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Optimal Lot-Sizing/Vehicle-Dispatching Policies Under Stochastic Lead Times and Stepwise Fixed Costs

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  • Osman Alp

    (University of Alberta, School of Business, Finance and Management Science Department, Edmonton, Alberta, Canada T6G 2R6)

  • Nesim K. Erkip

    (Middle East Technical University, Industrial Engineering Department, Ankara 06531 Turkey)

  • Refik Güllü

    (Middle East Technical University, Industrial Engineering Department, Ankara 06531 Turkey)

Abstract

We characterize optimal policies of a dynamic lot-sizing/vehicle-dispatching problem under dynamic deterministic demands and stochastic lead times. An essential feature of the problem is the structure of the ordering cost, where a fixed cost is incurred every time a batch is initiated (or a vehicle is hired) regardless of the portion of the batch (or vehicle) utilized. Moreover, for every unit of demand not satisfied on time, holding and backorder costs are incurred. Under mild assumptions we show that the demand of a period is satisfied from at most three distinct production (dispatching) epochs. We devise a dynamic programming algorithm to compute the production/dispatching quantities and times.

Suggested Citation

  • Osman Alp & Nesim K. Erkip & Refik Güllü, 2003. "Optimal Lot-Sizing/Vehicle-Dispatching Policies Under Stochastic Lead Times and Stepwise Fixed Costs," Operations Research, INFORMS, vol. 51(1), pages 160-166, February.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:1:p:160-166
    DOI: 10.1287/opre.51.1.160.12799
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    References listed on IDEAS

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    Cited by:

    1. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    2. Gürler, Ülkü & Alp, Osman & Büyükkaramikli, Nasuh Çağdaş, 2014. "Coordinated inventory replenishment and outsourced transportation operations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 70(C), pages 400-415.
    3. Thevenin, Simon & Ben-Ammar, Oussama & Brahimi, Nadjib, 2022. "Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1199-1215.
    4. Daniela Favaretto & Alessandro Marin & Marco Tolotti, 2023. "A theoretical validation of the DDMRP reorder policy," Computational Management Science, Springer, vol. 20(1), pages 1-28, December.
    5. Achin Srivastav & Sunil Agrawal, 2020. "On a single item single stage mixture inventory models with independent stochastic lead times," Operational Research, Springer, vol. 20(4), pages 2189-2227, December.
    6. Sıla Çetinkaya & Halit Üster & Gopalakrishnan Easwaran & Burcu Baris Keskin, 2009. "An Integrated Outbound Logistics Model for Frito-Lay: Coordinating Aggregate-Level Production and Distribution Decisions," Interfaces, INFORMS, vol. 39(5), pages 460-475, October.
    7. Chung-Yee Lee & Sila Çetinkaya & Wikrom Jaruphongsa, 2003. "A Dynamic Model for Inventory Lot Sizing and Outbound Shipment Scheduling at a Third-Party Warehouse," Operations Research, INFORMS, vol. 51(5), pages 735-747, October.
    8. Yue Jin & Ana Muriel, 2009. "Single‐warehouse multi‐retailer inventory systems with full truckload shipments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(5), pages 450-464, August.
    9. Gel, Esma S. & Salman, F. Sibel, 2022. "Dynamic ordering decisions with approximate learning of supply yield uncertainty," International Journal of Production Economics, Elsevier, vol. 243(C).
    10. Ayşegül Toptal & Sıla Çetinkaya, 2006. "Contractual agreements for coordination and vendor‐managed delivery under explicit transportation considerations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(5), pages 397-417, August.
    11. Osman Alp & Woonghee Tim Huh & Tarkan Tan, 2014. "Inventory Control with Multiple Setup Costs," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 89-103, February.
    12. Daniela Favaretto & Alessandro Marin & Marco Tolotti, 2021. "A data-driven and risk-based prudential approach to validate the DDMRP planning and control system," Working Papers 09, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    13. Mathieu Van Vyve, 2007. "Algorithms for Single-Item Lot-Sizing Problems with Constant Batch Size," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 594-613, August.
    14. Osman Alp & Nesim K. Erkip & Refik Güllü, 2003. "Outsourcing Logistics: Designing Transportation Contracts Between a Manufacturer and a Transporter," Transportation Science, INFORMS, vol. 37(1), pages 23-39, February.

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