Modified base-stock policies for continuous-review, lost-sales inventory models with Poisson demand and a fixed lead time

2013 ◽  
Vol 143 (2) ◽  
pp. 379-384 ◽  
Author(s):  
Søren Glud Johansen
Keyword(s):  
Lead Time ◽  
Base Stock ◽  
Lost Sales ◽  
Inventory Models ◽  
Continuous Review ◽  
Poisson Demand ◽  
Base Stock Policies

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.

Multi-Location Inventory Model Considering Bidirectional and Unidirectional Transshipments Simultaneously

2013 ◽  
Vol 694-697 ◽  
pp. 2742-2745
Author(s):  
Jin Hong Zhong ◽  
Yun Zhou
Keyword(s):  
Process Model ◽  
Approximate Calculation ◽  
Inventory Model ◽  
Inventory System ◽  
Death Process ◽  
Birth And Death Process ◽  
Inventory Models ◽  
Continuous Review ◽  
Poisson Demand ◽  
Queue Theory

Abstract. A cross-regional multi-site inventory system with independent Poisson demand and continuous review (S-1,S) policy, in which there is bidirectional transshipment between the locations at the same area, and unidirectional transshipment between the locations at the different area. According to the M/G/S/S queue theory, birth and death process model and approximate calculation policy, we established inventory models respectively for the loss sales case and backorder case, and designed corresponding procedures to solve them. Finally, we verify the effectiveness of proposed models and methods by means of a lot of contrast experiments.

Understanding the Performance of Capped Base-Stock Policies in Lost-Sales Inventory Models

2020 ◽  
Author(s):  
Linwei Xin
Keyword(s):  
Base Stock ◽  
Superior Performance ◽  
Lead Times ◽  
Lost Sales ◽  
Index Policy ◽  
Stock Level ◽  
New Family ◽  
Base Stock Policy ◽  
Stock Policy ◽  
Base Stock Policies

Single-sourcing lost-sales inventory systems with lead times are notoriously difficult to optimize. In this paper, we propose a new family of capped base-stock policies and provide a new perspective on constructing a practical hybrid policy combining two well-known heuristics: base-stock and constant-order policies. Each capped base-stock policy is associated with two parameters: a base-stock level and an order cap. We prove that for any fixed order cap, the capped base-stock policy converges exponentially fast in the base-stock level to a constant-order policy, providing a theoretical foundation for a phenomenon by which a capped dual-index policy converges numerically to a tailored base-surge policy recently observed in other work in a different but related dual-sourcing inventory model. As a consequence, there exists a sequence of capped base-stock policies that are asymptotically optimal as the lead time grows. We also numerically demonstrate its superior performance in general (including small lead times) by comparing it with otherwell-known heuristics.

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