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Inventory Cost Rate Functions with Nonlinear Shortage Costs

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  • Kaj Rosling

    (Department of Industrial Engineering, Växjö University, SE-351 95 Växjö, Sweden)

Abstract

This article considers five cost-rate models for inventory control, each summarizing the expected holding and shortage costs per period as a function of the inventory position. All models have linear holding costs and shortage cost coefficients of dimension [ $/unit/period ], [ $/unit ], and [ $/period ]. The latter two coeficients may be the shadow costs of a fill-rate and a ready-rate service constraint, respectively. One of the cost-rate models is a new suggestion, intended to facilitate modeling of periodic-review inventory systems.If-and-only-if conditions on the demand process are presented for which the cost rate is quasi-convex in the inventory position. The typical sufficient condition requires that the cumulative demand distribution be logconcave, a condition that is met by most demand distributions commonly used in the inventory literature.The results simplify optimization and extend the known optimality of ( S , s ) and ( nQ , r ) policies to cost structures common in applications and to the presence of typical service constraints. As a prerequisite for the study, a series of new monotonicity results are derived for compound renewal processes.

Suggested Citation

  • Kaj Rosling, 2002. "Inventory Cost Rate Functions with Nonlinear Shortage Costs," Operations Research, INFORMS, vol. 50(6), pages 1007-1017, December.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:6:p:1007-1017
    DOI: 10.1287/opre.50.6.1007.346
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    References listed on IDEAS

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    1. Martin Beckmann, 1961. "An Inventory Model for Arbitrary Interval and Quantity Distributions of Demand," Management Science, INFORMS, vol. 8(1), pages 35-57, October.
    2. Awi Federgruen & Zvi Schechner, 1983. "Technical Note—Cost Formulas for Continuous Review Inventory Models with Fixed Delivery Lags," Operations Research, INFORMS, vol. 31(5), pages 957-965, October.
    3. Chen, Fangruo & Zheng, Yu-Sheng, 1993. "Inventory models with general backorder costs," European Journal of Operational Research, Elsevier, vol. 65(2), pages 175-186, March.
    4. Awi Federgruen & Yu-Sheng Zheng, 1992. "An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems," Operations Research, INFORMS, vol. 40(4), pages 808-813, August.
    5. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
    6. Blyth C. Archibald & Edward A. Silver, 1978. "(s, S) Policies Under Continuous Review and Discrete Compound Poisson Demand," Management Science, INFORMS, vol. 24(9), pages 899-909, May.
    7. Arthur F. Veinott, 1965. "The Optimal Inventory Policy for Batch Ordering," Operations Research, INFORMS, vol. 13(3), pages 424-432, June.
    8. Yu-Sheng Zheng & A. Federgruen, 1991. "Finding Optimal (s, S) Policies Is About As Simple As Evaluating a Single Policy," Operations Research, INFORMS, vol. 39(4), pages 654-665, August.
    9. Fangruo Chen, 2000. "Optimal Policies for Multi-Echelon Inventory Problems with Batch Ordering," Operations Research, INFORMS, vol. 48(3), pages 376-389, June.
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