Replenishing an inventory system permitting lost sales under Poisson demand and short lead times: Explicit performance and an efficient algorithm

2019 ◽  
Vol 137 ◽  
pp. 105998 ◽  
Author(s):  
Avi Herbon
Keyword(s):  
Efficient Algorithm ◽  
Inventory System ◽  
Lead Times ◽  
Lost Sales ◽  
Poisson Demand

1.79-Approximation Algorithms for Continuous Review Single-Sourcing Lost-Sales and Dual-Sourcing Inventory Models

2021 ◽  
Author(s):  
Linwei Xin
Keyword(s):  
Lead Time ◽  
Superior Performance ◽  
Lead Times ◽  
Lost Sales ◽  
Inventory Models ◽  
Worst Case ◽  
Dual Sourcing ◽  
Continuous Review ◽  
Poisson Demand ◽  
Single Sourcing

Stochastic inventory systems with lead times are often challenging to optimize, including single-sourcing lost-sales and dual-sourcing systems. Recent numerical results suggest that capped policies demonstrate superior performance over existing heuristics. However, the superior performance lacks a theoretical foundation. In “1.79-Approximation Algorithms for Continuous Review Single-Sourcing Lost-Sales and Dual-Sourcing Inventory Models,” the author provides a theoretical foundation for this phenomenon in two classical inventory models. First, in a continuous review lost-sales model with lead times and Poisson demand, he proves that a capped base-stock policy has a worst-case performance guarantee of 1.79 by conducting an asymptotic analysis under a large penalty cost and lead time. Second, in a more complex continuous review dual-sourcing model with general lead times and Poisson demand, he proves that a similar capped dual-index policy has a worst-case performance guarantee of 1.79 under large lead time and ordering cost differences. The results provide a deeper understanding of the superior numerical performance of capped policies and present a new approach to proving worst-case performance guarantees of simple policies in hard inventory problems.

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