Abstract: A warehouse has multiple storage partitions, and each partition's efficiency and cost of commodities are different, the purchase volume and storage strategy of commodities are the key factors affecting the sales profit. Because the purchase decision and storage strategy are interrelated, in order to help the managers make optimal decisions, a joint optimization problem of the multiple commodities purchase and partition storage under stochastic demand and price is studied. Current research on the issues related to the partition storage of commodities in warehouses rarely considers uncertain demand, which may lead to deviations in the actual operation of the warehouse and incur additional costs. By considering the stochastic demand of commodities, the partition storage problem of commodities can be effectively optimized, the purpose of reducing the total costs further achieved, and the research on storage-related problems enriched. Consumer's demand for each commodity is easily affected by factors such as season, price, promotion, etc., so it is uncertain and difficult to predict accurately. Different demand levels directly affect the actual outbound quantity of commodities, which has a greater impact on the storage costs and the profit of commodities. Studying the problem of multiple commodities joint procurement and partition storage considering stochastic demand can provide a decision-making reference for solving the actual commodity storage problem.
For each commodity, the purchase quantity and the storage location of the commodity needs to be determined before its demand occurs. After the demand occurs, the storage area of the remaining inventory can be reassigned. A two-stage stochastic programming model is established to maximize the total profit. The optimal solution is obtained by calling Gurobi solver to solve the two-stage stochastic programming model. The effectiveness of the joint optimization method based on two-stage stochastic programming model is verified by the simulation on different scale examples, sensitive analysis of some parameters and comparison with the deterministic method and phased optimization method. The shortage cost can be significantly reduced by 9.33% by considering the uncertainties. Besides, the profit obtained based on the joint optimization strategy is increased by 155.8% to that of multi-stage decision-making strategy. Allowing reassignment can reduce the total storage cost by 33.3%. Therefore, the research conclusions of this paper provide a theoretical basis for managers to formulate commodity purchase and storage plans.
The following management enlightenment can be obtained by this research. Firstly, when the storage capacity of each partition is limited, before the sales occur, the commodities with high demand should be stored in areas with low inbound and outbound costs, and the commodities with low demand should be stored in areas with low inventory space consumption costs. Secondly, if the remaining inventory of commodities in a certain area is large after sales, it is necessary to determine whether the remaining inventory needs to be transferredaccording to the sales volume of the commodities in the next cycle, by comparing the unity transferring cost and the unity inventory occupancy cost reduction from current area to the target area. Thirdly, with an increase in storage area capacity, the total profit increases too, but the marginal profit brought by increasing the storage area capacity shows a decreasing trend. When the storage area capacity reaches a certain threshold, the marginal profit brought by continuing to increase the capacity will be zero, so enterprises should comprehensively consider the storage area expansion cost and other factors, and reasonably determine the best capacity of each area.
This paper provides a theoretical basis for e-commerce enterprises to make purchasing and storage decisions by studying the joint optimization of multiple commodity procurement and storage with multiple storage areas. The main contribution is to provide a theoretical basis for the transformation of e-commerce enterprise warehouses from traditional warehouses to new automated ones, or when traditional warehousing and automated warehousing areas exist at the same time, it provides a theoretical basis for formulating a variety of commodity procurement, storage and other strategies, considers the stochastic demand for different commodities in different random scenarios, and helps enterprises improve their management level and obtain maximum profit and value.
In order to simplify the problem, this paper simplifies the law of demand and price change into a finite discrete scenario. In practice, there are many factors affecting demand and price, and simplifying the statistical law of historical data into a limited number of discrete scenarios to describe the future sales volume distribution law may produce certain errors. When there is more historical data, we can consider directly using a continuous probability distribution to describe the random distribution of demand to obtain a more realistic decision-making scheme. In addition, this paper does not consider the correlation between multiple commodities, such as complementary commodities, substitute commodities, etc., in the future, the correlation between different commodities can be considered, and how to reasonably obtain the joint optimization scheme of procurement and storage of commodities.

Key words: multiple commodities, stochastic demand, purchase and partition storage, joint optimization, two stage stochastic program

摘要： 当一个仓库有多个分区,不同分区的商品出入库效率和成本存在差异时,商品采购量与存储策略均是影响销售利润的关键因素。由于采购决策与存储策略相互关联,且商品需求量具有随机性,为了帮助管理者做出最优决策,研究了随机需求下多种商品的采购与分区存储联合优化问题。以总利润最大化为目标建立两阶段随机规划模型,在需求发生前确定每种商品的采购量并分配到存储区域,在需求发生后对剩余库存的存储区域进行调整。通过Python调用Gurobi求解两阶段随机规划模型得到最优解。利用不同规模算例进行模拟计算,并对模型的部分参数进行了灵敏度分析,以及与确定型方法和分阶段优化方法进行对比,验证了本文所提出的方法在降低成本、提升收益方面的有效性。结果显示:考虑需求、售价等不确定因素可显著降低9.33%的缺货成本;利用联合优化模型得到的采购、分区存储、出库以及倒库策略可提升155.8%的利润;允许倒库可降低33.3%的存储总成本。

关键词: 多商品, 随机需求, 采购与分区存储, 联合优化, 两阶段随机规划