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Approximations for the single-product production-inventory problem with compound Poisson demand and service-level constraints. (English) Zbl 0532.90043

Summary: We consider a production-inventory problem in which the production rate can be continuously controlled in order to cope with random fluctuations in the demand. The demand process for a single product is a compound Poisson process. Excess demand is backlogged. Two production rates are available and the inventory level is continuously controlled by a switch- over rule characterized by two critical numbers. In accordance with common practice, we consider service measures such as the average number of stockouts per unit time and the fraction of demand to be met directly from stock on hand. The purpose of the paper is to device practically useful approximations for the switch-over levels of the control rule such that a pre-specified value of the service level is achieved.

MSC:

90B30 Production models
90B05 Inventory, storage, reservoirs
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