Abstract: With the increasing global awareness of environmental sustainability, waste separation management in urban areas has become increasingly critical. Recently, to enhance the accuracy of waste separation, waste source-separation facilities equipped with intelligent monitoring systems have been introduced in many residential districts in China. The location and number of intelligent source-separation facilities have a significant impact on the investment cost of the facilities, residents’ enthusiasm for participating in waste separation, and subsequent collection costs. Therefore, it is necessary to optimize the location and deployment of source-separation facilities from a systematic perspective.
In foreign countries, waste collection is generally conducted by municipal collection vehicles using door-to-door or curbside collection methods that directly access waste drop-off points. However, in most urban residential communities in China, the waste from drop-off points needs to be first transported by property management to centralized collection points before being collected by municipal vehicles. Currently, there is no research specifically addressing the location-allocation and capacity optimization problem that covers both drop-off points and centralized collection points in the context of waste source separation in China. Additionally, previous studies have generally assumed that residents’ satisfaction is inversely related to the distance to the drop-off points. However, residents exhibit a “semi-aversion” psychology towards waste disposal facilities, where satisfaction is affected if the drop-off distance is either too far or too close. Moreover, previous research rarely considers the significant fluctuations in the generation rate of different types of waste on weekends and holidays.
This paper examines the two-level location-allocation and capacity optimization problem for intelligent separation facilities in urban residential waste management. Several intelligent facilities with supervision functions need to be deployed at drop-off points and centralized collection points. Each drop-off point is equipped with bins for different categories of waste, while centralized collection points are located near main roads accessible to municipal collection vehicles. Based on the generation rates of various types of waste under different scenarios, the location and allocation of all facilities, the number of bins, and the collection frequency for each type of waste at each point must be decided. The objective is to minimize the investment cost of the facilities, the supervision, and the subsequent collection costs.
We first construct a mixed-integer programming model to address the two-level location-allocation and capacity optimization problem with dynamic collection frequencies. The model incorporates a satisfaction function that considers both the semi-aversion psychology effect and the environmental external effect. On one hand, residents are dissatisfied if the drop-off facilities are too near or too far. On the other hand, residents are willing to bear a longer walking distance to drop-off points in the waste separation context than to traditional mixed drop-off points. To solve the model, the nonlinear constraints are transformed by introducing auxiliary variables. Then, based on the relationship between waste collection frequency and the number of waste bins, we introduce conditional inequalities as enforcement constraints to simplify the model and improve computational efficiency. Lastly, a scenario-based stochastic programming method is employed to analyze the impact of waste generation uncertainty.
This study selects seven residential communities in Dalian. The number of people per household is estimated based on the characteristics of the building types. The actual walking distances are measured according to the community road network. Four sets of instances with different scales are established. The deterministic model and the stochastic model are solved using AMPL and the Gurobi solver version 10.0 on a computer with a 2.50 GHz processor and 4GB RAM.
The results of the four instance sets indicate that adding conditional inequalities as enhanced constraints can reduce the required solving time by 90%. When considering resident satisfaction constraints, the average walking distance for residents to dispose of waste will be reduced, thereby increasing satisfaction levels by approximately 20%. However, this requires more drop-off points, leading to higher facility investment, supervision, and collection costs. When considering variable collection frequency, the frequency at points with lower waste generation rates can be reduced (e.g., every two days). This requires more waste bins, increasing facility investment costs, but reduces collection costs, resulting in a slight decrease in total costs. If both resident satisfaction constraints and variable collection frequency are considered simultaneously, resident satisfaction can increase by an average of 13%, with a rise in total costs of less than 5%. Additionally, as the scale of the problem increases, the cost advantage of adopting variable frequency collection becomes more significant.
In addition, when considering the fluctuations in waste generation on weekends and holidays, we find that the deterministic model can provide stable facility location and allocation solutions through flexible adjustments in bin numbers and collection frequency. The stochastic model, on the other hand, can offer a more robust solution. These research findings provide a systematic and cost-effective facility deployment solution that also considers social benefits and environmental impacts, contributing to the promotion of sustainable urban development.

Key words: waste separation, location and allocation, customer satisfaction, stochastic optimization

摘要： 垃圾分类设施的科学选址与布局对提升源头分类的质量与数量至关重要。本研究以我国现行的集中分类投放为背景,建立了涵盖垃圾分类投放点与收集点的两级选址分配和容量优化模型,系统考虑了分类设施的前期投入成本、后续收集过程中的经济与环境成本以及分类监督的成本。同时,针对居民对于垃圾投放设施的半厌恶心理以及垃圾分类所带来的环境外部效应,设置了新的居民满意度函数。通过对收集频率与其他变量的耦合关系分析,在模型中加入了条件不等式以提高模型求解效率。最后,采用了基于情景的随机规划方法以分析垃圾产生量的不确定性对选址决策的影响。基于大连市居民小区的实例求解结果显示,加入条件不等式作为增强约束可以将模型求解时间减少90%。当同时考虑居民满意度约束与可变的收集频率时,优化方案能使居民的平均满意度提升13%,而总成本的增长幅度不超过5%。同时,研究还发现,垃圾产生量的波动仅影响每个点的垃圾箱配置数量和收集频率,不影响投放点和收集点的选址和分配决策,采用随机规划模型能给出更具鲁棒性的解。

关键词: 垃圾分类, 选址分配, 居民满意度, 随机优化