IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/60545.html
   My bibliography  Save this paper

Optimal inventory policies with an exact cost function under large demand uncertainty

Author

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

Abstract

In this paper we investigate the minimization process of the exact cost function for a continuous review (Q,R) inventory model with non-negative reorder point and fixed lead-time. Backorders are allowed and the unit shortage cost is used to determine the expected annual shortage cost. Provided that the lead-time demand has J-shaped or unimodal distribution satisfying specific assumptions we derive the general condition when the minimum cost is attained at a positive reorder point or at a reorder point equal to zero. Based on this condition a general algorithm is developed. Some numerical experimentation based on this algorithm using parameter values from the relevant literature indicates that with large demand uncertainty measured by the coefficient of variation the optimal inventory policies lead to excessively large orders and zero reorder points.

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:60545
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/60545/1/MPRA_paper_60545.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, January.
    4. 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.
    5. Lau, Amy Hing Ling & Lau, Hon-Shiang, 2008. "An improved (Q, R) formulation when the stockout cost is incurred on a per-stockout basis," International Journal of Production Economics, Elsevier, vol. 111(2), pages 421-434, February.
    6. Lau, Amy Hing-Ling & Lau, Hon-Shiang, 2002. "RETRACTED: 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. 77(2), pages 173-185, May.
    7. 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.
    8. 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.
    9. Chandrasekhar Das, 1988. "Note---On the Minimum of a Nonconvex Inventory Function," Management Science, INFORMS, vol. 34(8), pages 1023-1026, August.
    10. Paul Zipkin, 1986. "Inventory Service-Level Measures: Convexity and Approximation," Management Science, INFORMS, vol. 32(8), pages 975-981, August.
    11. 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.
    12. David E. Platt & Lawrence W. Robinson & Robert B. Freund, 1997. "Tractable (Q, R) Heuristic Models for Constrained Service Levels," Management Science, INFORMS, vol. 43(7), pages 951-965, July.
    Full references (including those not matched with items on IDEAS)

    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. "On the convexity of the cost function for the (Q,R) inventory model," MPRA Paper 55675, University Library of Munich, Germany.
    2. 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.
    3. Chiang, Chi, 2010. "An order expediting policy for continuous review systems with manufacturing lead-time," European Journal of Operational Research, Elsevier, vol. 203(2), pages 526-531, June.
    4. Lee, Jun-Yeon & Schwarz, Leroy B., 2007. "Leadtime reduction in a (Q,r) inventory system: An agency perspective," International Journal of Production Economics, Elsevier, vol. 105(1), pages 204-212, January.
    5. 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.
    6. 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.
    7. Tang, Shaolong & Wang, Wenjie & Cho, Stella & Yan, Hong, 2018. "Reducing emissions in transportation and inventory management: (R, Q) Policy with considerations of carbon reduction," European Journal of Operational Research, Elsevier, vol. 269(1), pages 327-340.
    8. 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.
    9. Duran, Alfonso & Gutierrez, Gil & Zequeira, Romulo I., 2004. "A continuous review inventory model with order expediting," International Journal of Production Economics, Elsevier, vol. 87(2), pages 157-169, January.
    10. 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.
    11. Tamer Boyacı & Guillermo Gallego, 2002. "Managing waiting times of backordered demands in single‐stage (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 557-573, September.
    12. Fangruo Chen, 1999. "94%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand," Management Science, INFORMS, vol. 45(12), pages 1679-1696, December.
    13. Amy Hing‐Ling Lau & Hon‐Shiang Lau & David F. Pyke, 2002. "Degeneracy in inventory models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 686-705, October.
    14. 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.
    15. 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.
    16. Kevin H. Shang & Jing-Sheng Song & Paul H. Zipkin, 2009. "Coordination Mechanisms in Decentralized Serial Inventory Systems with Batch Ordering," Management Science, INFORMS, vol. 55(4), pages 685-695, April.
    17. 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.
    18. 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.
    19. Andersson, Jonas & Marklund, Johan, 2000. "Decentralized inventory control in a two-level distribution system," European Journal of Operational Research, Elsevier, vol. 127(3), pages 483-506, December.
    20. 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.

    More about this item

    Keywords

    Inventory; Continuous review model; Exact cost function; Convexity; Cost parameter values; General algorithm.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:60545. 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.