Assortment optimization with log-linear demand: Application at a Turkish grocery store

Abstract

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 O(n(2)) while other two well-known heuristics' complexities are O(n(3)) and O(n(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.