A Decomposition Approach for a Class of Capacitated Serial Systems

• Published in: Operations research Vol. 57; no. 6; pp. 1384 - 1393
• Main Authors: Janakiraman, Ganesh, Muckstadt, John A
• Format: Journal Article
• Language: English
• Published: Hanover, MD INFORMS 01.11.2009; Institute for Operations Research and the Management Sciences
• Subjects: Analysis; Applied sciences; Cost allocation methods; Demand; discounted; Exact sciences and technology; finite; infinite; Integers; Inventories; Inventory control; Inventory control, production control. Distribution; inventory/production; lead times; Logistics; Marketing strategies; Markov analysis; Markov modulated demands; Mathematical vectors; Operational research and scientific management; Operational research. Management science; optimal policies; Optimal policy; Pipelines; planning horizon; policy; Retail stores; Serials control; Shipments; Studies; Unit costs; United States; Markov process; Discount; planning horizon: finite, infinite, discounted; Optimal policy; lead times; Production management; Finite horizon; inventory/production: policy, optimal policies; Ordering; Base stock; Setup time; Inventory control; Capacity constraint; Markov modulated demands; Production capacity; Infinite horizon; Planning; State dependence
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1080.0680

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.