In retail sector, product variety increases faster than shelf spaces of retail stores where goods are presented to consumers. Hence, assortment planning is an important task for sustained financial success of a retailer in a competitive business environment. In this study, we consider the assortment planning problem of a retailer in Turkey. Using empirical point-of-sale data, a demand model is developed and utilized in the optimization model. Due to nonlinear nature of the model and integrality constraint, we find that it is difficult to obtain a solution even for moderately large product sets. We propose a greedy heuristic approach that generates better results than the mixed integer nonlinear programming in a reasonably shorter period of time for medium and large problem sizes. We also proved that our method has a worst-case time complexity of ( ) n O 2 while other two well-known heuristics’ complexities are ( ) n O 3 and ( ) n O 4 . Also numerical experiments reveal that our method has a better performance than the worst-case as it generates better results in a much shorter run-times compared to other methods.

Introduction

Retailing business and all its dimensions went through a drastic change with the turn of the century due to increasingly personalized consumer needs, growing number of products, and drastically changing way the sales are conducted (Clay et al., 2002). Empirical evidence indicates that increasing amount of customers seek products that are suited to their individual needs (Ulu et al., 2012). Personalized consumer demand lead manufacturers to design different products to stay competitive as consumers rarely hesitate to switch to another brand (or retail store) when they are dissatisfied with the actual one, a.k.a. low consumer loyalty. To keep up with this drift, supermarkets tend to increase the range and variety of products that they offer to their customers. Highly diversified customer needs and increasing number of candidate products force supermarkets to increase the variety of goods on their shelves for serving to larger number of consumers and maintain their market shares. However, shelf spaces of supermarkets usually stay the same as it requires significant amount of investment to increase them. Quelch and Kenny (1994) report that the number of goods in supermarkets increased by 16% per year between 1985 and 1992, while shelf space expanded by only 1.5% per year in the same period. In addition to limited shelf space, increasing product variety stands for higher handling costs, more frequent markdowns, and possible loss of economies of scale due to smaller order quantities. Therefore, finding the correct product assortment out of a large candidate set and offering them in a limited shelf space is critical for financial success of supermarkets (Cadeaux, 1999).