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A production/inventory system consisting of multiple stages in series with arbitrary processing times and with intermediate buffer inventories is considered. There is a finished product warehouse at which demand occurs for the finished products according to a compound Poisson process. Inventory levels of both intermediate and finished stocks are controlled by a continuous-review (R, r) inventory control policy. Production at a stage continues until the inventory level in the downstream buffer reaches its target value R. Once the inventory level drops to its reorder level r, the stage undergoes a set-up and production resumes. An approximation method is developed to obtain the steady-state performance measures of the system. Numerical examples are presented to show the accuracy of the proposed method.
Altıok et al. (1995) studied this question.