Pricing, assortment, and inventory decisions under nested logit demand and equal profit margins

We consider the interdependent decisions on assortment, inventory and pricing of substitutable products that are differentiated by some primary and secondary attributes captured by a nested logit consumer choice. We examine a newsvendor-type setting with several products competing for demand over a single selling season. We assume that all products have equal profit margins. The demand has a multiplicative-additive structure where both variance and coefficient of variation depend on the common profit margin, which adds to the model applicability at the expense of tractability. Under a Taylor series-type approximation, we show that the expected profit is unimodal in the common margin of products in a given assortment. Then, we compare the optimal profit margin to the case under ample inventory, which allows understanding the effect of inventory on pricing. We also study the optimal assortment problem under exogenous pricing. We show that the classic result on the optimality of popular sets holds under tight approximations of the profit function. We finally propose a heuristic for jointly deciding on assortment, pricing, and inventory decisions, which assumes equal profit margins of products, and exploit popular sets only. Our detailed numerical study shows that this equal-margin heuristic produces high quality solutions.