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Myopic optimal policy for a multi-period, two-delivery-lead-times, stochastic inventory problem with minimum cumulative commitment and capacity

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  • Xu, Ningxiong

Abstract

This paper studies a single-product, multi-period, stochastic inventory problem that imposes the lower and upper bounds on the cumulative order quantity during a planning horizon and allows two delivery lead times. This model includes three features. The first one is that a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer's total cumulative order quantity during the planning horizon is constrained with the capacity. The second one is that the buyer agrees to purchase the product at least a certain percentage of the purchased capacity during the planning horizon. The third one is that the supplier allows the buyer to order the product with two-delivery-lead-times. We identify conditions under which a myopic ordering policy is optimal. We also develop an algorithm to calculate the optimal capacity when the minimum cumulative order quantity commitment is a certain percentage of the capacity. We then use the algorithm to evaluate the effect of the various parameters on the buyer's minimum expected total cost during the planning horizon. Our computation shows that the buyer would benefit from the commitments and two-delivery-lead-times.

Suggested Citation

  • Xu, Ningxiong, 2011. "Myopic optimal policy for a multi-period, two-delivery-lead-times, stochastic inventory problem with minimum cumulative commitment and capacity," International Journal of Production Economics, Elsevier, vol. 133(2), pages 719-727, October.
    • Handle: RePEc:eee:proeco:v:133:y:2011:i:2:p:719-727
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    2. Cheaitou, Ali & Cheaytou, Rima, 2019. "A two-stage capacity reservation supply contract with risky supplier and forecast updating," International Journal of Production Economics, Elsevier, vol. 209(C), pages 42-60.
    3. Jakšič, M. & Fransoo, J.C., 2018. "Dual sourcing in the age of near-shoring: Trading off stochastic capacity limitations and long lead times," European Journal of Operational Research, Elsevier, vol. 267(1), pages 150-161.
    4. Cheaitou, Ali & van Delft, Christian & Jemai, Zied & Dallery, Yves, 2014. "Optimal policy structure characterization for a two-period dual-sourcing inventory control model with forecast updating," International Journal of Production Economics, Elsevier, vol. 157(C), pages 238-249.
    5. Xiting Gong & Youhua (Frank) Chen & Quan Yuan, 2022. "Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 511-528, February.
    6. Cai, Jianhu & Hu, Xiaoqing & Jiang, Feiying & Zhou, Qing & Zhang, Xiaoyang & Xuan, Liyuan, 2019. "Optimal input quantity decisions considering commitment order contracts under yield uncertainty," International Journal of Production Economics, Elsevier, vol. 216(C), pages 398-412.
    7. Tong Wang & Xiting Gong & Sean X. Zhou, 2017. "Dynamic Inventory Management with Total Minimum Order Commitments and Two Supply Options," Operations Research, INFORMS, vol. 65(5), pages 1285-1302, October.
    8. Saif Benjaafar & David Chen & Rowan Wang, 2017. "Managing Production-Inventory Systems with Scarce Resources," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 216-229, May.

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