Abstract: This paper delves into how an online retailer, operating within cash constraints, manages multi-period, multi-product inventory and financing decisions, while grappling with stochastic customer demand. It particularly investigates the use of credit-based loans and order-based loans, available on Chinese e-commerce platforms, typically with a term not more than one year. Order-based loans offer a specialized financing avenue designed to expedite the retailer’s cash flow. Upon acceptance of an order, the platform promptly disburses payments to the retailer upon confirmation of delivery. Subsequently, the retailer repays the loan, along with interest, within a predetermined timeframe. Credit-based loans resemble traditional bank loans, where the e-commerce platform provides a predetermined cash sum to the retailer, and the retailer repays the loan with interest over a specified period.
   To address this issue, we employ the scenario tree method to depict demand uncertainty, in which each demand realization value is represented by a node in the scenario tree. Then, we develop Mixed Integer Programming (MIP) models for two financing scenarios and solve them using the Gurobi 9.0.3 solver in Python 3. The scenario trees are constructed using the moment matching method, considering the mean, variance and skewness of the demand distribution. By minimizing the Euclidean distance between specified moments and those derived from the scenario tree, demand realization values along with the corresponding possibilities are obtained.
   However, when the planning horizon is extended, the scenario tree becomes expansive, leading to an exponential increase in the number of constraints and decision variables in the MIP models. To expedite computation, we employ the forward reduction method to scale down the scenario tree. The concept behind forward reduction is as follows: first, select the scenario with the least weighted distance to other scenarios, where the weights represent the probabilities of demand realizations in the scenarios; then, choose the scenario with the second least weighted distance, and continue this process until the required number of scenarios are selected; finally, add the probability of each unselected scenario to its respective nearest scenario.
   To validate the efficacy and efficiency of our modeling and solving approaches, we utilize real data obtained from an online electronics retailer and fit stochastic demand to lognormal distribution based on the demand data for three products: keyboards, mice and headsets. Historical monthly demand is assessed from the frequency of customer comments scraped from the retailer’s online stores in the Tmall platform. The numerical results demonstrate that the scenario tree method exhibits both in-sample and out-of-sample stability in solving the problem. In-sample stability entails that computational results across different scenario trees should not vary significantly, while out-of-sample stability implies that computational results should remain relatively consistent after fixing the first-stage decision obtained from other scenario trees. Moreover, in terms of the managerial insights gleaned from this study, we observe that both financing services can enhance the retailer’s profit and mitigate cash shortage issues. On the other hand, across various combinations of initial cash, overhead costs, payment delay length, loan quantity, interest rates and demand fluctuation pattern, credit-based loans prove to be more effective in addressing cash shortages compared to order-based loans while order-based loans display strengths when the payment delay length is long. Retailers can leverage the stochastic modeling approach presented in this paper, considering their cost and revenue parameters, to select the appropriate financing services and make informed inventory decisions.

Key words: credit-based loan, order-based loan, multi-period inventory, scenario tree, demand fitting

摘要： 本文考虑一家具有资金约束的线上零售商,在电商平台提供信用贷款与订单贷款服务时,如何进行多阶段、多产品的库存融资决策。由于常规库存模型难于求解该问题,本文使用情景树表示需求的不确定性,并构建不同融资服务情形下的混合整数规划模型;在问题规模较大时,使用情景缩减技术加快问题的求解速度。为了验证建模与求解方法的有效性,本文使用网络爬虫抓取一家线上零售商的数据,拟合出顾客的随机需求分布,代入模型中求解。算例显示,情景树方法在本文的研究问题中具有抽样内稳定性以及抽样外稳定性;在大多数情况下,信用贷款比订单贷款更能有效地缓解零售商的资金短缺问题,而当零售商的收益延迟较长时,订单贷款具有一定优势。零售商可以根据自己的成本收益参数,使用本文的随机建模方法选择合适的贷款服务以及管理库存。

关键词: 信用贷款, 订单贷款, 多阶段库存, 情景树, 需求拟合