货架管理模型的选品与布局启示——以自动售货机为例

随着中国在线支付技术的发展，货架管理问题已成为零售企业面临的热点问题。具体而言，出于日益增加的商品种类数量与有限货架空间之间的矛盾，如何科学地决策自动售货机的商品种类以及设计货架商品布局以提高零售企业收益尤为关键。本研究提出了同时决策选品与货架布局的货架管理模型，目标是最大化期望总收益，约束是满足某些真实商业规则。然而该模型的约束中存在二次项难以直接求解，本研究进一步通过线性化技术将原始货架管理模型转化为整数线性规划模型，并提出与零售价、边际利润以及需求相关的管理启示，以指导零售商进行选品以及设计货架布局：一方面，当需求与边际利润满足某些关系时，随着增大，决策将由需求导向转变为边际利润导向；另一方面，当需求与零售价满足某些关系时，决策始终是零售价导向的。其优势在于零售商可以直接根据商品历史零售价、边际利润以及需求信息，决策选品以及设计货架布局，而无需求解一个整数规划模型。最后，本研究提出原始货架管理模型的抽样平均近似模型，并给出数值例子验证管理启示。

Insights of Assortment and Allocation on Shelf Management: Taking Vending Machine as an Example

With the development of online payment technology in China, shelf management has become a hot issue for retail enterprises. Specifically, due to the contradiction between the increasing number of commodity types and limited shelf space, how to scientifically determine the commodity types of vending machine and design layout to improve the profit is particularly critical. In this paper, we propose a shelf management model which integrates assortment and shelf allocation and also satisfies some business rules with the goal of maximizing the expected revenue. However, this model can not be solved efficiently due to the bilinear term in the constraints, thus we use the linearization technology to transform the original shelf management model into an integer linear program, and propose some managerial insights with respect to the selling price, marginal profit and demand of commodities, which can help retailers make decisions about assortment and shelf allocation directly without solving an integer program: on the one hand, if the demand and marginal profit satisfy some conditions, decision will be changed from demand orientation to marginal profit orientation; on the other hand, under some conditions between demand and retail price, the decision is always dominated by selling price. Finally, we develop the sample average approximation model and some numerical experiments justify the proposed managerial insights of our model.