Inventory Management with Stochastic Lead Times

34 Pages Posted: 11 Dec 2013  

Kumar Muthuraman

University of Texas at Austin - McCombs School of Business

Sridhar Seshadri

Indian School of Business

Qi Wu

Case Western Reserve University, Weatherhead School of Management

Date Written: December 10, 2013

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.

Keywords: Inventory control, lead times, stochastic lead times, free boundary

JEL Classification: E22

Suggested Citation

Muthuraman, Kumar and Seshadri, Sridhar and Wu, Qi, Inventory Management with Stochastic Lead Times (December 10, 2013). Available at SSRN: https://ssrn.com/abstract=2366053 or http://dx.doi.org/10.2139/ssrn.2366053

Kumar Muthuraman

University of Texas at Austin - McCombs School of Business ( email )

Austin, TX 78712
United States

Sridhar Seshadri

Indian School of Business ( email )

Hyderabad, Gachibowli 500 019
India

Qi Wu (Contact Author)

Case Western Reserve University, Weatherhead School of Management ( email )

10900 Euclid Ave.
Cleveland, OH 44106
United States

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