Pricing and inventory decisions of an assortment under equal profit margin -

Abstract

We consider the interdependent decisions on inventory and pricing of substitutable products in an assortment that is differentiated by some secondary attributes such as color, flavor, etc. We assume we have a newsvendor-type model with several products and one selling period under a logit consumer choice model. We also assume that all products in the assortment have equal profit margins. Demand assumes a multiplicative-additive structure where both variance and coefficient of variation depend on the pricing captured by the common profit margin. This is a realistic demand structure (Maddah et al., 2013) reflecting customers arriving according to a Poisson process and making purchases, at random, according to the logit model. Our problem is then to determine the common profit margin and the inventory levels of products in the assortment in a way that maximizes the expected profit. This problem has been studied in the literature for homogenous products, having equal unit costs or equal costs and average consumer valuations, but not for general assortments due to its complex nature. Under an adopted Taylor Series approximation, the profit function is proved unimodal in the common profit margin. Then, we compare the optimal profit margin to the “riskless” profit margin, where no inventory exists, in order to understand the effect of inventory considerations on pricing. We further perform a comparative static (sensitivity) analysis on demand and cost parameters to understand the environment impact on pricing. We continue to study the structure of the optimal assortment and establish dominance results.