Customer and retailer rebates under risk aversion
AbstractIn a supply chain setting, we analyze a manufacturer's customer and retailer rebates, which are sales incentives offered to the end buyers and retailers, respectively. The performance of both rebates is influenced by the retailer's objective and response to the promotion due to his intermediary position in the channel. Earlier studies investigating rebates in distribution channels have traditionally assumed that the retailer is risk neutral with the objective of maximizing expected profits. In our paper, we consider a risk-averse retailer. We formally model risk aversion by adopting the Conditional-Value-at-Risk (CVaR) decision criterion. Using a stochastic and (effective) price dependent demand, we analyze the manufacturer's rebate amount decisions and the retailer's joint inventory and pricing decisions in a game theoretical framework. We provide several structural properties of the objective functions and show monotonicity of the retailer's decisions in the degree of risk aversion. For the case of retailer rebates, we characterize the unique equilibrium, and for the case of customer rebates, we prove the existence of an equilibrium. Using numerical examples, we provide further insights on the impact of risk aversion. For example, given an exogenous wholesale price, we observe a threshold value on the retailer's risk-aversion parameter below (above) which the manufacturer is better off with retailer rebates (customer rebates); implying that the manufacturer's preferred rebate type can be different depending on whether the retailer is risk neutral or sufficiently risk averse.
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Bibliographic InfoArticle provided by Elsevier in its journal International Journal of Production Economics.
Volume (Year): 133 (2011)
Issue (Month): 2 (October)
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Web page: http://www.elsevier.com/locate/ijpe
Channel promotions Risk aversion Conditional-Value-at-Risk (CVaR) Retailer rebates Customer rebates Nash equilibrium;
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- Gotoh, Jun-ya & Takano, Yuichi, 2007. "Newsvendor solutions via conditional value-at-risk minimization," European Journal of Operational Research, Elsevier, vol. 179(1), pages 80-96, May.
- Wang, Charles X., 2010. "The loss-averse newsvendor game," International Journal of Production Economics, Elsevier, vol. 124(2), pages 448-452, April.
- Louis Eeckhoudt & Christian Gollier & Harris Schlesinger, 1995. "The Risk-Averse (and Prudent) Newsboy," Management Science, INFORMS, vol. 41(5), pages 786-794, May.
- Yang, Shilei & Munson, Charles L. & Chen, Bintong, 2010. "Using MSRP to enhance the ability of rebates to control distribution channels," European Journal of Operational Research, Elsevier, vol. 205(1), pages 127-135, August.
- Kurata, Hisashi & Yue, Xiaohang, 2008. "Trade promotion mode choice and information sharing in fashion retail supply chains," International Journal of Production Economics, Elsevier, vol. 114(2), pages 507-519, August.
- Qiang Lu & Sridhar Moorthy, 2007. "Coupons Versus Rebates," Marketing Science, INFORMS, vol. 26(1), pages 67-82, 01-02.
- Yuxin Chen & Sridhar Moorthy & Z. John Zhang, 2005. "Research Note---Price Discrimination After the Purchase: Rebates as State-Dependent Discounts," Management Science, INFORMS, vol. 51(7), pages 1131-1140, July.
- Vipul Agrawal & Sridhar Seshadri, 2000. "Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem," Manufacturing & Service Operations Management, INFORMS, vol. 2(4), pages 410-423, July.
- Ahmed, Shabbir & Cakmak, Ulas & Shapiro, Alexander, 2007. "Coherent risk measures in inventory problems," European Journal of Operational Research, Elsevier, vol. 182(1), pages 226-238, October.
- Gerstner, Eitan & Hess, James D, 1991. "A Theory of Channel Price Promotions," American Economic Review, American Economic Association, vol. 81(4), pages 872-86, September.
- Arcelus, F.J. & Kumar, Satyendra & Srinivasan, G., 2007. "Pricing and rebate policies for the newsvendor problem in the presence of a stochastic redemption rate," International Journal of Production Economics, Elsevier, vol. 107(2), pages 467-482, June.
- Ault, Richard W, et al, 2000. "Rebates, Inventories, and Intertemporal Price Discrimination," Economic Inquiry, Western Economic Association International, vol. 38(4), pages 570-78, October.
- Eitan Gerstner & James D. Hess, 1995. "Pull Promotions and Channel Coordination," Marketing Science, INFORMS, vol. 14(1), pages 43-60.
- Scott M. Gilpatric, 2009. "Slippage in Rebate Programs and Present-Biased Preferences," Marketing Science, INFORMS, vol. 28(2), pages 229-238, 03-04.
- Maurice E. Schweitzer & Gérard P. Cachon, 2000. "Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence," Management Science, INFORMS, vol. 46(3), pages 404-420, March.
- Wang, Charles X. & Webster, Scott, 2009. "The loss-averse newsvendor problem," Omega, Elsevier, vol. 37(1), pages 93-105, February.
- Wong, W.K. & Qi, J. & Leung, S.Y.S., 2009. "Coordinating supply chains with sales rebate contracts and vendor-managed inventory," International Journal of Production Economics, Elsevier, vol. 120(1), pages 151-161, July.
- Meghan Busse & Jorge Silva-Risso & Florian Zettelmeyer, 2006. "$1,000 Cash Back: The Pass-Through of Auto Manufacturer Promotions," American Economic Review, American Economic Association, vol. 96(4), pages 1253-1270, September.
- Liang, Donghan & Li, Gang & Sun, Linyan & Chen, Yubao, 2013. "The role of rebates in the hybrid competition between a national brand and a private label with present-biased consumers," International Journal of Production Economics, Elsevier, vol. 145(1), pages 208-219.
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