O.R. Applications Retail price markup commitment in decentralized supply chains Yong Liu a,1 , Michael J. Fry b, * , Amitabh S. Raturi c,2 a HSBC, 2700 Sanders Road, Prospect Heights, IL 60070, United States b Department of Quantitative Analysis and Operations Management, University of Cincinnati, 532 Lindner Hall, Cincinnati, OH 45221-0130, United States c Department of Quantitative Analysis and Operations Management, University of Cincinnati, 530 Lindner Hall, Cincinnati, OH 45221-0130, United States Received 4 January 2007; accepted 31 August 2007 Available online 11 September 2007 Abstract We investigate the operational decisions and resulting profits for a supply chain facing price-dependent demand under a policy where there is an ex-ante commitment made on the retail price markup. We obtain closed-form solutions for this policy under the assumption of a multiplicative demand function and we analytically compare its performance with that of a traditional price-only policy. We compare these results to results obtained when demand follows a linear additive form. These formulations are shown to be qualitatively different as the manufacturer’s wholesale pricing decision is independent of the retail price markup commitment in the multiplicative case, but not when demand is linear additive. We demonstrate that the ex-ante commitment can lead to Pareto-improving solutions under linear addi- tive demand, but not under the multiplicative demand function. We also consider the effect of pricing power in the supply chain by vary- ing who determines the retail price markup. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Supply chain management; Inventory; Pricing 1. Introduction Many traditional operations management models assume that retail prices are set exogenously. This can be a very limiting assumption that is not reflected in many industries where oligopolies and non-perfect market condi- tions exist. In many scenarios price is a decision variable that can be used to influence demand and, by extension, operational costs and revenues. Recent advances in research relating pricing and inventory decisions in decen- tralized models have been put forth by Emmons and Gilbert (1998), Wang et al. (2004), Cachon and Lariviere (2005) and others. We add to this body of research by examining the effect of ex-ante commitments to retail price markup in decentralized supply chains facing price-depen- dent demand. We also extend this area of investigation to include the effect of the division of pricing power between players in the supply chain, where pricing power refers to the player’s ability to influence the price markup in the sup- ply chain. We develop models for a retail fixed markup (RFM) policy where an ex-ante commitment is made to the retail price markup before wholesale prices have been set. Such a policy may arise in practice for a variety of reasons. Some retailers choose to follow a fixed markup pricing policy for convenience. Many retailers believe that there is a mini- mum markup over wholesale price that they must receive in order to be profitable. In order to keep the retail price as low as possible, the retailer may choose to simply increase the wholesale price by this minimum markup. Fur- thermore, it can be difficult for a retailer with thousands of products in stock to investigate the demand curve and find 0377-2217/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2007.08.036 * Corresponding author. Tel.: +1 513 556 0404. E-mail addresses: yong_liu2000@yahoo.com (Y. Liu), mike.fry@uc. edu (M.J. Fry), amit.raturi@uc.edu (A.S. Raturi). 1 Tel.: +1 847 291 2019. 2 Tel.: +1 513 556 7192. www.elsevier.com/locate/ejor Available online at www.sciencedirect.com European Journal of Operational Research 192 (2009) 277–292