Optimizing product assortment under customer-driven demand substitution

Abstract

The problem of product assortment and inventory planning under customer-driven demand substitution is analyzed and a mathematical model for this problem is provided in this paper. Realistic issues in a retail context such as supplier selection, shelf space constraints, and poor quality procurement are also taken into account. The performance of three modified models, one that neglects customers’ substitution behavior, another that excludes supplier selection decision, and one that ignores shelf space limitations, are analyzed separately with computational experiments. The results of the analysis demonstrate that neglecting customer-driven substitution or excluding supplier selection or ignoring shelf space limitations may lead to significantly inefficient assortments. The effects of demand variability and substitution cost on optimal assortment and supplier selection decisions as well as on the optimal revenue are also investigated. The main contribution of this paper is the development of a practical and flexible model to aid retailers in finding optimal assortments to maximize the expected profit.

Introduction

In order to survive in a competitive environment and to establish a strong position in the market, retailers should be able to manage their operational activities efficiently while providing an adequate customer service-level. Activities such as store and inventory management, establishing relationships with the suppliers, ordering and purchasing of products all contribute to operational costs, while additional costs, or rather loss of revenue, may incur due to poor quality procurement and customer dissatisfaction. An important trade-off in finding the right product assortment is that increasing variety increases customer satisfaction but has a negative effect on operational costs. As a result, when a retailer decides on which suppliers to work with and what product assortment to carry, it is important to understand the expectations and the purchasing behaviors of customers. Research on this topic shows that customers are frequently willing to buy a different color, size or brand within a product category if their favorite variant is either not offered or is temporarily out of stock, rather than going home empty handed. This behavior is indicated by the term customer-driven demand substitution and causes the demand for the remaining product types to increase, affecting their optimal order quantities and the product assortment decisions. In selecting what products to offer, retailers are subject to store related constraints such as shelf and storage space limitations. Therefore, maximizing profit in the existence of these operational issues is a challenging problem for retailers as they seek to rationalize assortment and inventory decisions at the category level.

Product assortment, demand substitution, supplier selection, and inventory management have been studied extensively; yet, to the best of our knowledge, there is no previous work that considers all these aspects together in the literature. This paper provides a tool for retailers to determine the product assortment, which considers supplier selection and inventory management decisions in the presence of shelf space limitations and substitution behavior of customers. The proposed tool optimizes these inter-related decisions for each product category with the goal of maximizing the retailer’s expected profits, under cost and demand parameters to be estimated by the retailer over a time horizon. Specifically, we introduce a mixed-integer programming model for the joint problem in order to determine which product types should be ordered from the suppliers, as well as the optimal ordering quantities for the offered product types. The model finds an optimal policy that maximizes expected total profit over a planning horizon for which demand and customers’ substitution preferences can be forecasted. By solving this model with different parameter settings designed in our computational experiments, we analyze the importance of various aspects of the problem. We identify the effect of substitution on the product assortment and profit by varying substitution cost parameters. In addition, we show numerically that incorporating the supplier selection decision into the determination of product assortment may result in significantly increased profit, and furthermore, considering shelf space limitations in the decision process leads to more profitable assortments.

The rest of the paper is organized as follows. Section 2 provides the necessary background and literature on product assortment, demand substitution, and supplier selection problems. The mathematical model for the problem with single-period, stochastic demand is presented in Section 3. An illustrative example is also presented in this section. In Section 4, the model is analyzed computationally. Conclusions are drawn in Section 5, where possible extensions to the proposed model are also discussed.