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A Multiplier Adjustment Method for Dynamic Resource Allocation Problems

Author

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  • Tassio A. Carvalho

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

  • Warren B. Powell

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

Abstract

Dynamic fleet management problems (with a homogeneous fleet) are classically formulated as dynamic networks, or linear programs with side constraints. Recently, a new dynamic control approach was introduced, called a logistics queueing network. Instead of a large linear program, the problem is decomposed into small subproblems that are guided by two control variables that push these local problems to produce a solution that is close to a global optimum. In prior work, these control variables were updated using a subgradient approximation. In this paper, we propose a multiplier adjustment method for solving the same problem. Numerical experiments show that this method produces better solutions with greater stability. The new method is somewhat slower, and is more difficult to implement. We believe that both methods will represent reasonable choices for solving the problem.

Suggested Citation

  • Tassio A. Carvalho & Warren B. Powell, 2000. "A Multiplier Adjustment Method for Dynamic Resource Allocation Problems," Transportation Science, INFORMS, vol. 34(2), pages 150-164, May.
    • Handle: RePEc:inm:ortrsc:v:34:y:2000:i:2:p:150-164
    DOI: 10.1287/trsc.34.2.150.12305
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    References listed on IDEAS

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    1. William C. Jordan & Mark A. Turnquist, 1983. "A Stochastic, Dynamic Network Model for Railroad Car Distribution," Transportation Science, INFORMS, vol. 17(2), pages 123-145, May.
    2. Teodor Gabriel Crainic & Michel Gendreau & Pierre Dejax, 1993. "Dynamic and Stochastic Models for the Allocation of Empty Containers," Operations Research, INFORMS, vol. 41(1), pages 102-126, February.
    3. Warren B. Powell & Tassio A. Carvalho, 1998. "Dynamic Control of Logistics Queueing Networks for Large-Scale Fleet Management," Transportation Science, INFORMS, vol. 32(2), pages 90-109, May.
    4. Warren B. Powell & Tassio A. Carvalho, 1998. "Real-Time Optimization of Containers and Flatcars for Intermodal Operations," Transportation Science, INFORMS, vol. 32(2), pages 110-126, May.
    5. Linos F. Frantzeskakis & Warren B. Powell, 1990. "A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems," Transportation Science, INFORMS, vol. 24(1), pages 40-57, February.
    6. Raymond K. Cheung & Warren B. Powell, 1996. "An Algorithm for Multistage Dynamic Networks with Random Arc Capacities, with an Application to Dynamic Fleet Management," Operations Research, INFORMS, vol. 44(6), pages 951-963, December.
    7. Warren B. Powell, 1996. "A Stochastic Formulation of the Dynamic Assignment Problem, with an Application to Truckload Motor Carriers," Transportation Science, INFORMS, vol. 30(3), pages 195-219, August.
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    Cited by:

    1. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, I: Single Period Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 21-39, February.
    2. Bojovic, Nebojsa J., 2002. "A general system theory approach to rail freight car fleet sizing," European Journal of Operational Research, Elsevier, vol. 136(1), pages 136-172, January.
    3. Huseyin Topaloglu & Warren B. Powell, 2007. "Sensitivity Analysis of a Dynamic Fleet Management Model Using Approximate Dynamic Programming," Operations Research, INFORMS, vol. 55(2), pages 319-331, April.
    4. Topaloglu, H., 2006. "A parallelizable dynamic fleet management model with random travel times," European Journal of Operational Research, Elsevier, vol. 175(2), pages 782-805, December.
    5. Huseyin Topaloglu & Warren Powell, 2007. "Incorporating Pricing Decisions into the Stochastic Dynamic Fleet Management Problem," Transportation Science, INFORMS, vol. 41(3), pages 281-301, August.
    6. G J King & H Topaloglu, 2007. "Incorporating the pricing decisions into the dynamic fleet management problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(8), pages 1065-1074, August.
    7. Larry Weatherford, 2017. "Do hybrid forecasting and forecast multipliers still work in a “perfectly tuned” PODS international network with four competing airlines?," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 16(6), pages 580-593, December.
    8. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, II: Multiperiod Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 40-54, February.

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