A new mathematical approach for the limited assortment planning problem with discount policy

In this paper we consider the problem of determining the optimal assortment and inventory levels for a set of products with various prices and costs in order to maximize expected profit in a single-period setting. Decisions related to assortment planning and inventory management issues have an undeniable impress in retail optimization owning to customer behavior in substituting the products in the case of shortage. On arrival, the customer checks the availability of different products in order of her preferences and buys a product if available or leaves the store without purchase if she cannot find a product in her priority list. Customer preferences are modeled through the definition of consumer types by arranging the potential products in order of preferences. In this study we also consider the capacity constraint and discount mechanism to model the problem. To solve the model, a genetic algorithm is developed and the numerical results show the reasonable performance of the developed algorithm.