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Single item inventory control under periodic review and a minimum order quantity

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  • Kiesmüller, G.P.
  • de Kok, A.G.
  • Dabia, S.

Abstract

In this paper we study a periodic review single item single stage inventory system with stochastic demand. In each time period the system must order none or at least as much as a minimum order quantity Qmin. Since the optimal structure of an ordering policy with a minimum order quantity is complicated, we propose an easy-to-use policy, which we call (R, S, Qmin) policy. Assuming linear holding and backorder costs we determine the optimal numerical value of the level S using a Markov Chain approach. In addition, we derive simple news-vendor-type inequalities for near-optimal policy parameters, which can easily be implemented within spreadsheet applications. In a numerical study we compare our policy with others and test the performance of the approximation for three different demand distributions: Poisson, negative binomial, and a discretized version of the gamma distribution. Given the simplicity of the policy and its cost performance as well as the excellent performance of the approximation we advocate the application of the (R, S, Qmin) policy in practice.

Suggested Citation

  • Kiesmüller, G.P. & de Kok, A.G. & Dabia, S., 2011. "Single item inventory control under periodic review and a minimum order quantity," International Journal of Production Economics, Elsevier, vol. 133(1), pages 280-285, September.
    • Handle: RePEc:eee:proeco:v:133:y:2011:i:1:p:280-285
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    References listed on IDEAS

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    1. Zhou, Bin & Zhao, Yao & Katehakis, Michael N., 2007. "Effective control policies for stochastic inventory systems with a minimum order quantity and linear costs," International Journal of Production Economics, Elsevier, vol. 106(2), pages 523-531, April.
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    Cited by:

    1. Shiyu Liu & Ou Liu & Xiaoming Jiang, 2023. "An Efficient Algorithm for the Joint Replenishment Problem with Quantity Discounts, Minimum Order Quantity and Transport Capacity Constraints," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    2. Nihan Kabadayı & Timur Keskintürk, 2015. "Comparison Of Periodic-Review Inventory Control Policies In A Serial Supply Chain," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 3(2), pages 27-34, December.
    3. Jong Soo Kim & Eunhee Jeon & Jiseong Noh & Jun Hyeong Park, 2018. "A Model and an Algorithm for a Large-Scale Sustainable Supplier Selection and Order Allocation Problem," Mathematics, MDPI, vol. 6(12), pages 1-19, December.
    4. Shin Hee Baek & Jong Soo Kim, 2020. "Efficient Algorithms for a Large-Scale Supplier Selection and Order Allocation Problem Considering Carbon Emissions and Quantity Discounts," Mathematics, MDPI, vol. 8(10), pages 1-17, September.
    5. F. Kleintje-Ell & G. Kiesmüller, 2015. "Cost minimising order schedules for a capacitated inventory system," Annals of Operations Research, Springer, vol. 229(1), pages 501-520, June.
    6. Ho, Jyh-Wen & Fang, Chih-Chiang, 2013. "Production capacity planning for multiple products under uncertain demand conditions," International Journal of Production Economics, Elsevier, vol. 141(2), pages 593-604.
    7. Zhu, Han & Liu, Xing & Chen, Youhua (Frank), 2015. "Effective inventory control policies with a minimum order quantity and batch ordering," International Journal of Production Economics, Elsevier, vol. 168(C), pages 21-30.
    8. Han Zhu, 2022. "A simple heuristic policy for stochastic inventory systems with both minimum and maximum order quantity requirements," Annals of Operations Research, Springer, vol. 309(1), pages 347-363, February.
    9. Muriel, Ana & Chugh, Tammana & Prokle, Michael, 2022. "Efficient algorithms for the joint replenishment problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 300(1), pages 137-150.
    10. Paul, Sanjoy Kumar & Sarker, Ruhul & Essam, Daryl, 2014. "Real time disruption management for a two-stage batch production–inventory system with reliability considerations," European Journal of Operational Research, Elsevier, vol. 237(1), pages 113-128.
    11. Klosterhalfen, Steffen T. & Holzhauer, Falk & Fleischmann, Moritz, 2018. "Control of a continuous production inventory system with production quantity restrictions," European Journal of Operational Research, Elsevier, vol. 268(2), pages 569-581.
    12. Perera, Sandun & Janakiraman, Ganesh & Niu, Shun-Chen, 2017. "Optimality of (s, S) policies in EOQ models with general cost structures," International Journal of Production Economics, Elsevier, vol. 187(C), pages 216-228.

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