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Single‐warehouse multi‐retailer inventory systems with full truckload shipments

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  • Yue Jin
  • Ana Muriel

Abstract

We consider a multi‐stage inventory system composed of a single warehouse that receives a single product from a single supplier and replenishes the inventory of n retailers through direct shipments. Fixed costs are incurred for each truck dispatched and all trucks have the same capacity limit. Costs are stationary, or more generally monotone as in Lippman (Management Sci 16, 1969, 118–138). Demands for the n retailers over a planning horizon of T periods are given. The objective is to find the shipment quantities over the planning horizon to satisfy all demands at minimum system‐wide inventory and transportation costs without backlogging. Using the structural properties of optimal solutions, we develop (1) an O(T2) algorithm for the single‐stage dynamic lot sizing problem; (2) an O(T3) algorithm for the case of a single‐warehouse single‐retailer system; and (3) a nested shortest‐path algorithm for the single‐warehouse multi‐retailer problem that runs in polynomial time for a given number of retailers. To overcome the computational burden when the number of retailers is large, we propose aggregated and disaggregated Lagrangian decomposition methods that make use of the structural properties and the efficient single‐stage algorithm. Computational experiments show the effectiveness of these algorithms and the gains associated with coordinated versus decentralized systems. Finally, we show that the decentralized solution is asymptotically optimal. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:56:y:2009:i:5:p:450-464
    DOI: 10.1002/nav.20353
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    References listed on IDEAS

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    1. Moustapha Diaby & Alain Martel, 1993. "Dynamic Lot Sizing for Multi-Echelon Distribution Systems with Purchasing and Transportation Price Discounts," Operations Research, INFORMS, vol. 41(1), pages 48-59, February.
    2. Steven A. Lippman, 1969. "Optimal Inventory Policy with Multiple Set-Up Costs," Management Science, INFORMS, vol. 16(1), pages 118-138, September.
    3. Chung-Lun Li & Vernon Ning Hsu & Wen-Qiang Xiao, 2004. "Dynamic Lot Sizing with Batch Ordering and Truckload Discounts," Operations Research, INFORMS, vol. 52(4), pages 639-654, August.
    4. Shoshana Anily & Michal Tzur, 2005. "Shipping Multiple Items by Capacitated Vehicles: An Optimal Dynamic Programming Approach," Transportation Science, INFORMS, vol. 39(2), pages 233-248, May.
    5. Dev Joneja, 1990. "The Joint Replenishment Problem: New Heuristics and Worst Case Performance Bounds," Operations Research, INFORMS, vol. 38(4), pages 711-723, August.
    6. 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.
    7. Lap Mui Ann Chan & Ana Muriel & Zuo-Jun Shen & David Simchi-Levi, 2002. "On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures," Operations Research, INFORMS, vol. 50(6), pages 1058-1067, December.
    8. POCHET, Yves & WOLSEY, Laurence A., 1993. "Lot-sizing with constant batches: formulation and valid inequalities," LIDAM Reprints CORE 1066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. 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.
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    Cited by:

    1. Oğuz Solyalı & Haldun Süral, 2012. "The one-warehouse multi-retailer problem: reformulation, classification, and computational results," Annals of Operations Research, Springer, vol. 196(1), pages 517-541, July.
    2. Hu, Weihong & Toriello, Alejandro & Dessouky, Maged, 2018. "Integrated inventory routing and freight consolidation for perishable goods," European Journal of Operational Research, Elsevier, vol. 271(2), pages 548-560.
    3. Haoqing Wang & Wen Yi & Yannick Liu, 2022. "Optimal Route Design for Construction Waste Transportation Systems: Mathematical Models and Solution Algorithms," Mathematics, MDPI, vol. 10(22), pages 1-13, November.

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