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Demand Allocation in Systems with Multiple Inventory Locations and Multiple Demand Sources

Author

Listed:
  • Saif Benjaafar

    () (Graduate Program in Industrial Engineering, Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455)

  • Yanzhi Li

    () (Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong)

  • Dongsheng Xu

    () (Department of Management Science, School of Business, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China)

  • Samir Elhedhli

    () (Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada)

Abstract

We consider the problem of allocating demand that originates from multiple sources among multiple inventory locations. Demand from each source arrives dynamically according to an independent Poisson process. The cost of fulfilling each order depends on both the source of the order and its fulfillment location. Inventory at all locations is replenished from a shared production facility with a finite production capacity and stochastic production times. Consequently, supply lead times are load dependent and affected by congestion at the production facility. Our objective is to determine an optimal demand allocation and optimal inventory levels at each location so that the sum of transportation, inventory, and backorder costs is minimized. We formulate the problem as a nonlinear optimization problem and characterize the structure of the optimal allocation policy. We show that the optimal demand allocations are always discrete, with demand from each source always fulfilled entirely from a single inventory location. We use this discreteness property to reformulate the problems as a mixed-integer linear program and provide an exact solution procedure. We show that this discreteness property extends to systems with other forms of supply processes. However, we also show that supply systems exist for which the property does not hold. Using numerical results, we examine the impact of different parameters and provide some managerial insights.

Suggested Citation

  • Saif Benjaafar & Yanzhi Li & Dongsheng Xu & Samir Elhedhli, 2008. "Demand Allocation in Systems with Multiple Inventory Locations and Multiple Demand Sources," Manufacturing & Service Operations Management, INFORMS, vol. 10(1), pages 43-60, October.
  • Handle: RePEc:inm:ormsom:v:10:y:2008:i:1:p:43-60
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    File URL: http://dx.doi.org/10.1287/msom.1070.0153
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    References listed on IDEAS

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    1. Colin E. Bell & Shaler Stidham, Jr., 1983. "Individual versus Social Optimization in the Allocation of Customers to Alternative Servers," Management Science, INFORMS, vol. 29(7), pages 831-839, July.
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    3. Saif Benjaafar & William L. Cooper & Joon-Seok Kim, 2005. "On the Benefits of Pooling in Production-Inventory Systems," Management Science, INFORMS, vol. 51(4), pages 548-565, April.
    4. Saif Benjaafar & Mohsen ElHafsi & Francis de VĂ©ricourt, 2004. "Demand Allocation in Multiple-Product, Multiple-Facility, Make-to-Stock Systems," Management Science, INFORMS, vol. 50(10), pages 1431-1448, October.
    5. Gary D. Eppen, 1979. "Note--Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem," Management Science, INFORMS, vol. 25(5), pages 498-501, May.
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