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The linear dynamic lot size problem with minimum order quantity

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  • Okhrin, Irena
  • Richter, Knut

Abstract

This paper continues the analysis of a special uncapacitated single item lot sizing problem where a minimum order quantity restriction, instead of the setup cost, guarantees a certain level of production lots. A detailed analysis of the model and an investigation of the particularities of the cumulative demand structure allow us to develop a solution algorithm based on the concept of atomic sub-problems. We present an optimal solution to an atomic sub-problem in an explicit form and prove that it serves as a construction block for the optimal solution of the original problem. Computational tests and a comparison with a published algorithm confirm the efficiency of the solution algorithm developed here.

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  • Okhrin, Irena & Richter, Knut, 2011. "The linear dynamic lot size problem with minimum order quantity," International Journal of Production Economics, Elsevier, vol. 133(2), pages 688-693, October.
    • Handle: RePEc:eee:proeco:v:133:y:2011:i:2:p:688-693
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    2. Absi, Nabil & Dauzère-Pérès, Stéphane & Kedad-Sidhoum, Safia & Penz, Bernard & Rapine, Christophe, 2016. "The single-item green lot-sizing problem with fixed carbon emissions," European Journal of Operational Research, Elsevier, vol. 248(3), pages 849-855.
    3. 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.
    4. Froese, Sarah & Kunz, Nadja C. & Ramana, M.V., 2020. "Too small to be viable? The potential market for small modular reactors in mining and remote communities in Canada," Energy Policy, Elsevier, vol. 144(C).
    5. 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.
    6. Kian, Ramez & Gürler, Ülkü & Berk, Emre, 2014. "The dynamic lot-sizing problem with convex economic production costs and setups," International Journal of Production Economics, Elsevier, vol. 155(C), pages 361-379.
    7. Chung-Lun Li & Qingying Li, 2016. "Polynomial-Time Solvability of Dynamic Lot Size Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-20, June.

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