Production, Manufacturing and Logistics A serial inventory system with supplier selection and order quantity allocation Abraham Mendoza a , José A. Ventura b, * a Department of Industrial Engineering, Universidad Panamericana, Guadalajara, Jalisco 45010, Mexico b Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, University Park, PA 16802, USA article info Article history: Received 11 August 2008 Accepted 23 June 2010 Available online 1 July 2010 Keywords: Supply chain management Supplier selection Order quantity allocation Multi-echelon inventory system Power-of-two policy abstract Given the prevalence of both supplier selection and inventory control problems in supply chain manage- ment, this article addresses these problems simultaneously by developing a mathematical model for a serial system. This model determines an optimal inventory policy that coordinates the transfer of items between consecutive stages of the system while properly allocating orders to selected suppliers in stage 1. In addition, a lower bound on the minimum total cost per time unit is obtained and a 98% effective power-of-two (POT) inventory policy is derived for the system under consideration. This POT algorithm is advantageous since it is simple to compute and yields near optimal solutions. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Many factors in today’s global market have forced companies to gain a competitive advantage by focusing attention to their entire sup- ply chain. Of the various activities involved in supply chain management, purchasing is one of the most strategic because it provides oppor- tunities to reduce costs and consequently increase profits. An essential task within the purchasing function is supplier selection. Proper supplier selection is important for companies given that the cost of raw materials and component parts represents the largest percentage of the total product cost in many industries. For instance, in high technology firms, purchased materials and services account for up to 80% of the total product cost (Weber et al., 1991). Inventory is recognized as one of the four major drivers in a supply chain, according to Chopra and Meindl (2007). High inventory levels increase the responsiveness of the supply chain but decrease its cost efficiency because of the cost of holding inventory. Hence, a relevant problem in supply chain management is to determine the appropriate levels of inventory at the various stages involved in the system. Gi- ven the prevalence of both supplier selection and inventory control problems in supply chain management, this article addresses these prob- lems simultaneously by analyzing a serial supply chain system that effectively ties these interrelated issues together by incorporating the supplier selection in a multi-stage context. To the authors’ knowledge, existing literature does not provide any model similar to the inte- grated mathematical model proposed in this article. In this research, the supplier selection process is assumed to occur in stage 1 of a serial supply chain system. An item is procured from a set of selected suppliers. Capacity, quality, setup cost, and unit price are considered as criteria for supplier selection. This item is processed and assembled into a final product as it flows through the various stages of the supply chain until it reaches the end customer. For the inventory control problem, a stationary inventory policy is developed to determine the inventory level held at each stage of the supply chain system to replenish subsequent stages accordingly. The objective of the proposed integrated model is to coordinate the replenish- ment decisions with the inventory at the various stages to minimize the total cost per time unit associated with the entire supply chain system while properly selecting the set of suppliers which best meets capacity limits and quality requirements. Although orders to each supplier can be placed with different frequencies, order quantities in stage 1 are restricted to be constant to insure that the resulting inven- tory policy is nested and stationary (Love, 1972; Muckstadt and Roundy, 1993). Although both researchers and practitioners would argue that the supplier selection process is driven primarily by replenishment cost, quality, and capacity, our model shows that in some cases lot sizing decisions, not only at the supply stage, but also at the remaining stages of the supply chain, may influence the final selection of suppliers. In an era where purchasing managers are responsible for hundreds or thousands of component parts, the proposed model 0377-2217/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2010.06.034 * Corresponding author. Tel.: +1 814 865 3841; fax: +1 814 863 4745. E-mail address: jav1@psu.edu (J.A. Ventura). European Journal of Operational Research 207 (2010) 1304–1315 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor