TECHNICAL NOTE---Optimal Control of an Assembly System with Multiple Stages and Multiple Demand Classes

Saif Benjaafar (), Mohsen ElHafsi (), Chung-Yee Lee () and Weihua Zhou ()
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Saif Benjaafar: Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455
Mohsen ElHafsi: The A. Gary Anderson Graduate School of Management, University of California, Riverside, California 92521
Chung-Yee Lee: Department of Industrial Engineering and Logistics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Weihua Zhou: Department of Management Science and Engineering, Zhejiang University, Hangzhou, China

Operations Research, 2011, vol. 59, issue 2, 522-529

Abstract: We consider an assembly system with multiple stages, multiple items, and multiple customer classes. The system consists of m production facilities, each producing a different item. Items are produced in variable batch sizes, one batch at a time, with exponentially distributed batch production times. Demand from each class takes place continuously over time according to a compound Poisson process. At each decision epoch, we must determine whether or not to produce an item and, should demand from a particular class arise, whether or not to satisfy it from existing inventory, if any is available. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. In contrast to systems with exogenous and deterministic production lead times, we show that the optimal production policy for each item is a state-dependent base-stock policy with the base-stock level nonincreasing in the inventory level of items that are downstream and nondecreasing in the inventory level of all other items. For inventory allocation, we show that the optimal policy is a multilevel state-dependent rationing policy with the rationing level for each demand class nonincreasing in the inventory level of all nonend items. We also show how the optimal control problem can be reformulated in terms of echelon inventory and how the essential features of the optimal policy can be reinterpreted in terms of echelon inventory.

Keywords: production and inventory control; systems with multiple echelons; inventory rationing; Markov decision processes; make-to-stock queues (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (9)

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