Analysis of supply contracts with quantity flexibility.pdf

European Journal of Operational Research 196 (2009) 526–533Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier .com/locate /e jorProduction, Manufacturing and Logistics Analysis of supply contracts with quantity flexibility Zhaotong Lian a,*, Abhijit Deshmukh b a Faculty of Business Administration, University of Macau, Macau SAR, China bDepartment of Industrial and Systems Engineering, Texas AM University, TX 77843-3131, USA a r t i c l e i n f oArticle history: Received 7 February 2005 Accepted 5 February 2008 Available online 15 April 2008 Keywords: Supply contract Inventory Rolling horizon Quantity flexibility Dynamic programming0377-2217/$ - see front matter  2008 Published by doi:10.1016/j.ejor.2008.02.043 * Corresponding author. Tel.: +853 fax: E-mail address: lianzt@umac.mo (Z. Lian).a b s t r a c t This paper explores a class of supply contracts under which a buyer receives discounts for committing to purchases in advance. The further in advance the commitment is made, the larger the discount. As time rolls forward, the buyer can increase the order quantities for future periods of the rolling horizon based on updated demand forecast information and inventory status. However, the buyer pays a higher per-unit cost for the incremental units. Such contracts are used by automobile and contract manufacturers, and are quite common in fuel oil and natural gas delivery markets. We develop a finite-horizon dynamic pro- gramming model to characterize the structure of the optimal replenishment strategy for the buyer. We present heuristic approaches to calculate the order volume in each period of the rolling horizon. Finally, we numerically evaluate the heuristic approaches and draw some managerial insights based on the findings.  2008 Published by Elsevier B.V.1. Introduction This paper studies ordering policies for a specific supply con- tract model in which a buyer receives discounts for committ