Bounds and Asymptotics for Planning Critical Safety Stocks
Operations Research · 1997 · Volume 45 · Issue 2
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
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