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On the convexity of the cost function for the (Q,R) inventory model

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  • Halkos, George
  • Kevork, Ilias
  • Tziourtzioumis, Chris

Abstract

In this paper we investigate the convexity of the annual total cost function for the Hadley & Whitin (1963) continuous review (Q,R) inventory model with backorders and fixed lead-time, when the reorder point is non-negative and the cost per unit backordered is used to calculate the expected annual shortage cost. Efficient procedures for finding the order quantity and reorder point which ensure a global minimum are provided when the demand in the lead time follows the Normal and Log-Normal distributions. Convexity conditions are obtained for each distribution and numerical examples are given to explain how the values of the model cost parameters affect the optimal solution. The results indicate strong interaction between convexity and cost parameters as their values determine when the minimum cost obtained from solving the first order conditions is global and when the global minimum is attained setting the reorder point to zero.

Suggested Citation

  • Halkos, George & Kevork, Ilias & Tziourtzioumis, Chris, 2014. "On the convexity of the cost function for the (Q,R) inventory model," MPRA Paper 55675, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:55675
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    References listed on IDEAS

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    4. Kevork, Ilias S., 2010. "Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions," Omega, Elsevier, vol. 38(3-4), pages 218-227, June.
    5. 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.
    6. Silver, Edward A, 1980. "Comments on the lognormal approximation of lead time demand," Omega, Elsevier, vol. 8(6), pages 701-702.
    7. Janssen, Elleke & Strijbosch, Leo & Brekelmans, Ruud, 2009. "Assessing the effects of using demand parameters estimates in inventory control and improving the performance using a correction function," International Journal of Production Economics, Elsevier, vol. 118(1), pages 34-42, March.
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    Cited by:

    1. Halkos, George & Kevork, Ilias & Tziourtzioumis, Chris, 2014. "Optimal inventory policies with an exact cost function under large demand uncertainty," MPRA Paper 60545, University Library of Munich, Germany.

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    More about this item

    Keywords

    Logistics; Continuous review inventory model; Expected total cost function; Convexity conditions; Cost parameters.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • M21 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics - - - Business Economics

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