Production, Manufacturing and Logistics Optimal selection of retailers for a manufacturing vendor in a vendor managed inventory system Yugang Yu a,b , Zhaofu Hong a,d,⇑ , Linda L. Zhang c , Liang Liang b , Chengbin Chu d a School of Management, Lanzhou University, Lanzhou, PR China b School of Management, University of Science and Technology of China, Hefei, PR China c IESEG School of Management (LEM-CNRS), Catholic University of Lille, Lille, France d Laboratoire Génie Industriel, Ecole Centrale Paris, France article info Article history: Received 17 May 2011 Accepted 25 September 2012 Available online xxxx Keywords: Supply chain management Vendor managed inventory Retailer selection Stackelberg game theory Hybrid algorithm abstract A Vendor Managed Inventory (VMI) system consists of a manufacturing vendor and a number of retailers. In such a system, it is essential for the vendor to optimally determine retailer selection and other related decisions, such as the product’s replenishment cycle time and the wholesale price, in order to maximize his profit. Meanwhile, each retailer’s decisions on her willingness to enter the system and retail price are simultaneously considered in the retailer selection process. However, the above interactive decision mak- ing is complex and the available studies on interactive retailer selection are scarce. In this study, we for- mulate the retailer selection problem as a Stackelberg game model to help the manufacturer, as a vendor, optimally select his retailers to form a VMI system. This model is non-linear, mixed-integer, game-theo- retic, and analytically intractable. Therefore, we further develop a hybrid algorithm for effectively and efficiently solving the developed model. The hybrid algorithm combines dynamic programming (DP), genetic algorithm (GA) and analytical methods. As demonstrated by our numerical studies, the optimal retailer selection can increase the manufacturer’s profit by up to 90% and the selected retailers’ profits significantly compared to non-selection strategy. The proposed hybrid algorithm can solve the model within a minute for a problem with 100 candidate retailers, whereas a pure GA has to take more than 1 h to solve a small sized problem of 20 candidate retailers achieving an objective value no worse than that obtained by the hybrid algorithm. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction VMI (Vendor Managed Inventory) is a popular inventory man- agement strategy that allows a vendor to access his retailers’ sales data and manage his retailers’ inventory levels. The implementa- tion of VMI is beneficial for both the vendor and his retailers (Sahin and Robinson, 2002; Waller et al., 1999) since the vendor can man- age the inventory without information distortion, and coordinate the product replenishment of multiple retailers. Such coordination enables the vendor to adopt a common replenishment cycle for all retailers to reduce inventory level and cost. The successful applica- tions of VMI implementation have been widely reported. For instances, the VMI-type partnership between Procter & Gamble (P&G) and Wal-Mart dramatically improves P&G’s on-time deliver- ies and Wal-Mart’s sales by 20–25% and the inventory turnover by 30% (Yu et al., 2009a). Barilla made an inventory reduction by nearly 50% at its retailers through VMI in 1988 (Hammond, 2003). Dell and HP also operate efficient supply chains through VMI to reduce inventory level and cost (Tyan and Wee, 2003). Selecting retailers suggests itself to be a fundamental decision process for the vendor in a VMI system; the vendor has to decide whether to accept a retailer or not, and vice versa. This is especially true for manufacturers with limited production capacity. As the vendor, the manufacturer has to select retailers, and determines the total demand of the selected retailers within his production capacity. Even if the manufacturer has certain redundant capacity, involving more retailers for increasing capacity utilization may not be an acceptable option. This is because the additional retailers may lead to high delivery costs, inventory costs, etc. Moreover, selecting retailers often entails an interactive game process. When the manufacturer decides to add a new retailer, he needs to take into account changes on his other decisions, e.g., the wholesale price. Meanwhile, all retailers respond to the manufacturer’s decision changes, and may decide to quit the VMI system. Due to the complexities involved, decision making in the above interactive selection process is likely to be difficult. Consequently, 0377-2217/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ejor.2012.09.044 ⇑ Corresponding author at: Laboratoire Génie Industriel, Ecole Centrale Paris, France. Tel.: +33 (0)1 41 13 18 15. E-mail address: hongms06@gmail.com (Z. Hong). European Journal of Operational Research xxx (2012) xxx–xxx Contents lists available at SciVerse ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Please cite this article in press as: Yu, Y., et al. Optimal selection of retailers for a manufacturing vendor in a vendor managed inventory system. European Journal of Operational Research (2012), http://dx.doi.org/10.1016/j.ejor.2012.09.044