O.R. Applications Approximate analysis and optimization of batch ordering policies in capacitated supply chains Abdullah Karaman * , Tayfur Altiok Industrial and Systems Engineering, Rutgers University, Piscataway, NJ 08854, USA Received 11 April 2007; accepted 9 October 2007 Available online 18 October 2007 Abstract Devising manufacturing/distribution strategies for supply chains and determining their parameter values have been challenging prob- lems. Linking production management to stock keeping processes improves the planning of the supply chain activities, including material management, culminating in improved customer service levels. In this study, we investigate a multi-echelon supply chain consisting of a supplier, a plant, a distribution center and a retailer. Material flow between stages is driven by reorder point/order quantity inventory control policies. We develop a model to analyze supply chain behavior using some key performance metrics such as the time averages of inventory and backorder levels, as well as customer service levels at each echelon. The model is validated against simulation, yielding good agreement of robust performance metrics. The metrics are then used within an optimization framework to design the supply chain so as to minimize expected total system costs. The outcome of the optimization framework specifies how to move inventory throughout the supply chain and how to set inventory control parameters, i.e., reorder levels and replenishment batch sizes. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Supply chains; Batch ordering policies; Finite production rate; Stochastic lead-times 1. Introduction Improving decision-making practices in a supply chain is a major source of competitive advantage in today’s uncertain business environments. For years, different echelons in a supply chain have operated almost independently. However, there is strong evidence of success in supply chain performance in cases with high coordination among echelons. Efforts to link production management to various stock keeping processes result in better planning of the supply chain activities, better management of the materials, culminating in improved customer service levels and lower inventories. A typical supply chain has a topology consisting of a number of stores where customer demand occurs, distribution centers feeding stores and other distribution centers, manufacturing plants supplying distribution centers, as well as ven- dors supplying raw materials to plants. Clearly, a concerted activity is needed across all the nodes for effective material flow in the supply chain. Controlling the material flow in a cost-effective manner has been a major challenge in practice. It depends on how well the demand from a customer or the next stage is forecasted at all levels and integrated into decision and control mechanisms. Inventory control policies are used for this purpose to achieve replenishment at the right quantity and the right time at each level. In this paper, we study a multi-echelon supply chain and its operational rules. The supply chain under consideration consists of a supplier, a plant, a distribution center (DC), and a retailer. Material flow between stages is achieved by reorder point/batch size inventory control policies. The production rate at the plant is finite and transportation times between 0377-2217/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2007.10.018 * Corresponding author. Tel.: +1 732 216 4630. E-mail addresses: akaraman@eden.rutgers.edu (A. Karaman), altiok@rci.rutgers.edu (T. Altiok). www.elsevier.com/locate/ejor Available online at www.sciencedirect.com European Journal of Operational Research 193 (2009) 222–237