Publication Type

Journal Article

Version

acceptedVersion

Publication Date

6-2017

Abstract

We consider a single-item continuous-review (r, q) inventory system with a renewal demand process and independent, identically distributed stochastic lead times. Using a stationary marked-point process technique and a heavy-traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent. We also establish closed-form expressions for the optimal policy parameters and system cost in heavy-traffic limit, the first of their kind, to our knowledge. These expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts. For example, the results demonstrate that the well-known square-root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment. We further extend the study to periodic-review (S, T) systems with constant lead times.

Keywords

inventory system, (r, q) policy, stochastic leadtime, asymptotic analysis, heavy traffic limit.

Discipline

Operations and Supply Chain Management

Research Areas

Operations Management

Publication

Operations Research

Volume

65

Issue

5

First Page

1414

Last Page

1428

ISSN

0030-364X

Identifier

10.1287/opre.2017.1623

Publisher

INFORMS

Embargo Period

6-11-2018

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1287/opre.2017.1623

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