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A Note on the Convexity of Service-Level Measures of the (r, q) System

Author

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  • Hongtao Zhang

    (Department of Information and Systems Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong)

Abstract

This note gives a simple proof that in a (r, q) system the average outstanding backorders and the average stockouts per unit time are jointly convex in the two control variables q and r.

Suggested Citation

  • Hongtao Zhang, 1998. "A Note on the Convexity of Service-Level Measures of the (r, q) System," Management Science, INFORMS, vol. 44(3), pages 431-432, March.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:3:p:431-432
    DOI: 10.1287/mnsc.44.3.431
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    References listed on IDEAS

    as
    1. Serfozo, Richard & Stidham, Shaler, 1978. "Semi-stationary clearing processes," Stochastic Processes and their Applications, Elsevier, vol. 6(2), pages 165-178, January.
    2. Paul Zipkin, 1986. "Inventory Service-Level Measures: Convexity and Approximation," Management Science, INFORMS, vol. 32(8), pages 975-981, August.
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    Citations

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    Cited by:

    1. Vipul Agrawal & Sridhar Seshadri, 2000. "Distribution free bounds for service constrained (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 635-656, December.
    2. Woonghee Tim Huh & Ganesh Janakiraman, 2010. "Base‐stock policies in capacitated assembly systems: Convexity properties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(2), pages 109-118, March.
    3. Ang, Marcus & Song, Jing-Sheng & Wang, Mingzheng & Zhang, Hanqin, 2013. "On properties of discrete (r, q) and (s, T) inventory systems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 95-105.
    4. Jingchen Wu & Xiuli Chao, 2014. "Optimal Control of a Brownian Production/Inventory System with Average Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 163-189, February.
    5. Vinayak Deshpande & Morris A. Cohen & Karen Donohue, 2003. "A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes," Management Science, INFORMS, vol. 49(6), pages 683-703, June.
    6. Uday S. Rao, 2003. "Properties of the Periodic Review (R, T) Inventory Control Policy for Stationary, Stochastic Demand," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 37-53, February.
    7. Awi Federgruen & Min Wang, 2013. "Monotonicity properties of a class of stochastic inventory systems," Annals of Operations Research, Springer, vol. 208(1), pages 155-186, September.
    8. Lode Li & Hongtao Zhang, 2000. "The Multistage Service Facility Start-Up and Capacity Model," Operations Research, INFORMS, vol. 48(3), pages 490-497, June.

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