We derive efficient and highly accurate approximations for the customer waiting-time distributions experienced in stochastic economic lot scheduling systems (SELSPs) that are governed by general base-stock policies under a cyclic or more general periodic item sequence. SELSPs involve settings where several items need to be produced in a common facility with limited capacity, under significant uncertainty regarding demands, unit production times, setup times, or combinations thereof. Under a base-stock policy one continues production of a given item until a specific target level is reached; the different items are produced in a given periodic sequence, possibly with idle times inserted between the completion of an item's production batch and the setup of the next item. We also demonstrate how base-stock levels can be specified efficiently to guarantee any prescribed fill rate within a specific service window or distribution of service windows.
Federgruen, Awi, and Ziv Katalan. "Customer waiting-time distributions under base-stock policies in single-facility multi-item production systems." Naval Research Logistics 43, no. 4 (1996): 533-548.
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