Bounds and Asymptotics for Planning Critical Safety Stocks

Paul Glasserman
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Paul Glasserman: Columbia Business School, New York, New York

Operations Research, 1997, vol. 45, issue 2, 244-257

Abstract: We develop bounds and approximations for setting base-stock levels in production-inventory systems with limited production capacity. Our approximations become exact as inventories become critical , meaning either that the target service level is very high or the backorder penalty is very large. Our bounds apply even without this requirement. We consider both single-stage and multi-stage systems. For single-stage systems, we find tight bounds and asymptotically exact approximations for optimal base-stock levels; for multistage systems, our results give partial characterizations of the optimal levels. Part of our analysis is a precise connection, in the critical regime, between a multistage system and an associated single-stage system consisting solely of the bottleneck facility.

Keywords: inventory/production; service level approximations; probability applications; rare events (search for similar items in EconPapers)
Date: 1997
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