1.79-approximation algorithms for continuous review single-sourcing lost-sales and dual-sourcing inventory models
63 Pages Posted: 20 Nov 2019 Last revised: 14 May 2020
Date Written: April 29, 2020
Stochastic inventory systems with lead times are often notoriously challenging to optimize, including single-sourcing lost-sales and dual-sourcing inventory systems. Recent numerical experiments have suggested that capped policies demonstrate superior performance compared with existing heuristics. However, the superior performance lacks of a theoretical foundation and why such policies generally perform so well remains a major open question.
In this paper, we provide a theoretical foundation for this phenomenon in two classical inventory models with lead times. First, in a continuous review lost-sales inventory model with lead times and Poisson demand, we prove that a so-called capped base-stock policy has a worst-case performance guarantee of 1.79 by conducting an asymptotic analysis under large penalty cost and lead time following Reiman (2004). Second, we extend the analysis to a more complex continuous review dual-sourcing inventory model with general lead times and Poisson demand, and also prove that a so-called capped dual-index policy has a worst-case performance guarantee of 1.79 under large lead time and ordering cost differences. Our results provide a deeper understanding of the superior numerical performance of capped policies, and presents a new approach to proving worst-case performance guarantees of simple policies in notoriously hard inventory problems.
Keywords: inventory, continuous review, lost-sales, dual-sourcing, lead time, capped base-stock policy, capped dual-index policy, approximation algorithm, asymptotic analysis
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