Multi‐period price promotions in a single‐supplier, multi‐retailer supply chain under asymmetric demand information

This paper considers a two‐stage supply chain in which a supplier serves a set of stores in a retail chain. We consider a two‐stage Stackelberg game in which the supplier must set price discounts for each period of a finite planning horizon under uncertainty in retail‐store demand. As a mechanism to stimulate sales, the supplier offers periodic off‐invoice price discounts to the retail chain. Based on the price discounts offered by the supplier, and after store demand uncertainty is resolved, the retail chain determines individual store order quantities in each period. Because the supplier offers store‐specific prices, the retailer may ship inventory between stores, a practice known as diverting. We demonstrate that, despite the resulting bullwhip effect and associated costs, a carefully designed price promotion scheme can improve the supplier’s profit when compared to the case of everyday low pricing (EDLP). We model this problem as a stochastic bilevel optimization problem with a bilinear objective at each level and with linear constraints. We provide an exact solution method based on a Reformulation‐Linearization Technique (RLT). In addition, we compare our solution approach with a widely used heuristic and another exact solution method developed by Al‐Khayyal (1992) in order to benchmark its quality.