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

See all articles by Linwei Xin

Linwei Xin

University of Chicago - Booth School of Business

Date Written: April 29, 2020

Abstract

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

Suggested Citation

Xin, Linwei, 1.79-approximation algorithms for continuous review single-sourcing lost-sales and dual-sourcing inventory models (April 29, 2020). Available at SSRN: https://ssrn.com/abstract=3484315 or http://dx.doi.org/10.2139/ssrn.3484315

Linwei Xin (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
84
Abstract Views
551
rank
325,731
PlumX Metrics