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Optimal Policy for a Multiechelon Inventory System with Batch Ordering and Fixed Replenishment Intervals

Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109
Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
xchao{at}umich.edu
zhoux{at}se.cuhk.edu.hk

In many production/distribution systems, materials flow in fixed lot sizes (e.g., in full truckloads or full containers) and under regular schedules (e.g., delivery every week). In this paper, we study a multiechelon serial system with batch ordering and fixed replenishment intervals. We derive the optimal inventory control policy, provide a distribution-function solution for its optimal control parameters, and present an efficient algorithm for computing those parameters. Further, we show that the optimal expected system cost is minimized when the ordering times for all stages are synchronized. In contrast to the known approach in the literature that develops a lower bound for the average cost of a given period for the classical serial system, we develop a lower bound for the average total cost over an appropriately defined cycle and then construct a policy that reaches the lower bound. We also discuss its extension to the nonlinear shortage cost case (i.e., the nonlinear cost case). This paper generalizes several recent results on the analysis of multiechelon systems.

Subject classifications: multiechelon system; optimal policy; synchronized ordering; nonlinear shortage costs; fixed replenishment intervals; batch ordering.
History: Received September 2005; revision received February 2008; accepted May 2008.