Joint Pricing and Inventory Decisions for Substitutable Products

Abstract

A pervasive problem for retailers is to make assortment and inventory procurement decisions of substitutable products with the goal of maximizing expected profits over a pre-defined selling horizon. Multiple inventory replenishments are not allowed. This problem is challenging because of demand substitution effects that are driven initially by the assortment decision and later by stockouts. We propose intuitive and easy-to-implement heuristic based on the sample average approximation method coupled with the Markov chain approximation to discrete choice modelling. We show that our heuristic is asymptotically optimal, and quite effective even in the non-asymptotic regime. Our heuristic exhibits very small optimality gaps and outperform, sometimes dramatically, traditional newsvendor solutions that ignore dynamic substitution effects. Our numerical analysis also reveals that the newsvendor heuristic may perform quite well when the assortment is properly chosen and demand variability is relatively low. These managerial insights help decide when to employ the traditional newsvendor solution. We also look into endogenous pricing and show that even a simple heuristic can significantly enhance profits if prices can be adjusted sufficiently often. Another finding is that price flexibility mitigates the need for safety stocks to the point that not hedging inventories is often better than hedging them.