A stochastic programming framework for pricing and market share optimization in retail systems

Abstract

This study examines a scenario where a manufacturer owns one retailer and collaborates with an independent retailer to sell a single product with Poisson demand over a multi-period selling horizon. The manufacturer protects the independent retailer’s profitability through price protection and mid-life and end-of-life return opportunities. The retailers are allowed to place replenishment orders throughout the selling horizon. The manufacturer-controlled and independent retailers manage their stocks through order-up-to policies and hybrid policies comprising order-up-to and dispose-down-to policies, respectively. We employ stochastic programming techniques to construct models to determine the manufacturer’s optimal pricing strategy. Retail Fixed Markdown (RFM) policy is assumed to determine the retail price at which the independent retailer sells the product. We also consider the impact of retail prices on the retailers’ market shares, which influence the mean demand observed by each retailer. We propose a modified version of the Stochastic Dual Dynamic Programming (SDDP) algorithm to determine the manufacturer’s approximately optimal pricing strategy. Then, we examine how price protection contract parameters affect the manufacturer’s approximately optimal pricing strategy and the retailers’ expected total profits. We also make comments on the selection of ideal values for the parameters.