Pricing and Inventory Decisions for an Assortment under a Generalized Nested Logit Choice

Abstract

This work explores pricing and inventory decisions for a selection of substitutable products, where each product differs based on main and secondary attributes. Customer preferences are modeled using a nested logit framework, allowing each nest to have its own degree of price responsiveness and substitution intensity—thereby generalizing previous models. On the operational side, we adopt a newsvendor-style setup, where demand is assumed to follow a Normal distribution derived from an approximated Poisson process. Inspired by earlier studies that ignore inventory costs (the “riskless” scenarios), we assume that product prices can be expressed using a single decision parameter, which implies that products in the same nest have equal profit margin.. A numerical study confirms that this assumption leads to nearly optimal outcomes. We then investigate how the expected profit responds to pricing and assortment decisions when inventory levels are set optimally. Finally, based on our analytical and numerical results, we develop an equal nest profit margin heuristic that exploits popular sets. We demonstrate via extensive numerical testing that this heuristic yields a small optimality gap (generally within 1%), while being fast and easy to implement.