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


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


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

    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. 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.
    2. 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.
    3. 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.
    4. 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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