OPERATIONS RESEARCH Vol. 00, No. 0, Xxxxx 0000, pp. 000–000 issn 0030-364X | eissn 1526-5463 | 00 | 0000 | 0001 INFORMS doi 10.1287/xxxx.0000.0000 c  0000 INFORMS Approximation Algorithms for Capacitated Stochastic Inventory Control Models Retsef Levi Sloan School of Management, MIT, Cambridge, MA, 02139., retsef@mit.edu, Robin O. Roundy School of ORIE, Cornell University, Ithaca, NY 14853, robin@orie.cornell.edu, David B. Shmoys School of ORIE and Dept. of Computer Science, Cornell University, Ithaca, NY 14853., shmoys@cs.cornell.edu, Van Anh Truong School of ORIE, Cornell University, Ithaca, NY 14853, truong@orie.cornell.edu, We develop the first algorithmic approach to compute provably good ordering policies for a multi-period, capacitated, stochastic inventory system facing stochastic non-stationary and correlated demands that evolve over time. Our approach is computationally efficient and guaranteed to produce a policy with total expected cost no more than twice that of an optimal policy. As part of our computational approach, we propose a novel scheme to account for backlogging costs in a capacitated, multi-period environment. Our cost-accounting scheme, called the forced marginal backlogging cost-accounting scheme, is significantly different from the period-by-period accounting approach to backlogging costs used in dynamic programming; it captures the long-term impact of a decision on system performance in the presence of capacity constrains. In the likely event that the per-unit order costs are large compared to the holding and backlogging costs, a transformation of cost parameters yields a significantly improved guarantee. We also introduce new semi-myopic policies based on our new cost-accounting scheme to derive bounds on the optimal base-stock levels. We show that these bounds can be used to effectively improve any policy. Finally, empirical evidence is presented that indicates that the typical performance of this approach is significantly stronger than these worst-case guarantees. Subject classifications : Stochastic Inventory Control; Heuristics; Approximation Algorithms. Area of review : Supply Chain Management. History : Submitted August 2005. Revised July 2006, December 2006, May 2007, September 2007, September 2007. 1. Introduction The periodic-review, capacitated inventory control problem for systems facing stochastic, non- stationary (time-dependent) demands that are correlated and evolve over time is an important classical problem that is widely recognized to be computationally challenging. We develop a new algorithmic approach to compute the order quantity for such a system. We build on the work of Levi et al. (2007), who used a marginal holding cost accounting scheme and cost balancing techniques to derive the first policies with worst-case performance guarantees for uncapacitated models. In this paper, we introduce a novel marginal backlogging cost accounting scheme that, in combination with their techniques, lead to analogous results for the much harder capacitated model. We believe that our new cost accounting scheme will have applications in many other settings. Our algorithm is guaranteed to compute a solution of total expected cost no more than twice that of an optimal policy for any instance of the problem. The algorithm is computationally efficient and implementable without having to enumerate exhaustively future scenarios and corresponding future decisions. In particular, the decision made in the current period is unaffected by any future decision. Thus, it can be implemented efficiently even in the presence of complex demand structures. 1