Int. J. Production Economics 106 (2007) 523–531 Effective control policies for stochastic inventory systems with a minimum order quantity and linear costs $ Bin Zhou, Yao Zhao à , Michael N. Katehakis Department of Management Science and Information Systems, Rutgers University, the State University of New Jersey, 180 University Avenue, Newark, NJ 07102, USA Received 11 November 2005; accepted 27 June 2006 Available online 1 November 2006 Abstract We consider a model of single-item periodic-review inventory system with stochastic demand, linear ordering cost, where in each time period, the system must order either none or at least as much as a minimum order quantity (MOQ). Optimal inventory policies for such a system are typically too complicated to implement in practice. In fact, the ðs; SÞ type of policies are often utilized in the real world. We study the performance of a simple heuristic policy that is easily implementable because it is specified by only two parameters ðs; tÞ. We develop an algorithm to compute the optimal values for these parameters in the infinite time horizon under the average cost criterion. Through an extensive numerical study, we demonstrate that the best ðs; tÞ heuristic policy has performance close to that of the optimal policies when the coefficient of variation of the demand distribution is not very small. Furthermore, the best ðs; tÞ policy always outperforms the best feasible ðs; SÞ policies and on average the percentage differences are significant. Finally, we study the impact of MOQ on system performance. r 2006 Elsevier B.V. All rights reserved. Keywords: Minimum order quantity; Stochastic inventory systems; Heuristic policy; Multiple periods 1. Introduction Economies of scale are important concerns in many industries. This is especially true for compa- nies that manufacture and/or distribute pharmaceu- tical, apparel, consumer packaged goods or chemical products. Most companies use one of the following three ways to achieve the economies of scale in production and distribution: charging fixed ordering cost, or requiring batch orders, e.g., full truck load, or setting minimum order quantity (MOQ) for their customers. MOQ is widely used in practice. A celebrated example of MOQ is the fashion sport ski-wear manufacturer and distributor: Sport Obermeyer (Hammond and Raman, 1996). While the produc- tion base of Sport Obermeyer in Hong Kong sets a MOQ of 600 garments per order, its production base in China requires 1200 garments. The MOQ constraints can be applied to a particular item or a group of items, such as all colors of a parti- cular style. We refer the reader to Hammond and Raman (1996) for more detailed descriptions of the ARTICLE IN PRESS www.elsevier.com/locate/ijpe 0925-5273/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2006.06.020 $ Research supported in part by a Faculty Research Grant from Rutgers Business School–Newark and New Brunswick. à Corresponding author. Tel.: +1 973 353 5003. E-mail address: yaozhao@andromeda.rutgers.edu (Y. Zhao).