The multi-product competitive price-setting newsvendor problem

Abstract

We consider the problem where a number of firms simultaneously compete in price and inventory level decisions. Each firm offers a line of several products, both complementary products and substitutes, the product line demand is also sensitive to prices of outside competitors' products. We also consider the case of excess demand, where the firm faces part of the demand its competitors could not satisfy because of stock-out, and an application of the proposed approach to the serial inventory problem. Although in most practical settings, multi-product dynamic pricing problems are approximately solved by decoupling across products and solving a large number of single-product problems. In this paper, we propose an iterative relaxation algorithm that solves the multi-product problem, and we prove sufficient conditions for convergence of the algorithm. Finally, we present extensive computational examples and a real-world case study derived from the successful testing and implementation of our models and algorithms in several industries.