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

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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. 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.
    2. 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.
    3. Straubert, Christian, 2024. "A continuous approximation location-inventory model with exact inventory costs and nonlinear delivery lead time penalties," International Journal of Production Economics, Elsevier, vol. 268(C).
    4. 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.
    5. 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.
    6. Lode Li & Hongtao Zhang, 2000. "The Multistage Service Facility Start-Up and Capacity Model," Operations Research, INFORMS, vol. 48(3), pages 490-497, June.
    7. 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.
    8. 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.
    9. 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.

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