Closed-Form Approximations for Optimal (r,q) and (S,T) Policies in a Parallel Processing Environment

49 Pages Posted: 12 Jan 2015 Last revised: 7 Aug 2016

See all articles by Marcus Ang

Marcus Ang

Singapore Management University - Lee Kong Chian School of Business

Karl Sigman

Columbia University

Jing-Sheng Jeannette Song

Duke University - Fuqua School of Business

Hanqin Zhang

National University of Singapore (NUS) - NUS Business School

Date Written: August 2, 2016

Abstract

We consider a single-item continuous-review (r,q) inventory system with a renewal demand process and i.i.d. stochastic leadtimes. 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 leadtimes.

Keywords: inventory system, (r,q) policy, stochastic leadtime, asymptotic analysis, heavy-traffic limit

JEL Classification: C69

Suggested Citation

Ang, Marcus and Sigman, Karl and Song, Jing-Sheng Jeannette and Zhang, Hanqin, Closed-Form Approximations for Optimal (r,q) and (S,T) Policies in a Parallel Processing Environment (August 2, 2016). Available at SSRN: https://ssrn.com/abstract=2548064 or http://dx.doi.org/10.2139/ssrn.2548064

Marcus Ang (Contact Author)

Singapore Management University - Lee Kong Chian School of Business ( email )

469 Bukit Timah Road
Singapore 912409
Singapore

Karl Sigman

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Jing-Sheng Jeannette Song

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Duke University
Durham, NC 27708
United States

HOME PAGE: http://people.duke.edu/~jssong/

Hanqin Zhang

National University of Singapore (NUS) - NUS Business School ( email )

1 Business Link
Singapore, 117592
Singapore

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