A serial inventory system with lead-time-dependent backordering: A reduced-state approximation

Date
2022-05-04
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
IISE Transactions
Print ISSN
2472-5854
Electronic ISSN
2472-5862
Publisher
Taylor & Francis Inc.
Volume
55
Issue
3
Pages
259 - 270
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Series
Abstract

We study a serial inventory system where the external customers may have a maximum time that they would be willing to wait for delivery in cases of stock-out and the demand would be lost if the remaining delivery lead time of the next available item is longer. This lead-time-dependent backordering behavior subsumes the models of partial backordering regardless of the wait that a customer would experience. In the inventory literature, this behavior has only been analyzed in single-location settings. We study this behavior in a multi-stage setting. We consider continuous review (S−1,S) policies at all stages facing external Poisson demands. Using the method of supplementary variables, we define the stochastic process representing the inventory system and obtain the expressions for the operating characteristics of the inventory system. Based on the solution structures for the special cases, we propose an approximate solution which rests on replacing the state-dependent purchasing decision of the customer with an averaged-out purchase probability computed using only the age of the oldest item. An extensive numerical study indicates that the proposed approximation performs very well. Our numerical study provides additional insights about the sensitivity and allocation of stock levels across stages.

Course
Other identifiers
Book Title
Keywords
Inventory theory and control, Multi-echelon inventory, Lead-time-dependent backordering, Method of supplementary variables
Citation
Published Version (Please cite this version)