O.R. Applications A supply chain under limited-time promotion: The effect of customer sensitivity Konstantin Kogan * , Avi Herbon Department of Interdisciplinary Studies, Bar-Ilan University, Ramat-Gan 52900, Israel Received 5 February 2007; accepted 10 April 2007 Available online 18 April 2007 Abstract We consider a two-echelon supply chain with a supplier and a retailer facing stochastic customer demands. The supplier is a leader who determines a wholesale price. In response, the retailer orders products and sets a price which affects cus- tomer demands. The goal of both players is to maximize their profits. We find the Stackelberg equilibrium and show that it is unique, not only when the supply chain is in a steady-state but also when it is in a transient state induced by a supplier’s promotion. There is a maximum length to the promotion, however, beyond which the equilibrium ceases to exist. More- over, if customer sensitivity increases, then the wholesale equilibrium price decreases, product orders increase and product prices drop. This effect, well-observed in real life, does not, however, necessarily imply that the promotion is always ben- eficial. Conditions for the profitability of a limited-time promotion are shown and analyzed numerically. We discuss both open-loop and feedback policies and derive the conditions necessary for them to remain optimal under stochastic demand fluctuations. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Supply chain management; Gaming; The maximum principle 1. Introduction Surveys published in Progressive Grocer steadily report that manufacturing, wholesale, and chain store executives claim that promotional programs are a top concern for their firms. Though large manufacturers traditionally dominate trade deals, retailers armed with abundant information on profitability, product move- ment, and customer demand for a class of goods are developing sophisticated purchase and storage policies to take advantage of the trade promotions available from manufacturers. A retailer, for instance, may engage in ‘‘forward buying’’, that is, purchasing more goods during a promotional period than he expects to sell (Zer- rillo and Iacobucci, 1995). On the other hand, increased use of promotions (e.g., weekend and holiday tariffs) 0377-2217/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2007.04.012 * Corresponding author. Tel.: +972 3 5318459; fax: +972 3 5353329. E-mail address: kogank@mail.biu.ac.il (K. Kogan). Available online at www.sciencedirect.com European Journal of Operational Research 188 (2008) 273–292 www.elsevier.com/locate/ejor