On the use of phase-type distributions for inventory management with supply disruptions
Author
Balcıoǧlu, B.
Gürler, Ü.
Date
2011Source Title
Applied Stochastic Models in Business and Industry
Print ISSN
1524-1904
Electronic ISSN
1526-4025
Publisher
John Wiley & Sons
Volume
27
Issue
6
Pages
660 - 675
Language
English
Type
ArticleItem Usage Stats
126
views
views
98
downloads
downloads
Abstract
Maintaining the continuity of operations becomes increasingly important for systems that are subject to disruptions due to various reasons. In this paper, we study an inventory system operating under a (q, r) policy, where the supply can become inaccessible for random durations. The availability of the supply is modeled by assuming a single supplier that goes through ON and OFF periods of stochastic duration, both of which are modeled by phase-type distributions (PTD). We provide two alternative representations of the state transition probabilities of the system, one with integral and the other employing Kolmogorov differential equations. We then use an efficient formulation for the analytical model that gives the optimal policy parameters and the long-run average cost. An extensive numerical study is conducted, which shows that OFF time characteristics have a bigger impact on optimal policy parameters. The ON time characteristics are also important for critical goods if disasters can happen.