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Optimal Policies for Inventory Systems with Separate Delivery-Request and Order-Quantity Decisions

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  • Qing Li

    (School of Business and Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Xiaoli Wu

    (School of Business and Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Ki Ling Cheung

    (School of Business and Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

Abstract

Motivated by logistics practices, we consider a retailer that replenishes its inventory by making a delivery request without specifying a quantity, then deciding the quantity when the delivery vehicle arrives after one period. A fixed cost is incurred whenever a delivery request is made, regardless of the quantity ordered later. The new feature of this research relative to previous work is the separation of the delivery request and the quantity decision, or the postponement of ordering until one-period demand information is observed. Due to such separation, both the state space and the action space must be augmented in the model. We show that the optimal policy for delivery requests is of a threshold type: A delivery request is made if and only if the inventory on hand is below a threshold. The optimal decision on ordering is more complex, and there might be multiple order-up-to levels. Our numerical studies show, nonetheless, that the cost of an ordering policy that considers (at most) two order-up-to levels is close to the minimal when the planning horizon is not too short. We also identify conditions under which a base-stock policy is optimal for ordering. To understand the effects of ordering postponement, we compare our model with the traditional model in which the two decisions must be made at the same time. We show that postponement leads not only to a lower cost, but also a higher threshold for making delivery requests.

Suggested Citation

  • Qing Li & Xiaoli Wu & Ki Ling Cheung, 2009. "Optimal Policies for Inventory Systems with Separate Delivery-Request and Order-Quantity Decisions," Operations Research, INFORMS, vol. 57(3), pages 626-636, June.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:3:p:626-636
    DOI: 10.1287/opre.1090.0696
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    References listed on IDEAS

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    2. Özen, Ulaş & Doğru, Mustafa K. & Armagan Tarim, S., 2012. "Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem," Omega, Elsevier, vol. 40(3), pages 348-357.
    3. Qing Li & Peiwen Yu, 2012. "Technical Note---On the Quasiconcavity of Lost-Sales Inventory Models with Fixed Costs," Operations Research, INFORMS, vol. 60(2), pages 286-291, April.
    4. Saghiri, Soroosh S. & Barnes, Stuart J., 2016. "Supplier flexibility and postponement implementation: An empirical analysis," International Journal of Production Economics, Elsevier, vol. 173(C), pages 170-183.
    5. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    6. Dural-Selcuk, Gozdem & Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2020. "The benefit of receding horizon control: Near-optimal policies for stochastic inventory control," Omega, Elsevier, vol. 97(C).
    7. Hong Sun & Yan Li, 2023. "Optimal Acquisition and Production Policies for Remanufacturing with Quality Grading," Mathematics, MDPI, vol. 11(7), pages 1-21, March.

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