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A Decomposition Approach for a Class of Capacitated Serial Systems

IOMS-OM Group, Stern School of Business, New York University, New York, New York 10012
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853
gjanakir{at}stern.nyu.edu
jam61{at}cornell.edu

We study a class of two-echelon serial systems with identical ordering/production capacities or limits for both echelons. Demands are assumed to be integer valued. For the case where the lead time to the upstream echelon is one period, the optimality of state-dependent modified echelon base-stock policies is proved using a decomposition approach. For the case where the upstream lead time is two periods, we introduce a new class of policies called "two-tier base-stock policies," and prove their optimality. Some insight about the inventory control problem in N echelon serial systems with identical capacities at all stages and arbitrary lead times everywhere is also provided. We argue that a generalization of two-tier base-stock policies, which we call "multitier base-stock policies," are optimal for these systems; we also provide a bound on the number of parameters required to specify the optimal policy.

Subject classifications: inventory/production; policy; optimal policies; Markov modulated demands; lead times; planning horizon; finite; infinite; discounted.
History: Received December 2003; revision received June 2008; accepted October 2008.