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A Multi-stage Monte Carlo Sampling Based Stochastic Programming Model for the Dynamic Vehicle Allocation Problem

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  • Fan, Wei
  • Machemehl, Randy

Abstract

Optimization under uncertainty has seen many applications in the industrial world. The objective of this paper is to study the stochastic dynamic vehicle allocation problem (SDVAP), which is faced by many trucking companies, container companies, rental car agencies and railroads. To maximize profits and to manage fleets of vehicles in both time and space, this paper has formulated a multistage stochastic programming based model for SDVAP. A Monte Carlo Sampling Based Algorithm has been proposed to solve SDVAP. A probabilistic statement regarding the quality of the solution from the Monte Carlo sampling method is also identified by introducing a lower bound and an upper bound of the obtained optimal solution. A five-stage experimental network was introduced for demonstration of this algorithm. The computational results indicated a solution of high quality when Monte Carlo sampling based algorithm is used for solving SDVAP, strongly suggesting that these algorithms can be used for real world applications for decision making under uncertainty.

Suggested Citation

  • Fan, Wei & Machemehl, Randy, 2004. "A Multi-stage Monte Carlo Sampling Based Stochastic Programming Model for the Dynamic Vehicle Allocation Problem," 45th Annual Transportation Research Forum, Evanston, Illinois, March 21-23, 2004 208244, Transportation Research Forum.
    • Handle: RePEc:ags:ndtr04:208244
    DOI: 10.22004/ag.econ.208244
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    References listed on IDEAS

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    1. Zenios, Stavros A. & Holmer, Martin R. & McKendall, Raymond & Vassiadou-Zeniou, Christiana, 1998. "Dynamic models for fixed-income portfolio management under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 22(10), pages 1517-1541, August.
    2. Raymond K. Cheung & Chuen-Yih Chen, 1998. "A Two-Stage Stochastic Network Model and Solution Methods for the Dynamic Empty Container Allocation Problem," Transportation Science, INFORMS, vol. 32(2), pages 142-162, May.
    3. Raymond K.-M. Cheung & Warren B. Powell, 2000. "Shape -- A Stochastic Hybrid Approximation Procedure for Two-Stage Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 73-79, February.
    4. Warren B. Powell, 1986. "A Stochastic Model of the Dynamic Vehicle Allocation Problem," Transportation Science, INFORMS, vol. 20(2), pages 117-129, 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. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    7. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    8. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
    9. John R. Birge, 1985. "Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs," Operations Research, INFORMS, vol. 33(5), pages 989-1007, October.
    10. Fleten, Stein-Erik & Hoyland, Kjetil & Wallace, Stein W., 2002. "The performance of stochastic dynamic and fixed mix portfolio models," European Journal of Operational Research, Elsevier, vol. 140(1), pages 37-49, July.
    11. Kouwenberg, Roy, 2001. "Scenario generation and stochastic programming models for asset liability management," European Journal of Operational Research, Elsevier, vol. 134(2), pages 279-292, October.
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