mathematics and an essential subject in operations research, the Game theory provides help for this study to analyze the game behavior of manufacturers, retailers, and banks in the dual-channel supply chain. The study considers a supply chain model consisting of a single retailer and a single manufacturer, where the manufacturer is financially constrained and sells products through retail and direct sales channels. There is a stackelberg game between retailers and suppliers; retailers are the leaders. Based on this model, this paper analyzes the choice of dual channel pricing and financing strategy of small and medium-sized manufacturers when facing strong retailers. At the same time, the study uses numerical examples to fit and analyze the pricing and financing decisions of supply chain parties under endogenous interest rates, as well as the profit ranges of manufacturers under different logistics risks.
The research results indicate that when the financing rates are the same, manufacturers will set higher wholesale prices under the retail financing model, exacerbating the double marginalization effect. Retailers will choose to reduce marginal profit, yield to manufacturers with less profits for stimulating market demand, and gain more income from financing services. Secondly, when the financing interest rate is endogenous, under the retailer's financing strategy, retailers, as the strong side of both the marginal profit and the financing interest rate, often need to make a trade-off between their retail revenue and financing revenue, which is mainly affected by the proportion of market share. With an increase in demand for direct marketing channels, manufacturers' bargaining power is enhanced, and retailers will reduce marginal profit, increase interest rates, and prefer financing income. That is to say, the dominant position of retailers in the supply chain gives them more flexible profitability. On the other hand, when manufacturers face logistics risks through their direct channels, banks will further reduce financing rates with increased risk, but retail financing is still the first choice. This study is different from other dual-channel studies led by manufacturers, and the results obtained can improve the financing decision-making of dual-channel supply chain management from another perspective, which has particular guiding significance for supply chain operation management problems with financial constraints.
This paper only considers the situation where the direct sales market is relatively small compared to the retail market. However, some small enterprises have gradually shifted their focus on direct sales to that on the more significant direct sales market, such as live streaming sales. Therefore, in the future, it can be studied whether retailers are willing to provide financing services to manufacturers when direct sales channels have higher demand and how the financing strategies of manufacturers will change. In addition, the focus of this study is channel competition, so it is assumed that market demand mainly depends on price. However, in production practice, demand may also be influenced by other factors, such as consumer behavior and low-carbon factors, which can be explored in different scenarios.

With the rapid development of e-commerce and mobile technology, many manufacturers begin to join the online platform for online sales, and they first face the problem of choosing online sales mode. At the same time, in order to solve various information security problems in the online product sales chain, manufacturers have introduced blockchain technology to achieve traceability and transparency of product information, so as to win effectively the trust of consumers. Based on this, this study attempts to solve the following questions: How does the manufacturer choose the optimal sales model under the scenario with or without blockchain technology support? When should the manufacturer introduce blockchain technology to provide online traceability products? What impact does the introduction of blockchain technology have on the manufacturer's sales model selection and balance results? It is hoped that it can guide manufacturers to make a reasonable choice of sales model and provide them with new insights.
Aiming at the two-level supply chain composed of a manufacturer and an online platform, this paper considers the consumer market structure and the product information traceability, establishes the manufacturer-led resale model (the Stackelberg game) and the agent model of revenue sharing under two scenarios with or without blockchain technology, and studies the equilibrium strategy and optimal decision of sales model selection under these two scenarios. Finally, it explores the conditions of use of blockchain technology and its impact on supply chain sales model selection.
The results of the study show that without the support of blockchain technology, the manufacturer should not blindly choose a sales model, which should be based on the specific situation. When the commission rate is low (high), the agent (resale) model can bring more profits to the manufacturer, and it should choose the agent (resale) model. With the support of blockchain technology, the commission rate is not the only determining factor for the sales model selection. Even if the commission rate is very low (high), the manufacturer does not always choose the agent (resale) model, and it is also affected by the blockchain cost coefficient. When the commission rate is low (high) and the blockchain cost coefficient is large, the manufacturer can achieve higher profits by adopting the agent (resale) model, and then the agent (resale) model is the best choice. Although blockchain can eliminate consumers' uncertainty about product information and improve the level of information traceability, it also increases the operating costs of the manufacturer. Whether the manufacturer introduces blockchain is determined by the blockchain cost coefficient and the proportion of information insensitive consumers. In the resale or agency model, when the blockchain cost coefficient is small (large) and the proportion of information insensitive consumers is large (small), the introduction of blockchain can enable the manufacturer to obtain more objective profits, so it should adopt blockchain at this time. Finally, the use of blockchain in either mode may not always be beneficial to the manufacturer and the platform. Whether blockchain can bring more profits to both depends on the blockchain cost coefficient and the proportion of information insensitive consumers. In the resale or agency model, when the blockchain cost coefficient is small (large) and the proportion of information insensitive consumers is large (small), the introduction of blockchain will increase the price and profit of both.

With the increasing deterioration of the global environment, many enterprises are becoming aware of the importance of protecting the environment, and maximizing the use of resources is one of the initiatives of some manufacturing enterprises. For example, Taylor Guitars used to use only the most top-quality raw materials to produce their products, and the remaining raw materials were discarded, which resulted in a huge waste. But now Taylor Guitar uses the remaining raw materials wasted before to produce low-end co-products, and sells them through e-commerce platforms. We establish a secondary supply chain consisting of an original manufacturer, a co-product manufacturer, and an e-commerce platform. Considering the better environmental protection characteristics of co-products, e-commerce platforms choose to promote co-products to increase consumers' favorability towards them. In this paper, we consider the two most common forms of promotion: subsidies and marketing efforts. Firstly, this paper establishes a Stackelberg game model to study the optimal marketing decisions of the manufacturer and the platform for co-products under no promotion of by-products by the platform (Model B), subsidy promotion (Model S) and marketing effort promotion (Model E), respectively.
It is found that the price of co-products is not only influenced by the minimum quality of raw materials for co-products, but also closely related to the level of consumers' environmental awareness. In Model B and Model E, when consumers' environmental awareness is at a low level, the better the quality of the remaining raw materials, the higher the price of co-products; but when consumers' environmental awareness is high, the minimum quality of the remaining raw materials will not lead to a sustained increase in the price of co-products, but rather a downward trend followed by a rebound. This indicates that enterprises should fully consider various factors such as consumers' demands and expectations when making green marketing decisions, and make different production and marketing decisions according to the differences of consumer groups.
Next, we compare the optimal prices of the two products under the three models. This is a very important issue because it will directly affect the marketing decisions and product promotion decisions of the manufacturer and e-commerce platform. The quality of co-products and the commission rate of the e-commerce platform simultaneously affect the price of co-products. The results show that when the quality of the co-product is low, the price of the co-product will be the highest under the subsidy promotion and the lowest under the marketing effort promotion if the commission rate is low. If the commission rate is at a moderate level, the price of the co-product is still the highest under subsidy promotion and the lowest under no promotion. If the commission rate is high, the price of the co-product is the highest under marketing effort promotion and the lowest under no promotion. In the case of high co-product quality, if the commission rate is low, the price of a co-product will be the highest when subsidy promotion is carried out and the lowest when marketing effort promotion is carried out. If the commission rate is at a medium-high level, the co-product's price will be the highest under subsidy promotion, but the price will be the lowest under no promotion.
Finally, the optimal promotion decision of the co-product is made according to the demand of the two products. Between Model B and Model S, it will be more efficient for the platform to adopt subsidy promotion when the quality of the co-product is low. When the quality of the co-product is high, more consumers can be attracted to choose the co-products without promotion. When the quality of co-products is at a medium level, the level of consumers' environmental awareness should also be taken into account. The choice between no promotion and marketing effort to promote depends on the quality of the remaining raw materials and the environmental awareness of consumers. When the quality of the remaining raw materials is low, the platform will not need to promote them, and the green degree of co-products will have an obvious advantage. When the quality of the remaining raw materials is high, it will be wise for the platform to adopt marketing effort. When the quality of the remaining raw materials is at a medium level, the choice of promotion strategy will depend on the environmental awareness of the consumers. If the environmental awareness of the consumers is low, there will be no need for promotion. If the consumers pay more attention to environmental protection, then the marketing effort will play a significant role.

Sharing economy has become a hot topic in the field of management science, especially the operation and management of a sharing platform. The resources-sharing platform runs in a leasing mode, in which customers can obtain the usage right of products during a short time by paying a one-time fee if needed. However, waste sharing products have not been effectively dealt with. A typical case is the sharing bike, which not only occupies public space and land resources but also produces solid waste after reaching the three-year scrappage period. Practical and theoretical research show that recycling and remanufacturing can save costs. Consequently, they are widely incorporated into the product “whole life cycle management” process of bike-sharing enterprises.
Unlike the recycling of waste products from customers in the traditional sales mode, sharing products belong to the platform. Therefore, recycling and remanufacturing raise the question of how to reconcile costs and benefits between the manufacturer and platform inside the supply chain. On the one hand, the residual value of scrap products belongs to the platform, so the manufacturer should pay certain subsidies to the platform when recycling products. On the other hand, the manufacturer bears the cost of recycling and dismantling, which releases the environmental protection department of the government of the pressure. The platform should provide subsidies to the manufacturer to encourage recycling and remanufacturing. Comprehensively, the subsidy coordination between two members needs to be verified. Meanwhile, two supply chains consisting of two manufacturers and two platforms will compete with each other.
To investigate the interaction between members inside the supply chain, and figure out the competition between two supply chains, three structures are divided according to whether recycling and remanufacturing are performed. Under the premise of supply chain competition, the pricing of shared products in two supply chains with remanufacturing but without recycling, one with both recycling and remanufacturing, and one in only one supply chain with both recycling and remanufacturing are studied respectively. Both supply chains consist of a manufacturer and a sharing platform, to which the manufacturer sells new and remanufactured products, and the platform provides the use (rental) service for customers. By constructing the model of the intra-chain Stackelberg game and inter-chain Nash non-cooperative game, the optimal wholesale price and lease price are derived under different structures and thus the intra-chain coordination and inter-chain competition mechanism are investigated.
The results show that recycling and remanufacturing are a win-win strategy. Namely, they offer the lowest leased price, so manufacturers and platforms benefit from cost savings. As long as the subsidy given to the platform by the manufacturer does not exceed the positive threshold, the wholesale price will be the lowest when both members recycle and remanufacture, while it will be the highest when both members do not do so. The same conclusion holds for the optimal lease price without any preconditions. Moreover, the structures will spontaneously evolve from no-recycling to both-recycling. The recovery subsidy realizes the profit coordination between the manufacturer and the platform by affecting the wholesale price. Namely, when the subsidy is larger than zero, the unit subsidy given by the manufacturer to the platform will be recovered by raising the wholesale price; and when it is less than zero, unit subsidies given by the platform to manufacturers will be returned in the form of reduced wholesale prices. The saving cost is distributed according to a certain proportion. The fiercer the competition is, the more the platform occupies. And competition coefficient positively influences decision price and optimal return. Furthermore, manufacturers could relinquish part of cost savings to encourage platforms to order more remanufactured products. In addition, the analysis of parameter self-elasticity and competition elasticity shows that the revenue is mainly affected by its own parameters, and the influence of competition parameters is relatively slight.

Existing studies mainly focus on the positive relationship between the manufacturer's green efforts and market demand under different decision-making backgrounds, but ignore the correlation between the supply reliability of products and the manufacturer's green effort. As a result, they may fail to consider its impact on the green supply chain operational decisions. Especially when considering the learning ability of the manufacturer, the level of green technology of the manufacturer is uncertain, which ultimately results in the supply risk of the manufacturer. Furthermore, the manufacturer still has a great decision-making concern about the level of green effort due to the huge cost that green investment may bring about. In view of this, this paper constructs a two-level supply chain consisting of a single retailer and a single manufacturer, in which the manufacturer is responsible for deciding the green effort level, and the follower retailer determines the optimal selling price. Considering the different green effort costs, this paper analyses the manufacturer's optimal green effort level under the exogenous and endogenous wholesale price, respectively. Furthermore, this paper measures impacts of risk-sharing contract and risk aversion contracts on operational performances of the green supply chain, respectively. The former indicates that regardless of the level of green effort put in by the manufacturer, the retailer should pay off the purchase cost of the products according to its order quantity; the former refers to the fact that the retailer pays off the purchase cost based on the manufacturer's expected final output. To sum up, this paper intends to systematically consider the following three research questions: (1)When supply reliability is positively related to the manufacturer's green effort level, how should the green supply chain optimize its effort level and operational strategy to maintain a balance between the economic and social benefits? (2)How do different risk contracts affect the manufacturer's green efforts and the operational performance of the supply chain? (3)How will the manufacturer and retailer adjust their operational strategies and improve their operational performance in the case of exogenous or endogenous wholesale price setting, respectively?
By formulating the manufacturer-dominated channel and defining the pressure coefficient of green effort level on supply chain, this paper accurately describes the optimal operational policies of the green supply chain. (1)Under exogenous wholesale price setting: (i)the risk-sharing contract enables the manufacturer to trade-off among three green effort strategies. Especially when the pressure coefficient is relatively higher, the manufacturer will choose the no green effort strategy; (ii)under the risk aversion contract, the manufacturer will keep the same green efforts since the retailer shares the part of the investment cost of green efforts; (iii)this paper accurately distinguishes the manufacturer's preferences towards different contracts. Especially when the pressure coefficient is rather larger, the manufacturer will be more inclined to the risk-averse contract. (2)Under the endogenous wholesale price, when the pressure coefficient is less than 1/8, the manufacturer will choose the risk-sharing contract, otherwise, the manufacturer will make contract selection based on the production cost. That is, when the production cost is relatively lower, the manufacturer will choose the risk-averse contract. Instead, the manufacturer will choose the risk-sharing contract. (3)In the long run, relying on the manufacturer to improve the green degree is a burden too heavy on the whole supply chain. Even if they can coordinate the competition and cooperation of the supply chain through contracts, the profits of the supply chain members will be greatly affected in many cases, and as a result, the members of the manufacturer will not even make green efforts. As the policy maker, the government can timely give some incentives to the supply chain, which may achieve better green results.
In view of this, the work of this paper can be further expanded from the following two dimensions. (1)Considering the importance and urgency of the two-carbon target, the government can further strengthen the green input level of the supply chain through a variety of mechanisms. For example, fiscal subsidies can be used to reduce enterprises' green costs and carbon emissions caused by production can be charged to restrict enterprises' operational strategy choices. (2)Considering manufacturers' green costs, the retailer can adjust its operational mechanisms to share the benefits, such as allowing the manufacturer to open direct channels, increase advertising investment to promote green product.

With the continuous advancement of information and internet technology, reservation-based travel has emerged as a prominent trend in developing public transport services. The demand responsive bus has gained significant attraction in various regions of China. These buses generate customized routes with flexible stops and schedules, catering to the personalized needs of passengers based on their travel reservation information. The demand responsive bus enhances the quality of public transportation services and mitigates the resource wastage associated with fixed bus schedule, making it particularly suitable for serving short-distance regional trips and accommodating weak spatiotemporal regularity travel patterns. The demand responsive bus service is divided into three components: demand travel information collection, route generation, and service provision. In particular, route generation is the most critical component in demand responsive bus service, which directly affects system ability and service quality. Due to its importance, researchers have dedicated their efforts to studying demand responsive bus routing problem. However, current research remains largely focused on routing optimization models using either a unitary pickup and delivery strategy or a single vehicle type. In fact, these simple operational methods are not enough to accommodate the complexity and variability of actual demand patterns. To overcome this gap, we attempt to incorporate diverse pickup and delivery operation strategies, which is beneficial for not only increasing the flexibility advantages of demand responsive bus, but also enriching operational methods to meet diversified service needs. Furthermore, we introduce multiple capacity vehicle types into demand responsive bus routing optimization, which facilitates a better allocation of passengers with various vehicle resources and provides more space for route optimization.
Hence, we propose a demand responsive bus routing optimization problem with multiple capacity vehicle types, incorporating two operational strategies: the pickup and delivery separation strategy and the pickup and delivery mixture strategy. In order to take into account both the interests of passengers and the bus company, we minimize the system cost as the objective, which comprises the cost of measuring service quality and operational costs. In the model, we also take buffer time, minimum load rate, and detour coefficients constraints into account. As a typical NP-hard problem, the difficulty of solving the model increases exponentially as the scale of the problem grows. To accelerate the solution, we propose a decomposition method that combines an elite genetic algorithm and solver. Subsequently, we take the demand responsive bus stops in the Wangjing area of Beijing as a case study, and generate randomly travel demands. We evaluate the service quality by applying the pickup and delivery separation strategy and the pickup and delivery mixture strategy across various demand scenarios, buffer times, detour coefficients, and fleet sizes.
The experiments results demonstrate what follows: (1)The pickup and delivery separation strategy is effective in reducing system operating costs. Compared to the pickup and delivery mixture strategy, the average operating cost is reduced by up to 27.5%. (2)The pickup and delivery mixture strategy is conducive to improving both the demand service rate and the average vehicle occupancy rate, which can significantly increase the system service rate by 24.5%, and the average vehicle occupancy by a maximum of 10.7% compared to the pickup and delivery separation strategy. (3)The buffer time is an essential feature affecting the system service rate and the average vehicle occupancy. In particular, when the system service rate has reached 1.0, continuing to prolong the buffer time can also contribute to the re-assignment of passengers to improve the average vehicle occupancy. (4)The vehicle detour coefficient, as one of the factors on the system service ability and total cost, has a crucial threshold of 2.0 in the experiment. When the detour coefficient exceeds the threshold, the system service ability and total cost remain constant. (5)The fleet size has a significant impact on the overall cost of the system. A small vehicle fleet leads to poor service ability, while a large fleet may result in a reduction of vehicle utilization. Furthermore, different pickup and delivery strategies exhibit their respective preferences for high-capacity vehicles when vehicle resources are sufficient in the case.
In conclusion, this paper offers valuable methodologies and a theoretical foundation for the practical design of demand responsive bus routes. It extensively examines the practical operation effectiveness of both the pickup and delivery separation strategy and the pickup and delivery mixture strategy in the responsive bus routing optimization model. At the same time, it also investigates the effects of incorporating multiple capacity vehicle types in the routing optimization problem. Moreover, the paper conducts several sensitive experiments to explore the impact of different detour coefficients and vehicle fleet sizes. In the future, we will be able to quantitatively evaluate the effectiveness of different pickup and delivery strategies, based on real reservation information and multi-source traffic data, and provide more customized demand responsive bus service with detailed demand scenarios.

Although online retail has been growing consistently in rural areas, it has issues with costs and delivery efficiency because of poor road infrastructure and scattered population. Moreover, in western rural areas, there are mainly plateaus and mountains. Thus, it is difficult for a truck to provide door-to-door delivery service. As drones are not restricted by road infrastructure, logistics companies, such as JD and ZTO, have used drones for delivery in rural areas. However, drones have limited capabilities and flight range. Hence, trucks carrying drones for collaborative delivery have been used in real-world logistics applications. In addition, logistics companies or local governments introduce crowdsourced delivery systems where ordinary people carry out last-mile deliveries with their own trucks to reduce delivery costs. For example, the logistic service platform, “Cun Ge Huo Di”, developed by the county of Xiushan, in the city of Chongqing, uses crowdsourced vehicles to deliver goods for a fee in rural areas.
Motivated by the above real-life logistics applications in rural areas, we introduce a new variant of the vehicle routing problem, namely, Vehicle Routing Problem with Drones and Crowd-shipping (VRPDC). The contributions of this study are as follows: (1)we propose VRPDC based on the practical delivery applications in rural areas. Compared with the classical VRP, VRPDC integrates more practical requirements, such as capacity restrictions and synchronization constraints for enterprise-owned trucks, crowdsourced trucks, and drones; (2)we formulate VRPDC as an integer linear programming model. Then, we decompose it into a path-based Master problem (MP) model and a pricing Sub-Problem (SP) model based on Danzig-Wolfe decomposition; (3)we propose an exact solution technique, a Branch-and-Price (BP) algorithm. New labeling extension and domination rules for drone-truck paths and crowdsourced trucks are introduced, respectively. Heuristic pricing techniques are developed to speed up the proposed algorithm for the label extension of drone and truck paths. Also, a unique acceleration strategy for crowdsourced trucks is proposed. Thus, the proposed algorithm can solve VRPDC optimally within a reasonable time.
To examine the performance of the proposed branch-and-price algorithm, a large number of experiments are implemented with Python 3.9, where small-scale and large-scale instances are randomly generated based on the instance generation rules proposed by existing studies. The exact solver, Gurobi, and a heuristic algorithm—Adaptive Large Neighborhood Search (ALNS) are used for comparison. In addition, to investigate the performance of the proposed heuristic pricing techniques and acceleration strategy for SPs, experiments are made for comparisons. The results show that the proposed BP performs the best in terms of solution quality and computation time for all instances. Also, the proposed heuristic pricing technique and acceleration strategy are effective. Finally, to examine the impact of introducing crowdsourced vehicles on the total cost of the delivery system, instances of different scales are randomly selected for experiments. Comparisons are made between the drone-truck delivery system with crowdsourced vehicles and one without them. The results show that using crowdsourced vehicles for delivery helps reduce logistics costs. More real-life requirements will be considered in our future work, such as heterogeneous drones and trucks, dynamic demand, the energy consumption of drones, and weather effects.

In recent years, large-scale natural disasters have frequently occurred in China, seriously threatening the lives and property of the people. The field of emergency management has gradually attracted the attention of scholars. The Chinese government increasingly emphasizes concepts such as “people-oriented, life comes first” and “saving lives is the first priority of emergency rescue” in emergency management. However, in the field of post-earthquake rescue, there are still very few studies that directly use the number of deaths as an optimization goal. An efficient emergency dispatch plan can greatly reduce the mortality rate caused by earthquake disasters. However, the disaster situation at each disaster site is different, and there is also a certain difference in the urgency of the demand for rescue resources. Therefore, after an earthquake occurs, how to comprehensively consider the disaster situation at various disaster sites and determine the optimal path plan for the deployment of rescue vehicles to minimize personnel casualties caused by disasters is of practical significance.
This paper takes earthquake events as the research background, builds a mixed integer programming model intending to minimize the number of deaths based on the prediction of the number of casualties and material needs at each disaster site, and analyzes vehicle travel time during the instability of the post-earthquake road network, in the consideration of time-varying disaster conditions, and by the introduction of the “death rate-time” function. An improved hybrid optimization algorithm is designed to solve the model. The introduction of the “death rate-time” function can establish the relationship between “rescue vehicle arrival time” and “cumulative death rate at disaster site”, with “rescue vehicle arrival time” as an intermediate variable to make “cumulative death rate at disaster site” a decision variable and determine the number of deaths when rescue vehicles arrive at the disaster site. This objective function embodies the core concept of “life comes first” in emergency rescue and is also significantly different from the objective functions of most existing VRP variants. The numerical experiments have shown that the model proposed in this paper can effectively reduce the number of deaths compared to traditional rescue time minimization models, with an average reduction rate of 30.85%. This study is a variant of the VRP problem and belongs to the NP-hard problem, so an algorithm needs to be designed to solve it. This paper designs an optimization algorithm that combines large-scale neighborhood search and simulated annealing and improves the destruction operator of the large neighborhood search algorithm and the cooling function of the simulated annealing algorithm. Statistical indicators are used for comparative analysis in numerical experiments. The results show that compared with conventional algorithms, the hybrid optimization algorithm proposed in this paper has optimization rates of 2.8% and 3.5% on optimal value and average value respectively, proving that the designed algorithm has better global search performance.
The numerical experiments integrate the research work of the whole paper and prove that the model and algorithm proposed in this paper could provide decision-makers with scientific and reasonable optimization schemes for post-earthquake emergency material dispatch. Moreover, the research of the whole paper also suggests that post-earthquake emergency rescue decision-making should not have simply considered time-saving, but should have comprehensively considered the disaster situation and rescue time at each disaster site.

The traditional facility location problem, such as the covering problem, mostly assumes that once facilities are established, they will operate smoothly. However, in the real environment, the lifecycle of facility is generally long, and they are inevitably impacted by numerous uncertain factors during operation. These factors include adverse weather conditions, natural disasters, and deliberate human sabotage. As a result, facility interruptions occur, and the opening facilities may not always be reliable. Facility interruptions lead to higher transportation costs, lower service levels, and even the inability of the system to operate normally. For example, in the context of emergency facility location problems, natural disasters like earthquakes and floods can cause emergency facilities to interrupt. As a result, residents assigned to these interrupted facilities are unable to enjoy the corresponding services. More severely, their livelihoods and personal safety can be compromised. Therefore, considering the reliability of facilities is crucial in addressing facility location problems. Facility reliability has attracted widespread attention from both industry and academia.
In this paper, the reliability facility location problem is studied based on the uncertain interruption probability of facility, and the classical set covering model is extended to ensure that the probability of user points being covered is not lower than the given system reliability level. Reliability facility location model under random interruption probability is proposed. Then, we assume that the facility is interrupted with a probability, and the probability of interruption is uncertain, and the value is taken in a symmetrically bounded interval. The reliability facility location problem under uncertain interruption is suggested based on the budget-of-uncertainty robust approach. The model ensures that the probability of user points being covered is not lower than the given system reliability level even if some of the interruption probability values the worst case. The formulation of the reliability facility location problem is clearly nonlinear. By introducing auxiliary variables and using means of strong duality theory, we derive two propositions to reformulate the model as a linear optimization model. The robust counterpart programming is computationally tractable and easy to be applied to solve real-world problems.
Finally, numerical case studies are conducted using data from 88 city nodes in the United States. The results of the numerical experiments demonstrate that the topology of the facility network varies significantly under different combinations of uncertain budgets and system reliability levels. This indicates a significant impact of uncertain budgets on the facility location solution. Furthermore, an analysis is conducted to examine the influence of uncertain budgets on locating costs. The results reveal that locating costs increase as the uncertain budget increases. Similarly, locating costs also increase as the system reliability level improves. When the reliability level is relatively low, the increase in locating costs will be relatively slow. However, when the reliability level is high, the increase in locating costs will be rapid. The proposed model in this study offers a scientific basis and technical support for addressing reliable facility location problems in environments with uncertain facility interruption probabilities, such as emergency facilities and post-disaster medical facilities.
Compared with the existing similar research, the main contributions and novelty of this paper are highlighted as follows: (1)We assume that the facility is interrupted with a probability, where the probability of interruption is uncertain, and the value is taken in a symmetrically bounded interval. The budget-of-uncertainty robust approach is employed to deal with the problem, which can completely control the conservatism of the model and adjust the effect on the objective function. (2)The proposed non-linear model can be reformulated as a linear programming equivalently by introducing auxiliary variables and using means of strong duality theory. The resulting linear programming is computationally tractable and easy to be applied to solve real-world problems. (3)We provide insights into the different optimal locations corresponding to different protection levels and the system reliability level. The impact of uncertain budget on facility location cost is further analyzed, as well as how the facility location cost changes with the system reliability level. The model's contributions are expected to enhance the reliability and effectiveness of facility location strategies in critical sectors, benefiting emergency management, disaster response, and public services.

In recent years, the frequent occurrence of sudden disasters has not only caused huge economic losses but also seriously endangered people's physical and mental health. Accelerating the rapid distribution of emergency materials after a disaster can effectively reduce the harm done to personnel in the affected areas due to the lack of emergency services. As an important part of the emergency relief system, the location of the emergency material distribution center determines the efficiency of material distribution for the entire relief system. Currently, there are studies on facility location models divided into three categories: (1)The p-center problem, which selects p facilities that minimize the maximum distance between the demand point and the nearest used candidate emergency facility. (2)The p-median problem, which selects the p facilities that minimize the demand-weighted average distance between the demand point and the nearest candidate emergency facility. (3)The maximum coverage problem, minimizing the number of selected emergency facilities while covering all demand points, or maximizing the number of covered demand points by locating the number of emergency p facilities.
However, the simple location model of the emergency material distribution center does not fit well with the real post-disaster rescue scenario, due to the inherent abruptness, uncertainty, and great destructiveness of disasters. Post-disaster demand data are difficult to collect accurately, whereas an accurate emergency material demand assessment can not only help decision-makers arrange suitable emergency material distribution center services for demand points in the face of limited materials but also improve the utilization rate of emergency materials while reducing the distribution cost of emergency materials. The main ways to deal with the uncertainty of emergency location demands are robust optimization, fuzzy theory, stochastic programming, and connection number. Although the robust method can optimize uncertain problems, it considers only the worst-case scenario and obtains relatively conservative results. In addition, demand in affected areas changes over time, so it is difficult to obtain the reliable prior data needed for stochastic programming.
In conclusion, this paper proposes a model for the location of emergency material distribution centers based on uncertain demand and service utility. The research of the model focuses on how demand points can select emergency material distribution centers at the same construction cost. We propose ROLNSWOA to solve the problem in the paper to overcome the shortcomings of the basic non-dominated sorting whale optimization algorithm (NSWOA), such as slow convergence, low accuracy, and falling into local optimization, and also better fit the model in this paper. A series of improvements have been made to the algorithm. ROLNSWOA is compared to NSWOA, Non-dominated Sorting Genetic Algorithm II(NSGA-II), Strength Pareto Evolutionary Algorithm 2(SPEA2), Multi-objective Evolutionary Decomposition Algorithm(MOEA/D), and Multi-objective Particle Swarm Optimization Algorithm(MOPSO), by performing the real case data in the context of Shanghai, China. From the experimental results, it can be seen that the ROLNSWOA algorithm proposed in this paper significantly outperforms the other algorithms in all the evaluation metrics, although this requires more computational time, which is within the acceptable range. The results of this experiment further validate the effectiveness and accuracy of the model and algorithm.
Although the proposed model for the location of emergency material distribution centers based on uncertain demand and service utility, along with the ROLNSWOA, has demonstrated strong performance in the experiments, there is still room for further research. First, the current study does not fully account for the dynamic path constraints caused by post-disaster damage to the transportation network. Future work could integrate dynamic traffic recovery models to jointly optimize distribution routing. Second, in real-world scenarios, demand points may exhibit multi-level and multi-type demand characteristics. Therefore, subsequent research could extend the model to incorporate hierarchical collaborative distribution and multi-type material classification and scheduling mechanisms. Furthermore, although ROLNSWOA shows excellent performance in terms of precision and convergence, its computational efficiency may decrease when handling large-scale data. Future studies may explore the integration of distributed computing and deep learning-assisted optimization strategies to enhance the practicality and intelligence of the algorithm.

Climate change has become a significant challenge for humanity. Therefore, developing a low-carbon economy is extremely urgent and critical. Remanufacturing is a sustainable manufacturing process that emphasizes the recycling of waste materials and promotes low-carbon economic development, which has received widespread attention from both enterprises and academia. However, the scalable and standardized development of the remanufacturing industry relies on advancements in remanufacturing job shop scheduling technology. Thus, research on the remanufacturing job shop scheduling problem holds significant theoretical and practical value in advancing the growth of the remanufacturing industry.
Currently, there exists a research gap in the current studies that solve the problem of multiple uncertainties and disturbances in remanufacturing shops. To address the aforementioned gap, this study proposes a new robust optimization-based remanufacturing job shop dynamic scheduling (RO-RJSDS) model, which divides the remanufacturing scheduling process into two phases: a pre-scheduling phase and a dynamic scheduling phase. In the pre-scheduling phase, a discrete scenarios set is utilized to characterize the multiple uncertainties in the remanufacturing job shop. The robust optimization approach is employed to construct a mathematical model with the objective of minimizing the makespans and the difference in makespans under various scenarios, in order to obtain stable solutions that perform effectively in all possible scenarios. Once the remanufacturing process begins, the disturbances will trigger the remanufacturing system to enter the dynamic scheduling phase. In the dynamic scheduling phase, the final scheduling solution is determined based on the pre-scheduled solution and disturbances, while ensuring scheduling efficiency and minimizing performance differences with the pre-scheduled solution. Therefore, a hybrid rescheduling strategy is designed to handle disturbances that may decrease the efficiency of the remanufacturing system. In this study, an effectiveness indicator is used to evaluate the efficiency of the dynamic scheduling solution, which is measured by the makespan. Meanwhile, a robustness indicator is utilized to assess the performance gap, which is measured by the difference in performance between the pre-scheduling solution and the dynamic scheduling solution.
The proposed RO-RJSDS model is a typical NP-hard problem that cannot be solved using exact methods, such as the Lagrangian relaxation method and branch-and-bound methods. The biogeography-based optimization algorithm is widely used to solve NP-hard problems due to its good performance. However, the basic biogeography-based optimization algorithm suffers from insufficient population diversity and premature convergence. Therefore, an extended biogeography-based optimization (EBBO) algorithm with a new two-dimensional unequal-length representation scheme is proposed to solve the RO-RJSDS model. The proposed algorithm employs a sinusoidal migration model and designs new migration and mutation operators to facilitate efficient population migration. In addition, a local search strategy is proposed to enhance the convergence and distribution of the EBBO algorithm.
In this study, each simulation experiment data is randomly generated within the corresponding range. Simulation experiments are conducted to verify the algorithm's superior performance and validate that the proposed hybrid rescheduling strategy can efficiently respond to disturbances. Firstly, the EBBO algorithm is compared with three other baseline algorithms on eight different-scaled instances to comprehensively evaluate its performance. Secondly, simulation experiments are conducted to compare the performance of the proposed hybrid rescheduling strategy with that of a complete rescheduling strategy in the dynamic scheduling phase. The results indicate that the solution obtained by executing the hybrid rescheduling strategy dominates all the solutions obtained by executing the complete rescheduling strategy. Finally, simulation experiments are conducted to compare the proposed robust optimization-based remanufacturing job shop scheduling model with the traditional deterministic remanufacturing job shop scheduling model.
These findings offer valuable insights for future research. Firstly, future studies should consider various disturbances such as worker factors, quality failures, and urgent order insertions in the model. Secondly, researchers should adopt search strategies with lower computational complexity in the algorithm and explore the integration of machine learning methods to enhance the efficiency and performance of the algorithm.

The rapid development of the digital economy has led to the prosperity of online retail industry. To meet the individual needs of customers, it causes a lot of order fulfilment problems, especially the problem of order splitting and combining delivery. The existing literature usually only optimizes the two problems independently, ignoring the intrinsic connection that exists between them. And joint research of the two are an effective means to reduce the cost of order fulfilment. The inventory layout of “multiple warehouses in one place” is the key to solving the problem of order fulfilment and through the horizontal transfer between warehouses to achieve splitting of orders and combining delivery. It can meet the individual needs of customers, reduce the number of order deliveries and the delivery cost of orders, and realize the optimal order fulfilment process.
In this paper, we consider the complete order fulfilment process, which is to pick out the order customer's demand by splitting the category and quantity according to the warehouse situation (warehouse location, product category and quantity, etc.) and the order characteristics (customer location, order product category and quantity, order delivery time, etc.) under the warehouse layout model of “multiple warehouses in one place”. Then, the splitting orders are assigned to the appropriate warehouse, and the sub-orders belonging to the same customer are transferred horizontally between warehouses. Finally, the packing operation is performed at the consolidation warehouse, and the combined parcels are delivered to the customer. In addition, this paper constructs a mixed integer planning model by considering the combining and packing capacity and time constraints to minimize order fulfilment cost from three perspectives: order forwarding cost, order combining and pack cost, and order delivery cost.
In order to solve the model, the artificial rule of thumb is applied to construct the order-warehouse priority sequence matrix, and the depth-first search algorithm DFS is designed to quickly generate the initial feasible solution that meets the reality and is better, and the optimization scheme with the minimum cost is obtained by iterating based on the Improved Genetic Algorithm (IAPGA) framework. Since order splitting and consolidated delivery considered is a new combinatorial optimization problem, there are no benchmark calculations in the literature. Therefore, the validity of the model and algorithm are verified by adding data on the ability to construct combined packages and the latest time allowed for delivery of orders. And we set the data in the context of the reality that there may be a mass ordering of products based on two numerical experiments in the relevant literature.
The results show that: (1)It can be obtained that as the number of orders increases, the total cost of order fulfilment increases. At a certain number of orders, with an increase in the number of warehouses and with the order splitting and combining delivery solutions becoming more, the algorithm solution time increases, but the total order fulfilment cost can be reduced to a certain extent. (2)Under different consolidations of inventory size and order quantity, the order fulfilment cost increases as the number of orders increases. And when the number of orders is certain, the order fulfillment cost decreases as the inventory size increases. This is because the increase in inventory size reduces order splitting, and packing costs, transshipment costs, and distribution costs all decrease. (3)Under different consolidations of combined packing capacity and different order quantities, the order fulfilment cost increases as the number of orders increases. When the number of orders is certain, the order fulfilment cost decreases as the combination and packing capacity increases due to the relaxation of the combination and packing capacity constraint, which allows more order packing operations to be completed in the same consolidated warehouse, thus reducing the order transfer distance and delivery distance.

In the context of the booming development of Internet technology, people's lifestyle is constantly changing, and the functional demand of the Internet is also increasingly emphasized. As an important livelihood issue closely related to people's life and health, the combination of medical care and information technology is very necessary. During the rapid development of online retail industry, it coincides with the government departments, continuous introduction of policies to encourage medical institutions to use the Internet to provide more convenient and efficient diagnosis and treatment services for the public, and the online medical form emerges at the historic moment. It not only has basic medical services such as online consultation and online prescription, but also provides users with drug distribution services. Compared with other commodities, drugs have the particularity of strong rigid demand and complex categories, which lead to higher requirements for timeliness and safety in the process of drug distribution. Therefore, in the process of drug distribution, how to comprehensively consider the characteristics of drug distribution, rationally plan the distribution path, so as to improve the distribution efficiency and achieve the optimal cost has become an urgent problem to be solved in drug distribution.
Firstly, based on the fact that the user's satisfaction with the delivery service will affect the delivery cost in the process of drug delivery, and the drug distribution adopts the principle of non-contact delivery, the rider will not cause losses to the user when the order is delivered earlier than the expected time window of the delivery center, that is, the penalty coefficient before the earliest expected delivery time of the system is 0. Combined with the waiting cost caused by the lack of inventory in chain pharmacies and the delay in taking medicine caused by other merchants, a PDVRP model with asymmetric soft time window considering customer satisfaction is established. The total cost of delivery in the model is composed of three parts: transportation cost, waiting cost and penalty cost, and the path optimization is carried out with the goal of minimizing the total cost.
Secondly, considering the NP-hard characteristics of the delivery path problem with time window, in order to improve the problem of insufficient local search ability and slow convergence speed of the genetic algorithm, an improved genetic algorithm based on Cauchy mutation strategy is designed. The chromosome representing the delivery route of the rider is constructed by integer coding, the reciprocal of the objective function is taken as the fitness function, and the ranking-based roulette selection is selected to eliminate the huge difference of the fitness value and make the advantages of the better individuals more obvious. A new adaptive forward continuous crossover operator is designed to retain its own excellent genes and avoid code loss, and the Cauchy mutation strategy is integrated to jump out of the local optimum and enhance the global search ability of the algorithm.
Finally, in order to verify the effectiveness of the model, two different test sets are generated based on the order-related data of a platform given in the reference. The model is solved by simulation under the two different test sets, and the rider order allocation, path arrangement and cost distribution under the optimal delivery path are obtained. Then the model is solved by the traditional genetic algorithm and the improved genetic algorithm without the fusion of Cauchy mutation, and the evolution curves of the three algorithms and the cost structure under the optimal solution of each algorithm are compared. The results show that the convergence speed and the optimal solution of the improved genetic algorithm with the fusion of Cauchy mutation are better than the other two algorithms. Therefore, the effectiveness and superiority of the model and algorithm in this paper are verified.
In summary, the research content of this paper improves the problems of previous studies, such that few studies comprehensively have considered the particularity of drug distribution and customer satisfaction, but most have ignored the benefits of drug distribution efficiency, resulting in excessive penalty cost and too ideal inventory estimate for chain pharmacies. An improved genetic algorithm combined with Cauchy mutation, which can improve the convergence speed of the algorithm and jump out of the local optimum, is proposed for the optimization scheme of drug distribution path planning for chain pharmacies, which has certain reference significance for future drug distribution research. In further research, the dynamic changes of order quantity and actual road conditions can be introduced into the cost model, and various complex problems such as the remaining life of distribution vehicles can be considered to expand the application scenarios of the algorithm.

Multiple attribute decision making is a prominent area of research in normative decision theory. This topic has been widely discussed and studied. Considering that experts may have vague knowledge about the preference degree of objective things, uncertain linguistic variables are often used for decision makers as the evaluation information in some complex multiple attribute decision-making problems. For the sake of aggregating the uncertain linguistic evaluation information in multiple attribute decision-making problems, some uncertain linguistic information aggregation operators are developed and designed. However, it is worth noting that most of the uncertain linguistic information aggregation operators do not take into account the interrelationship between data and the overall balance of data simultaneously, which is unreasonable for the decision results in uncertain linguistic multiple attribute decision making problems. Therefore, it is necessary to pay attention to this issue.
In order to better solve this issue, we combine uncertain linguistic variables, power averaging operator, and Bonferroni mean operator to define the uncertain linguistic power Bonferroni mean (ULPBM) operator and the uncertain linguistic weighted power Bonferroni mean (ULWPBM) operator, which is able to make the decision results more accurate. The ULPBM operator and ULWPBM operator have some characteristics in the process of aggregating uncertain linguistic variables. On the one hand, two new operators utilize the crossover operation of the Bonferroni mean (BM) operator to represent the interrelationship between data. On the other hand, two new operators use the support degree coefficient of the power averaging (PA) operator to denote the overall balance of data. At the same time, the commutativity, idempotency, boundary, and monotonicity of these operators are investigated, which validates that these operators are feasible. Based on the above analysis, the ULWPBM operator is used for solving uncertain linguistic multiple attribute decision making problems, and a novel uncertain linguistic multiple attribute decision making method with the ULWPBM operator is put forward.
The talent selection is an important part for the development of enterprises, and the enterprises that own some excellent talents will make more profits and gain more space for survival. In this scenario, how to effectively find the most appropriate talent from several candidates has become a significant problem for every enterprise. However, there are a lot of factors that affect the capacity of talents, including ideology and morality, work attitude, work style, cultural level, knowledge structure, etc. Moreover, the experts often use uncertain linguistic variables when they evaluate the preference of these factors with regard to the enterprise talent selection. It is obvious that the enterprise talent selection is a classical uncertain linguistic multiple attribute decision-making problem. Therefore, we take an example with regard to the enterprise talent selection to prove the feasibility and effectiveness of the proposed method. The research results show that not only can the proposed method better solve the interrelationship between attributes, but the proposed method can also effectively alleviate the adverse influence of abnormal attribute values.
The main contributions of this paper are that we define the ULPBM operator and ULWPBM operator, and then we put forward a novel uncertain linguistic multiple attribute decision making method with ULWPBM operator. It should be noted that two new operators are the supplement and improvement of uncertain linguistic information aggregation operators, and the proposed method can give some references for solving real-world complex decision-making problems. In the future, the power Bonferroni mean operator could be extended to hesitant fuzzy linguistic preference relations and probabilistic linguistic environments. In addition, the uncertain linguistic multiple attribute group decision making approach with ULWPBM operator is also an interesting research topic, which needs further investigation.

In order to effectively control the queue size and reduce the cost caused by the frequent switching, the investigation concerning queueing models with control policy and server vacation is worth doing. The earliest works on the control policy of queueing systems were the N-policy, T-policy and D-policy. As to the study of vacation models, most works concentrated on studying models with multiple vacations, single vacation and multiple adaptive vacations. Based on the actual background of the production plant, this paper characterizes the acceptance of orders and their production process by a queueing service process, and studies the performance indicators of the system based on an M/G/1 queueing model with (p,N)-policy and uninterrupted multiple vacations. Here, the (p,N)-policy and uninterrupted multiple vacations mean that once the system becomes empty, the server immediately turns the system off and takes an uninterrupted vacation. When the server returns from vacation and finds the number of customers waiting in the system is greater than or equal to the threshold N, he/she immediately begins serving the waiting customers until the system becomes empty again. If there are arrivals in the vacation but the number of customers arriving in the system is less than N, the server is activated for work with probability p(0p1) or the server is idle but on duty with probability (1-p) until the number of arriving customers in the system reaches N and immediately begins serving the waiting customers. If there is no arrival in the vacation, the server begins another vacation at once.
Firstly, applying the well-known stochastic decomposition theorem of the steady-state queue size of the queueing system, we obtain the steady-state stochastic decomposition result of the system's order number and present the expression of the expected order number through direct algebraic operations. Meanwhile, we use the Little's formula to obtain the expression of the expected waiting time for any order in the system. Secondly, under a given cost structure model, we derive the explicit expression of the long-run expected cost per unit time of the system by using the renewal reward theorem. Without the constraint of average waiting time, we discuss the cost optimization problem of the system. Several numerical examples are presented to investigate the one-dimensional optimal threshold N^* for starting production to minimize the long-run expected cost as well as the two-dimensional optimal threshold (N^*,T^*) when the vacation time is fixed as T. Obviously, if the waiting time is too long, it will reduce customer satisfaction and may even lead to system congestion and customer loss. Therefore, it is of great theoretical importance and application value to consider the cost optimization problem of the system under the expected waiting time constraint. Inspired by the fact above, we further discuss the cost optimization problem of the system under the constraint of average waiting time, and also numerically determine the one-dimensional optimal control policy N^* and the two-dimensional optimal control policy (N^*,T^*). At last, the effects of the probability p on the optimal threshold and the minimum cost are also discussed.
From our study, it is suggested that in some systems where customers are not sensitive to waiting time, system managers can disregard the waiting time constraint and directly choose the threshold value that minimizes the cost of starting the service. In systems such as hospitals and transportation, where customers are more sensitive to waiting time, managers adopt a control policy that minimizes the cost of starting the service within the acceptable waiting time of customers. For future research, the continuous time queueing model studied in this paper can be extended to discrete-time queueing model.

In recent years, China's online game industry has experienced a significant and sustainable growth as a crucial component of the country's digital content sector, and gained a considerable industrial momentum and cultural influence. The influx of capital has infused vitality into the industry, whereas it has also introduced latent risks, necessitating more stringent and comprehensive online game supervision. Presently, academic circles primarily analyze and evaluate game supervision either at an overarching level or by examining the conduct of game manufacturers. However, it is essential to consider the two crucial stages of game development: publishing and operation. Consequently, regulatory efforts must encompass both stages. In light of the existing research and the current realities of regulatory challenges in China's online game industry, this study aims to optimize the regulatory model based on the distinct characteristics of game publishing and operation.
Firstly, this paper identifies the relevant stakeholders and their decision-making behaviors involved in the process of publishing and operating online games while making key assumptions for the game model. Secondly, based on the aforementioned assumptions, an evolutionary game model for regulatory authorities and online game manufacturers during the stages of game publishing approval and operation is developed. By conducting a partial equilibrium stability analysis, the evolutionary stable strategies and the impact of significant parameters during both stages are determined. The resulting stable strategy set from both stages is then combined to achieve a comprehensive equilibrium solution for the entire evolutionary game model. Thirdly, dynamic optimization deduction is employed to analyze the behavior transformation process during the stages of game publishing and operation, validating prior inferences. Moreover, considering the actual supervision practices of online games in China during both stages, the optimal approval and supervision approaches are proposed, respectively. Finally, based on the stability analysis and dynamic optimization deduction of the evolutionary game, this paper presents optimization suggestions for China's online game industry supervision.
The findings indicate that during the stage of online game publishing and approval, regardless of whether regulatory authorities opt for strict or lenient approval strategies, game manufacturers tend to publish and submit games that breach regulations due to reduced publishing costs and the limited sunk costs of not obtaining version number approval. The current approval model fails to effectively control the illicit distribution of games. Consequently, relevant regulatory authorities should suspend the approval and issuance of game version numbers to regulate the online game market environment. In the stage of online game operation, the supervision of online game operation is in a transitional phase of mature development. During this stage, the level of supervision has undergone a process from strict regulation to non-regulation and back to strict supervision. Game manufacturers should also gradually transit to compliant operation strategies, taking into account the increased strictness of supervision and penalties. Ultimately, a balanced state is reached between the two where supervision becomes effective.
Drawing upon the model establishment and analysis process, this paper proposes the following regulatory optimization suggestions: Firstly, suspending the approval of game version numbers may do more harm than good, and thus, the game access system should be improved and optimized. The suspension of game version number approval has impeded the growth of domestic game manufacturers, limited choices for domestic online game players, and hindered the development of aesthetic identification abilities. To supervise online gameapprovals more effectively, the examination and approval system should be improved by clarifying the power and responsibility of each supervision entity. Secondly, the supervision mechanism for the game operation process should be enhanced, and a game classification review system should be established. Considering the unique situation of the country, a game grading review system should be implemented, accompanied by flexible review standards and a strict implementation of the real-name certification system to standardize game behavior and safeguard the rights and interests of game manufacturers and players. Thirdly, promoting diversified regulatory bodies and strengthening industry autonomy are crucial. Relying solely on government supervision departments to regulate the entire game industry is challenging, and it is necessary to establish and improve a seamless reporting and feedback mechanism to involve society, schools, and families in the supervision process. Concurrently, industry self-examination and responsibility should be strengthened, and the social responsibility of game manufacturers should be publicized and enhanced.

The hotel industry in China has suffered immensely due to the COVID-19 pandemic on top of some traditional challenges, including guest expectations for altered values, surging costs, fierce competition with international rivals and market share lost to peer-to-peer accommodation rentals. While many are struggling to keep their businesses afloat, the industry is witnessing a wave of culture-themed properties being launched across the country amidst market uncertainties. Therefore, it is quite necessary to carry out research in order to measure the effects of cultural offerings on customer sentiment, aiming to find out whether incorporating Chinese culture in the portfolio of hotel offerings could serve as a solution to achieving greater efficiency at less cost for the upcoming post-epidemic era, replacing the traditional asset-heavy approach which has been wide applied in the industry but is beyond the affordability of many a pandemic-stricken Chinese hotels, so that hoteliers can make better-informed decisions on strategic adjustments in their operations in the post-epidemic era. To serve the purpose, this study focuses on two research questions: (1)Do Chinese hotels' cultural offerings significantly enhance the positive sentiment of domestic and international guests? If so, what can be the correlation between the two?(2)What other attributes of hotel service also affect guest sentiment?
We conduct text analytics of online reviews from Chinese hotels' guests from both home and abroad markets, which are collected from TripAdvisor, the most visited travel and tourism website worldwide applying strict supervision on its guest review mechanism. Based on the widely applied topic model LDA, which has been proven highly efficient in extracting dimensions from a large corpus of text customer reviews, the method of manual annotation-aided LDA is established to obtain from the positive and negative online guest reviews the hotel service attributes that affect guest sentiment, with Chinese culture as our most concerned target attribute. Then a Logit regression is carried out, resulting in an econometric model with the correlation between Chinese culture, along with other Chinese hotel offerings, and the sentiment of domestic and international guests.
The findings of our research are as follows: (1)Our research results in an econometric model of guest sentiment for both domestic and international markets. Chinese culture as an attribute of Chinese hotel offerings is found to significantly contribute to the positive sentiment of both domestic and international guests. (2)Besides cultural offerings, other attributes that positively affect guest sentiment are found to be location, food and staff service. (3)A higher correlation is also proved between Chinese culture and positive guest sentiment than the correlation between Chinese hotels' other attributes and guest sentiment. (4)The quality of rooms and value for money are found to negatively affect guest sentiment.
Our research findings reveal the significant positive correlation between Chinese hotels' cultural offerings and guest sentiment, which can serve as empirical evidence for the effectiveness of some Chinese hotels' experimental practice in tapping into the potential of traditional culture as a solution to achieving greater efficiency at less cost. The novelty of our research lies in our following contributions: (1)We first introduce cultural offerings as an independent variable into the model for the measurement of hotel guest sentiment and suggest the significant positive correlation between the two. Our findings are expected to offer insights for hoteliers eager for an optimized portfolio of offerings that can enhance their guests' positive sentiment. (2)We extend the guest sentiment management literature by developing a model with cultural offerings incorporated respectively for the domestic market and the international markets with cultural offerings. Our research is intended to enrich existing literature that help Chinese hoteliers to evaluate the role of cultural offerings as part of their service portfolio and assist in decisions on optimized fine management.

In recent years, in order to deal with challenges such as global warming and resources shortage, all countries around the world have introduced the carbon trading policy to encourage and advocate manufacturing enterprises to vigorously develop a sustainable cycle operation mode that aims to reduce carbon emissions. The closed-loop supply chain of end-of-life product, as an effective way to recycle resources, is an effective way to transform to low carbon production. The government and enterprises are promoting the end-of-life products recycling and remanufacturing industry, which is beneficial to promoting carbon neutralization, and carbon peak strategic goal realization so as to achieve the purpose of social sustainable development. The difference in consumers' use time, way, and frequency of the product makes the loss degree of end-of-life product different. That eventually makes the quality of end-of-life products uneven. The quality heterogeneity of end-of-life products makes the income of remanufacturing uncertain. Meanwhile, the uncertainty of carbon emissions in remanufacturing due to the quality difference of end-of-life products further increases the difficulty of decision-making under the carbon trading policy. Therefore, in this paper, the end-of-life product closed-loop supply chain is addressed by considering the impact of the quality heterogeneity of end-of-life products on carbon emissions in the remanufacturing process. A Stackelberg game model consisting of the manufacturer and retailer is established to study the effects of the quality of end-of-life product and carbon trading policy on the decision-making of supply chain members under decentralized and centralized decision-making. The coordination of revenue-sharing and carbon trading cost-sharing on the supply chain is discussed.
This paper mainly draws the following conclusions: (1)The quality of end-of-life products is related to wholesale price, retail price and recycling rate. Therefore, the manufacturer and retailer should consider the impact of end-of-life product quality when making decisions. When recycling end-of-life waste products, the manufacturer should pre-detect the quality, and then remanufacture them to different degrees according to the quality of different waste products. (2)Under the carbon trading policy, the manufacturer reduces carbon emissions by reducing the production quantity of products and the recycling quantity of end-of-life products. Therefore, the carbon trading policy could effectively reduce carbon emissions of enterprises, but the reduction of market demand and recycling quantity is not conducive to the development of enterprises. (3)The higher the recycling quality of the end-of-life product, the less carbon emissions generated in the remanufacturing process. When the recycling quality exceeds a certain threshold, the profits of both the manufacturer and retailer would decrease under the carbon trading policy. Therefore, the manufacturer and retailer must pay attention to the quality of the end-of-life products in the decision-making process. (4)Under the joint influence of recycling quality and carbon trading price, the optimal decision of supply chain members is more influenced by carbon trading price than recycling quality. Therefore, when considering the influence of carbon trading price and recycling quality, the manufacturer and retailer should give priority to carbon trading price. (5)The revenue-sharing and carbon trading cost-sharing contract achieves the purpose of coordination by reducing the wholesale price and retail price. Both the manufacturer and retailer are willing to adopt this contract as long as the sharing and sharing ratio of the contract is reasonable.
This paper explores the decision-making of the manufacturer recycling model in the closed-loop supply chain under the carbon trading policy. There are high differences between different recycling models in terms of cost-effectiveness and recycling efficiency, which will also affect the strategic decisions of supply chain members. Therefore, in the future, the impact of quality heterogeneity on individual decision-making under different recycling modes could be studied based on the background of carbon trading policy.

In recent years, although the income of rural residents in China has grown relatively quickly, the Gini coefficient of urban-rural income has continued to increase. Therefore, how to promote faster income growth for rural residents has become a key issue in achieving common prosperity. Among the many macro and micro factors, the level of financial support often determines farmers' willingness and actions to increase their income. However, traditional finance is often unable to cover long-tail users represented by farmers due to the mismatch between returns and risks. Therefore, the development of fintech can utilize advanced digital technologies to serve long-tail groups better than the traditional financial system. To some extent, this will alleviate farmers' financing dilemmas and become one of the important breakthroughs for increasing farmers' income.
Theoretically, fintech can help promote economic growth at the macro level, assist industrial restructuring and upgrading at the meso level, and improve total factor productivity and technological innovation at the micro level. Similarly, it also plays an indispensable role in influencing farmers' income. Firstly, the emergence of fintech can change the traditional financial system's dependence on physical outlets. The financial services it provides break through the constraints of time and space and expand the coverage of financial products and services, enhancing the availability of financial services so that rural residents can also obtain more convenient and efficient financial services. Secondly, the digital technologies on which fintech relies can more accurately portray borrowers' real situation, helping reduce information asymmetry and increase the availability of loans for rural residents. Finally, the development of fintech also provides good underlying technical support for various information service platforms in rural areas, helping alleviate the information island problem in rural areas. It broadens the channels for rural residents to quickly access relevant information, allowing them to better grasp various market opportunities and increase their income.
To verify the theoretical analysis above, this paper uses the 2011-2020 panel data on fintech and farmers' income at the city level in China. Firstly, it constructs a “fintech-rural residents' income increase” research paradigm and elaborates on the impact mechanism and heterogeneous manifestations of fintech on the income increase in rural residents theoretically and empirically. Secondly, it identifies the mechanism path of fintech's impact on rural residents' income increase through the mediation effect model. Finally, based on the Broadband China pilot policy, it is investigated here whether improving digital infrastructure will affect the role of fintech in increasing rural residents' income. The empirical results show that fintech does promote the growth of farmers' income. Heterogeneity tests find that this promotion effect differs significantly across regions and different income categories. The effect is more significant in eastern regions and on wage income, but weaker on property income and operating income in central, western, and northeastern regions. Mechanism testing reveals that fintech's driving effect on increasing farmers' income is mainly achieved by improving non-agricultural employment, alleviating agricultural financing constraints, and increasing agricultural total factor productivity. Further research finds that policy synergy is an essential external condition for exerting fintech's driving effect. The collaboration with the “Broadband China” pilot policy and related policies can further leverage fintech's driving role in financial assistance and technological spillover to provide a better financial environment for increasing farmers' income.
Based on the conclusions, this paper puts forward policy recommendations to give full play to fintech's technological and financial power in driving the increase in farmers' income, fully consider regional differences in resources endowments and development levels, unblock the transmission channels for fintech to increase farmers' income, and attach great importance to the role of policy collaboration in increasing farmers' income. This provides new research perspectives to maximize fintech's financial support effectiveness and more possible policy portfolio options to increase farmers' income.

With the rapid development of platform economy, consumers, either young or old, have been embracing online shopping. Due to the increasing number of online consumers, both the upstart and leading manufacturers have been jumping on e-commerce platforms to sell their products to consumers. When manufacturers enter an e-commerce platform, an increasingly important issue is whether their products should be sold through the agency selling or the reselling mode. Under the agency selling mode, the e-commerce platform acts as an intermediary, charging a percentage of commission to the manufacturer and allowing the manufacturer to sell the product directly to the consumers (e.g. manufacturers open flagship stores on e-commerce platforms). Under the reselling mode, the e-commerce platform plays the role of a retailer, wholesaling products from the manufacturer and reselling them to consumers (e.g. self-operated flagship store of e-commerce platform). The key difference between the two modes is that the manufacturer charges the retail price under the agency selling mode and the e-commerce platform sets the retail price under the reselling mode.
In contrast with the extant entry mode selection that typically considers completely rational manufacturers, the entry strategy of overconfident manufacturers is explored. Overconfidence, distinguished from complete rationality, is a psychological term that refers to people showing excessive optimism and confidence in their own abilities and predictions about the future. According to the psychological studies, the psychological trait of overconfidence is common in humans. Furthermore, economic research also confirms that business managers are more likely to exhibit overconfident behavior. In fact, many important business decisions, especially about entering an existing market, are made under the impact of the behavior of overconfidence. For example, when manufacturers enter the online consumer market, they are often overconfident about the size of the market for their products. In this context, the entry mode selection of overconfident manufacturers settling in the e-commerce platform is well worth exploring.
Aiming at a platform supply chain consisting of a manufacturer and an e-commerce platform, we propose the case in which the manufacturer is overconfident in the market size, establish the condition under which the platform offers both the agency selling and reselling modes, and study the impact of overconfidence on the mode of manufacturers entering the e-commerce platform. The results show that: (1)If and only if both the platform's commission ratio and the manufacturer's overconfidence are sufficiently low, the platform will offer both the agency selling and reselling modes for the overconfident manufacturer to choose. (2)When the commission ratio is relatively high (low), the overconfident manufacturer will choose the reselling (agency selling) mode; when the commission ratio is moderate, the overconfident manufacturer will choose the reselling (agency selling) mode if its overconfidence is relatively high (low). (3)The mode selected by the overconfident manufacturer can be either a win-win, win-lose, or lose-lose scenario, however the mode selected by the completely rational manufacturer cannot be a lose-lose scenario. (4)By comparing the mode choice strategies of perfectly rational and overconfident manufacturers, it is found that perfectly rational manufacturers can always enter e-commerce platforms, while overconfident manufacturers may not be able to enter e-commerce platforms with larger commission ratios; as the commission ratio decreases, the optimal mode of manufacturers' entry into e-commerce platforms is shifted from reselling to agency selling, and the bar for shifting to a different mode is higher for overconfident manufacturers. That is, if and only if both the platform's commission ratio is moderate and the manufacturer's overconfidence is sufficiently high, the overconfident and completely rational manufacturers will choose a different mode to enter the e-commerce platform. Finally, a numerical simulation suggests that the perceived profit of the overconfident manufacturer is always higher than the real profit it obtains, and their deviation degree is higher (lower) under the reselling (agency selling) mode.
Future research could explore two main directions: (1)extending the single-manufacturer framework to multiple manufacturers to examine the entry mode selection for the entrant; (2)investigating manufacturer over-pessimism as a counterpart to the current overconfidence analysis.

In recent years, trade-in services have prevailed in the durable goods market such as automobiles, household appliances, and mobile phones. In reality, used products like mobile phones often have poor performance due to serious battery deterioration, thus some firms are increasingly providing battery replacement services. Battery replacement service refers to the process in which consumers only replace the battery of a product while keeping the old product and turn the old battery over to the merchant for recycling. Some firms provide battery replacement services, for example, Huawei provides battery replacement services for its mobile phones and notebooks, and Xiaomi provides battery replacement service for its mobile phones. Thus, considering that the battery replacement service will cannibalize the old replacement service and need a certain fee, the firms that provide the old replacement service are faced with the challenge of whether to provide the battery replacement service.
To cope with this challenge, this paper considers the optimal battery replacement strategy under the centralized supply chain, decentralized supply chain and coordinated supply chain, and develops theoretical models. With consumer utility theory, game methods and optimization methods, this paper optimizes the models and presents optimal decisions and profits. By comparing optimal decisions and profits, we obtain some implications. Moreover, this paper considers the influence of online reviews in the extension.
Regarding the battery replacement strategy, this paper finds that in the centralized supply chain and decentralized supply chain environment, when the battery replacement value increase rate is low, firms should not provide battery replacement services. In a moderate situation, when the fixed cost of battery replacement service is low (high), the firm should (not) provide battery replacement service. When the battery replacement value increase rate is relatively high, firms will choose to provide battery replacement services only when both the production cost of new batteries and the fixed cost of battery replacement services are low; otherwise, firms will choose not to provide battery replacement services. Different from the centralized supply chain and the decentralized supply chain, in the coordinated supply chain, the retailer's optimal battery replacement strategy depends on the increase rate of battery replacement value, the fixed cost of battery replacement service and the size of the contract fixed fee. Compared with the centralized supply chain, enterprises in the decentralized supply chain are more inclined to not provide battery replacement services. If the contract fixed fee of CONB is larger (smaller) than that of COYB, the enterprise is more inclined to coordinate the supply chain. Battery replacement service is provided (not provided). As online reviews of new batteries increase, the willingness of firms to provide battery replacements will increase. In terms of optimal decision-making, this paper finds that if firms intend to provide battery replacement services, they should maintain the original new product prices and trade-in discounts. Compared with centralized supply chains and coordinated supply chains, retailers should lower their retail prices in decentralized supply chains, but sometimes it is necessary to increase their trade-in discount and the price of new batteries. As the durability factor of used products increases, firms should increase the trade-in discount and the price of new batteries. As the residual value of used products increases, firms should increase their prices. They have trade-in discounts but should lower the price of their new batteries. Firms should increase the price of their new batteries as the rate of increase in battery trade-in value increases.
This paper only considers the single-cycle battery replacement strategy, and future research can consider two-cycle and multi-cycle situations. In addition, this paper only considers the single-channel situation, so dual-channel, omni-channel, and multi-channel can be included in future research. Finally, firms in the market are often in a competitive environment, so the issue of battery replacement strategies for multi-agent competition will be the future research direction.

Enterprise software is one of the important tools in the digital transformation of enterprises. The maturity and development of cloud computing technology have a certain impact on the distribution strategy of enterprise software. In addition to the traditional retail channel, pure SaaS channel and mixed channel have gradually attracted the market's attention. There are some differences between the retail and SaaS channel: First of all, the products of retail channel are installed on the users' servers, while in SaaS channel the products are installed on the vendor's servers, so the users only need to bear the infrastructure cost in the retail channel. However, considering data security, system stability and other issues, users' acceptance of SaaS channel is lower than that of retail channel. Second, users can get the ownership and the right to use the product at the same time when they buy the product in the retail channel, but in the SaaS channel, users only get the right for use through remote access to resources through the network, and the ownership always belongs to the vendor. Last but not least, the products of retail channel can be customized one-to-one according to the needs of users, while SaaS channel are usually standardized to meet the needs of multi-tenants but do not support in-depth customized development. Considering the advantages and disadvantages of the two channels, the vendor is faced with the dilemma of channel selection. On the other hand, in order to better meet the personalized needs of users, the vendor and retailer can provide customized development for retail channel users to enhance their purchase intention. Although this kind of activity can help the vendor or the retailer benefit from higher product pricing (price increase effect), and at the same time they also need to bear the relevant customization development cost (cost constraint effect), which reduces their motivation for customization.
Based on the above background, we divide the market according to users' preferences for customization, discuss the choice of software vendor among retail, SaaS and mixed channel strategies in three situations (no customization development, customization development by the vendor or by the retailer), and focus on the influence of customization development on vendor's optimal channel strategy. In addition, we also discuss the choice of channel strategy when the vendor has the advantage of customized development cost. The main purpose of this study is to provide a basis for vendors to choose channel strategies in practice and help vendors and retailers make reasonable customized development decisions.
The results show that: Firstly, pure retail channel may become the optimal channel strategy only when the retailer makes customized development, otherwise the vendor always chooses pure SaaS channel or mixed channel according to the tradeoff between the cost constraint effect and price increase effect. Specifically, when customized by the vendor, if the infrastructure cost faced by users is relatively low (high), the mixed channel (pure SaaS channel) is optimal. When customized by the retailer, the pure SaaS channel is optimal if the infrastructure cost is high. If the infrastructure cost is low, the vendor chooses retail SaaS or mixed channel according to the proportion of users with high customization preferences and their sensitivity to customization. It should be noted that with a decrease in the proportion of users with high customization preference and their sensitivity to customization, the optimal area of pure retail channel strategy is transformed into pure SaaS channel strategy. Secondly, customized development activities cannot always improve the profit of the vendor. When the infrastructure cost faced by users in the retail channel is relatively low, with an increase in users' acceptance of SaaS channel, the decision of customized development changes from retailer customization to vendor customization, and finally is without customized development. This is because the competition between retail channel and SaaS channel is gradually intensifying, and the price increase effect brought by providing customized development is relatively weak, and the cost constraint effect is dominant, which gradually makes customized development unprofitable. Last but not least, a counterintuitive conclusion is that the customized development activities carried out in the retail channel actually promote the vendor to transform from the mixed channel strategy to the pure SaaS channel strategy. When the retailer makes customized development, it has the strongest motivation to choose to provide pure SaaS channel strategy.
Our research also has some limitations. For example, we only consider the case where the software vendor or the retailer undertakes the customization development cost, and the model that the vendor and retailer jointly invest in customization can be further analyzed in the future. In addition, the channel strategy of vendor is considered in this study under the monopoly environment, and the competitive market environment is not considered yet. However, with the maturity and development of cloud computing, the competition between the cloud vendor and traditional vendor is becoming fiercer and fiercer, which can be further expanded and analyzed in future research.

Based on the two-sided market theory and utility theory, the‘search-match' decision of two types of users, the H-type user and the L-type user, with matching needs, as well as the service strategy and pricing strategy of the online platform are discussed and analyzed by constructing a game-theoretic model. In particular, we discuss and analyze the Nash equilibriums under four scenarios when the online platform provides the searching services firstly. All utility functions of two type users are listed and the equilibrium results are calculated, and by comparing the optimal profits of two types of users, their decisions on whether to use the online platform to search matchers and what conditions are to use the online platform are explored. In addition, with the similar research method, we also discuss the online platform's optimal service and pricing decisions when it provides ‘searching and authenticating' services at the same time.
The research finds that: (1)When the online platform only provides search services, the optimal service strategy of the online platform is jointly affected by the market structure, the ratio of the H-type users in the whole market, the quality difference between the two types of users. When the proportion of H-type users in the market is high and the difference between the two types of users is large, the optimal strategy of the online platform is to provide search services for H-type users by increasing the price of search services. Otherwise, it is the optimal strategy for the online platform to reduce the search pricing and provide the search services to the whole market. (2)When the online platform provides ‘search and authentication' services at the same time, the online platform's pricing and service strategies will also be affected by the market structure and the difference in the quality of the two types of users. In particular, when the price of the platform search service is low, both types of users will choose the online mode to carry out ‘search-match' process, but only H-type users will choose to purchase the authentication service when the price is low. With the improvement of market construction and the rise in the ratio of H-type users, the willingness of H-type users to purchase authentication services has gradually declined, and the pricing of search services and the pricing of authentication services will change in opposite directions. Furthermore, no matter how low the pricing of platform authentication services is, L-type users will not purchase them. (3)In addition, through the example analysis, we furtherly explore the relationships among the optimal pricing of searching, the optimal pricing of authentication, the market structure and the difference in two type users. The impact of market structure on the revenue of online platform is also analyzed by the example analysis. The research also finds that the online platform should pay more attention to the control of the cost of the authentication service when providing it, and the cost of the authentication service should be controlled within a specific range, otherwise, the online platform not only will be unable to profit from theauthentication service, but also may lose profits from the search services.
In a word, this paper expands the usage field of the two-sided market theory, provides a new perspective for the pricing and service strategies of online platforms, and also provides a theoretical support for the effective formulation and improvement of online platform operating policies.

The concept of graph energy originates from chemistry and physics, particularly organic chemistry and statistical physics. It was first introduced by Erich Hückel in 1978 through computing the total π-electron energy. Graph energy is a parameter defined on the molecular structure of matter, which is closely related to the molecular structure, and scientists use it as an approximation of the Hückel molecular orbit. In physics, HEILMANN and LIEB (1970) first proposed the concept of matching roots of molecular structural graphs. In 1972, they studied the matching roots of molecular structural graphs in their paper “Theory of Monomer-Dimer Systems”. They related the monomer-dimer problem to the Heisenberg and Ising models of magnetism and derived Christoffel-Darboux formulas for the partition functions of these models. They also proved that the roots of the matching polynomial of graphs are real, and computed the expression for a certain type of graph. At around the same time, mathematicians such as Godsil and Gutman independently proved this result by different approaches. Subsequently, more mathematicians began to explore the combinatorial properties of graph parameters related to matching roots, matching numbers, the number of perfect matchings, and matching energies of graphs.
GUTMAN and WAGNER (2012) introduced the concept of matching energy, defined as the sum of the absolute values of the roots of matching polynomial of a graph. They presented basic results for simple graphs and studied the matching energy of trees, unicyclic graphs, complete bipartite graphs, and approximation upper bound for the complete graphs.Their work laid the foundation for further research, leading to numerous publications on the matching energy of various classes of simple graphs. Researchers have calculated the largest matching energy and the minimum matching energy, the largest matching roots for trees, unicyclic, bicyclic, and tricyclic graphs, and “Unmarked” characterized the extremal graphs with the minimum or maximum matching energy.
Graph matching energy, Hosoya index, the largest matching root (also known as the matching index), and matching number are highly related parameters, though quantifying their exact relationships remains challenging. JI et al. (2013) studied the extremal matching energy of bicyclic graphs. ZHU (2013) also investigated the minimal energies of unicyclic graphs with perfect matchings, identifying the first seven minimal energies and addressing a conjecture. WANG and SO (2015) explored the minimum matching energy of graphs, examining the relationship between matching energy and several graph transformations. Most studies in this area involve computing the matching energies of graphs within specific classes and characterizing the corresponding extremal graphs. ZHANG and LIU (2021) studied the behavior of the largest matching root and the matching energy of graphs under two graph transformations. The results were published in the MATCH Communications in Mathematical and in Computer Chemistry in 2021.
In this paper, we investigate how the coefficients and the largest matching root of matching polynomials of graphs behave under two specific graph transformations. The result shows that the graph has the largest matching root but the minimum matching energy. The largest Hosoya index also induces the largest matching energy. As an application, we characterize the graphs with minimum matching energy among all trees and unicyclic graphs with a given matching number. We also provide numerical lower bounds for the matching energy of these graphs in terms of their matching number.

Intuitionistic fuzzy numbers (IFN), characterized by membership, non-membership, and hesitation degree have become pivotal in uncertain decision-making. However, existing ranking methods face critical limitations when hesitation degrees vanish (i.e., degenerate to fuzzy numbers) or when compared with negative-domain IFN. This study addresses these gaps by developing a unified ranking framework that maintains consistency with classical fuzzy number ranking principles while incorporating decision-maker attitudes.
We define subordinate lower fuzzy numbers and subordinate upper fuzzy numbers to bound the membership range of IFN. A preference-weighted centroid (x₀(A~),y₀(A~)) is formulated, where: x₀ integrates geometric centers of subordinate bounds, y₀ combines membership strength and hesitation through an attitude parameter α∈[0,1]. A sign function I_x0 resolves ambiguity in positive/negative IFN comparisons. The ranking index R(A~)=I_x0·x²₀+y²₀ ensures: compatibility with fuzzy number ranking when π_<sub>A~=0; attitudinal flexibility via α-weighting (pessimistic: α<0.5; neutral: α=0.5; optimistic: α>0.5). For trapezoidal/triangular IFN, closed-form centroid formulas prove that R(A~) degenerates to fuzzy centroid index (WANG and LEE, 2008) when π_<sub>A~=0.
Four comparative cases demonstrate the resolution of both counterintuitive rankings for negative IFN and attitude-driven outcome variations while maintaining transitivity. In selecting India's aerospace research center, weighted aggregation of trapezoidal IFN yields robustranking ₅>₁>₂>₄>₃, aligning with benchmark methods still offering explicit preference interpretation.
The proposed method overcomes the three limitations: hesitation-induced ranking failure, sign ignorance in distance metrics, rigidity to decision-maker attitudes. Future work may extend this framework to interval type-2 fuzzy sets and dynamic multi-period decision environments.

Under the influence of the COVID-19 pandemic, households used debt to meet the needs of consumption smoothing and asset allocation, helping to smooth out the fluctuations in household income and consumption caused by the impact of the pandemic. However, a disorderly expansion of debt will increase the debt burden of households and even threaten the stability of financial and economic systems through negative feedback effects. In recent years, the rapid development of digital finance has created a good external condition for meeting the capital needs of households. So, will the growth of digital finance lead to an increase in household debt burdens? On the one hand, digital finance forms an external financing market outside the banking system; on the other hand, digital finance makes the banking business cover a wider range of customers through competition effect. Both effects have altered the structure of financial supply and facilitated the expansion of household debt. If an increase in household debt is only used for consumption expenditure, the household debt burden will become heavier with the accumulation of consumption debts. At the same time, an increase in household debt does not necessarily increase the debt burden. Residents may use debt funds to support family entrepreneurship, optimize asset allocation, etc., resulting in income growth that will alleviate the debt burden on households. In addition, the macro-economic impact of the digital finance will also feed back household debt burdens. Therefore, the impact of digital finance on household debt burden is a complex system, and different motivations and mechanisms of indebtedness will have different impacts on household debt burden. It is particularly important to discuss how digital finance affects households' debt decision-making and debt burden, so that households can make reasonable use of the convenience brought by digital finance to alleviate negative impacts such as the epidemic while not continuously worsening household debt burden.
Using the matching data of Peking University Digital Financial Inclusion Index and China Household Finance Survey data (CHFS) for 2013, 2015, and 2017, this paper examines the impact of digital finance on household debt and debt burden. Heterogeneity analysis is carried out from the three aspects: digital finance sub-index, household characteristics and household debt status. This paper further discusses the macro and micro mechanisms of digital finance affecting household debt burden from the three aspects: consumption promotion effect, income growth effect and income inequality regulation effect.
The empirical results show that, overall, digital finance increases the probability and scale of household debt, and the debt burden of households considering the possible endogeneity problem, and the results are still valid by using instrumental variable regression. However, the results of the heterogeneity test show that digital finance does not necessarily increase the burden of household debt while increasing the probability and scale of household debt. The heterogeneity test of the digital finance sub-index shows that the depth of digital finance helps to alleviate household debt burden. The heterogeneity test of household characteristics shows that digital finance can help to reduce the debt burden of households with a high education level, but it has no significant impact on the debt burden of rural households. Heterogeneity tests based on household debt status show that digital finance can help alleviate the debt burden of households with reasonable levels of debt burden. The intermediary effect model is used to test the mechanism of digital finance affecting household debt burden. The results show that at the micro level, digital finance increases household debt and debt burden through consumption promotion effect, but it does not increase household debt burden while promoting household debt increase through income growth effect. At the macro level, digital finance simultaneously reduces the debt scale and alleviates the debt burden of households through the moderating effect of income inequality. The above results have certain enlightenment significance for fully understanding the impact of digital finance on household debt burden, and making good use of digital finance to meet household debt capital needs without increasing household debt burden.

In the past three years, with the outbreak and raging of COVID-19, the operation and survival of enterprises encountered difficulties. China State Shipbuilding Corporation (CSSC) has comprehensively implemented “cost engineering”, focusing on three kinds of cost since 2020: labor cost, procurement cost and outsourcing cost. There is a serious information asymmetry between the headquarter and the manufacturing unit (shipyard), especially in the setting of the man-hour quota. Due to several characteristics of man-hour in shipbuilding, unobservable and incomparable, accounting for a relatively high proportion (about 23% of the total construction cost), the deviation rate between the man-hour quota and the actual man-hour is as high as-62%~30.6%. The man-hour quota is determined by the superior (headquarters) of the manufacturing unit manager, taking into account the observed past performance. As a result, the better performance today triggers the lower man-hour quota in the future, causing the ratchet problem. The man-hour quota is related to the production cost, manufacturing cycle and economic benefits of enterprises. Existing studies on man-hour mostly start from the pure technical dimension, endeavoring to collect and allocate more clearly, predict accurately, and reduce it reasonably, but less considering the influence of managerial behavior, that is, the potential ratchet effect in the setting of the man-hour quota leads to low control efficiency. Rather than recording and studying technical data, we should emphasize contracts, incentives and control of human behavior, and replace Robinson Crusoe perspective with a game theory perspective.
A model is constructed with three basic elements: production relationship, ratchet, and incentive scheme. In order to focus on the influence of ratchet on the managerial behavior and simplify the production relationship, the flexible man-hour constraint can be realized at any time and the inherent man-hour of the manufacturing unit has been given, and the manufacturing unit manager selects the man-hour realization level within the constraints. A lower realized value of man-hour in the current period will lead to a lower man-hour quota in the next period. In order to avoid rigid plans in the future, managers tend to achieve a higher man-hour in the current period, resulting in ratchet effect. Giving a manufacturing unit manager (agent) is faced with a payment scheme: during the reporting period, the manager will receive a fixed salary if his/her behavior reaches or falls below a specific man-hour quota, plus a proportional reward for the difference between man-hour quota and realized man-hour. The headquarter adjusts the quota according to a concise rule, and finds the maximum present value of managers' expected rewards by the stochastic dynamic programming problem caused by solving the set of man-hour realization levels. The strategy improved by Howard algorithm is used to solve the reward value of the optimal strategy and the accompanying strategies. The fixed point theorem is used to prove that there are optimal man-hour quota and man-hour implementation strategy. The optimal managerial behavior for the headquarter is described and compared under different situations (where the inherent man-hour and the man-hour quotas decrease at the same rate, or the former decreases faster than the latter).
It is found that the appearance of managerial behavior with great difference depends on the strength of ratchet. A large reduction rate of quota can lead to a consistent level of effort at the inherent man-hour. However, under moderate taut conditions, the expected result occurs, that is, managers choose to produce at a higher realized value of man-hour rather than at the inherent man-hour, but the behavior can induce agents to signal accurate information about the reduction of the inherent man-hour to the principal. The research suggests that as long as the ratchet degree is not too taut, the optimal action requires the manufacturing unit manager to reveal the reduction rate of the average intrinsic man-hour, and if the headquarter slightly underestimates the reduction rate of the average intrinsic man-hour, then the manager will usually slightly overachieve the target, which is the optimal action.
The research prospect is to apply the method of determining the man-hour quota in this paper to the cost control of shipping enterprises, implement multiple case studies, and verify the feasibility and reliability of the research conclusions through practice.

The battery of AGV will affect the efficiency of the production system. For example, if the system knows that the battery power of an AGV is not sufficient to perform a task, it will assign the task to another AGV or assign the AGV to a charging station. For the production workshop using AGV for material handling, one of the bottlenecks to increase production capacity is the available production time of AGV. The method of increasing production capacity by increasing the number of AGVs is very expensive, and the layout of the production workshop is mostly compact. Too many AGVs may cause the system to be more blocked and reduce production efficiency. In current industrial production applications, the battery is managed as follows: when the AGV continues to operate until its power level drops below a certain threshold, it goes to the charging station to fill it up to 100%. In this decision, if the system is in an idle period, that is, the AGV in the system is idle and the battery power does not reach the threshold, limited by the power management method, the AGV cannot effectively use the idle time to go to the charging station. If the system is in a busy period, that is, the AGV in the system is in a full load state, when the AGV power level drops below the threshold, the current position of the AGV may be accidentally far away from the nearest charging station, which will increase the time required to go to the charging station to charge and return to perform the remaining tasks, or at this time, the task volume in the system is large, and the AGV is performing an emergency order task, which cannot consume a lot of time to wait for full power before continuing to perform the remaining tasks. AGV can make a more sensible decision, that is, not fully charged, but it still can complete the task of emergency orders. After the system busy period, AGV can decide to continue charging.
Therefore, this paper studies how to deal with a sudden increase in capacity demand in the production workshop by changing the charging mode of AGV without changing the number of AGVs and improve the production efficiency of the workshop. A general AGV charging model is proposed. This model studies the most widely used lead-acid battery as the research object, and considers AGV in both full load and non-full load state, aiming at the AGV automatic charging mode lacking in previous studies. The model aims at the shortest total time for all tasks to complete, and makes decisions on the time, placement, and duration of AGV charging tasks in its task sequence. The AGV's automatic charging model has three decision problems to be solved: (1)Whether charging is required after the i task site. (2)Which charging station to go to be charged? (3)How long to be charged? There are two possible situations in the production that need to be considered at the same time: (1)The system is relatively busy, the AGV is in full load operation, and the tasks in all task sequences are continuously performed. (2)AGV is in a non-full load operation state, and there is idle time in the process of executing the task sequence. In order to solve the model, a heuristic algorithm (PSO-NCMO) combining particle swarm optimization algorithm and nonlinear constrained multivariable optimization algorithm is proposed, and the improved particle evolution framework is used to optimize the model.
The experimental data come from a real electrode production workshop of a new energy enterprise. The data of small, medium, and large AGV task scales in the workshop are selected for simulation experiments. By comparing the optimization results of the industrial benchmark method and the proposed PSO-NCMO algorithm, the results show that when the AGV is at full load, the PSO-NCMO algorithm reduces the total execution time of the task including charging by an average of 23.55% compared with the benchmark. When the AGV is at non-full load, the algorithm can prioritize the AGV to use the idle time to go to the charging station. When the initial power and minimum power limit of AGV are changed, AGV ends the task with as little residual power as possible, which shows that the charging model and algorithm have strong power management effect and have certain versatility. The charging time can be adjusted according to the actual needs of the enterprise. The limitation of the text is that it does not consider the faults and congestion during AGV driving. In the future, we will use deep learning technology to establish a prediction model during AGV driving, making the AGV power consumption and charging model more suitable for actual production.