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

Marcus Ang (), Karl Sigman (), Jing-Sheng Song () and Hanqin Zhang ()
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Marcus Ang: Lee Kong Chian School of Business, Singapore Management University, 178899, Singapore
Karl Sigman: Fu Foundation School of Engineering and Applied Science, Columbia University, New York, New York 10027
Jing-Sheng Song: Fuqua School of Business, Duke University, Durham, North Carolina 27708
Hanqin Zhang: NUS Business School, National University of Singapore, 119245, Singapore

Operations Research, 2017, vol. 65, issue 5, 1414-1428

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; i.i.d. lead times; asymptotic analysis; heavy-traffic limit; closed-form solutions (search for similar items in EconPapers)
Date: 2017
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