Newsvendor pricing and assortment under Poisson decomposition

This article studies the structure of and the interdependence among the critical decisions on pricing, inventory, and assortment of a retailer’s product line. It considers substitutable retail products that are horizontally differentiated variants under a logit consumer choice model, within a newsvendor-type supply setting and homogeneous pricing. The focus of this article is on analyzing joint pricing and inventory decisions for a given assortment, within a natural Poisson decomposition setting, under a “multiplicative–additive” demand model, where both variance and coefficient of variation of the demand depend on the price. For this problem, a Taylor series-based approximation is developed for the inventory cost and its accuracy is subsequently demonstrated. It is then shown that, under this approximation, the expected profit is unimodal in the price, and sufficient conditions are provided for the “risky” price, at optimal inventory, to be above (or below) the “riskless” price, pertaining to a make-to-order system. It is also shown that inventory considerations alter the behavior of the risky price in demand and cost parameters. Furthermore, joint assortment and inventory decisions under exogenous pricing are considered, and the unimodularity of the expected profit in the assortment size is proven. Also, a comparative statics analysis is performed and insights are presented.