IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/55675.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/55675/1/MPRA_paper_55675.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tadikamalla, Pandu R, 1984. "A comparison of several approximations to the lead time demand distribution," Omega, Elsevier, vol. 12(6), pages 575-581.
    2. Lau, Amy Hing-Ling & Lau, Hon-Shiang, 2002. "A comparison of different methods for estimating the average inventory level in a (Q,R) system with backorders," International Journal of Production Economics, Elsevier, vol. 79(3), pages 303-316, October.
    3. Chandrasekhar Das, 1988. "Note---On the Minimum of a Nonconvex Inventory Function," Management Science, INFORMS, vol. 34(8), pages 1023-1026, August.
    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.
    8. anonymous, 1969. "On the Convexity of the Backorder Function for an E.O.Q. Policy," Management Science, INFORMS, vol. 15(7), pages 453-454, March.
    9. Hon-Shiang Lau, 1997. "Simple formulas for the expected costs in the newsboy problem: An educational note," European Journal of Operational Research, Elsevier, vol. 100(3), pages 557-561, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand," MPRA Paper 39650, University Library of Munich, Germany.
    3. Halkos, George & Kevork, Ilias, 2012. "The classical newsvendor model under normal demand with large coefficients of variation," MPRA Paper 40414, University Library of Munich, Germany.
    4. Prak, Dennis & Teunter, Ruud & Syntetos, Aris, 2017. "On the calculation of safety stocks when demand is forecasted," European Journal of Operational Research, Elsevier, vol. 256(2), pages 454-461.
    5. Halkos, George & Kevork, Ilias, 2012. "Unbiased estimation of maximum expected profits in the Newsvendor Model: a case study analysis," MPRA Paper 40724, University Library of Munich, Germany.
    6. Halkos, George & Kevork, Ilias, 2012. "Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand," MPRA Paper 36460, University Library of Munich, Germany.
    7. Halkos, George & Kevork, Ilias, 2013. "Forecasting the optimal order quantity in the newsvendor model under a correlated demand," MPRA Paper 44189, University Library of Munich, Germany.
    8. Su, Rung Hung & Pearn, Wen Lea, 2011. "Product selection for newsboy-type products with normal demands and unequal costs," International Journal of Production Economics, Elsevier, vol. 132(2), pages 214-222, August.
    9. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand," MPRA Paper 36205, University Library of Munich, Germany.
    10. Halkos, George & Kevork, Ilias, 2011. "Non-negative demand in newsvendor models:The case of singly truncated normal samples," MPRA Paper 31842, University Library of Munich, Germany.
    11. Lei Xu & Govindan Kannan & Xiaoli Yang & Jian Li & Xiukun Zhao, 2013. "Pricing and Allotment in a Sea-Cargo Supply Chain with Reference Effect: A Dynamic Game Approach," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-10, March.
    12. Tamjidzad, Shahrzad & Mirmohammadi, S. Hamid, 2015. "An optimal (r, Q) policy in a stochastic inventory system with all-units quantity discount and limited sharable resource," European Journal of Operational Research, Elsevier, vol. 247(1), pages 93-100.
    13. Ülkü, M. Ali & Gürler, Ülkü, 2018. "The impact of abusing return policies: A newsvendor model with opportunistic consumers," International Journal of Production Economics, Elsevier, vol. 203(C), pages 124-133.
    14. Banerjee, Pradeep K. & Turner, T. Rolf, 2012. "A flexible model for the pricing of perishable assets," Omega, Elsevier, vol. 40(5), pages 533-540.
    15. Marcus Ang & Karl Sigman & Jing-Sheng Song & Hanqin Zhang, 2017. "Closed-Form Approximations for Optimal ( r , q ) and ( S , T ) Policies in a Parallel Processing Environment," Operations Research, INFORMS, vol. 65(5), pages 1414-1428, October.
    16. Strijbosch, Leo W.G. & Syntetos, Aris A. & Boylan, John E. & Janssen, Elleke, 2011. "On the interaction between forecasting and stock control: The case of non-stationary demand," International Journal of Production Economics, Elsevier, vol. 133(1), pages 470-480, September.
    17. 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.
    18. Daniela Favaretto & Alessandro Marin & Marco Tolotti, 2023. "A theoretical validation of the DDMRP reorder policy," Computational Management Science, Springer, vol. 20(1), pages 1-28, December.
    19. Soham Ghosh & Sujay Mukhoti, 2023. "Non-parametric generalised newsvendor model," Annals of Operations Research, Springer, vol. 321(1), pages 241-266, February.
    20. Hing-Ling Lau, Amy & Lau, Hon-Shiang & Willett, Keith D., 2000. "Demand uncertainty and returns policies for a seasonal product: An alternative model," International Journal of Production Economics, Elsevier, vol. 66(1), pages 1-12, June.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:55675. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.