Inventory Management with Stochastic Lead Times

Muthuraman, K and Seshadri, S and Wu, Q (2015) Inventory Management with Stochastic Lead Times. Mathematics of Operations Research, 40 (2). pp. 302-327.

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Abstract

This article analyzes a continuous time back-ordered inventory system with stochastic demand and stochastic delivery lags for placed orders. This problem in general has an infinite dimensional state space and is hence intractable. We first obtain the set of minimal conditions for reducing such a system's state space to one dimension and show how this reduction is done. Next, by modeling demand as a diffusion process, we reformulate the inventory control problem as an impulse control problem. We simplify the impulse control problem to a Quasi-Variation Inequality (QVI). Based on the QVI formulation, we obtain the optimality of the (s, S) policy and the limiting distribution of the inventory level. We also obtain the long run average cost of such an inventory system. Finally, we provide a method to solve the QVI formulation. Using a set of computational experiments, we show that significant losses are incurred in approximating a stochastic lead-time system with a fixed lead-time system, thereby highlighting the need for such stochastic lead-time models. We also provide insights into the dependence of this value loss on various problem parameters.

Affiliation: Indian School of Business
ISB Creiators:
ISB Creators
ORCiD
Seshadri, S
http://orcid.org/0000-0002-7917-5537
Item Type: Article
Uncontrolled Keywords: inventory control,impulse control,stochastic lead times, free boundary problem
Subjects: Applied Statistics and Computing
Operations Management
Depositing User: Veeramani R
Date Deposited: 11 Oct 2018 10:58
Last Modified: 11 Oct 2018 10:58
URI: http://eprints.exchange.isb.edu/id/eprint/623
Publisher URL: https://doi.org/10.1287/moor.2014.0671
Publisher OA policy: http://www.sherpa.ac.uk/romeo/issn/0364-765X/
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