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A Two-Stage Stochastic Network Model and Solution Methods for the Dynamic Empty Container Allocation Problem

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  • Raymond K. Cheung

    (Department of Industrial Engineering and Engineering Management, Department of Civil and Structural Engineering, Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong)

  • Chuen-Yih Chen

    (Department of Transportation Management, National Cheng Kung University, Tainan, Taiwan, ROC)

Abstract

Containerized liner trades have been growing steadily since the globalization of world economies intensified in the early 1990s. However, these trades are typically imbalanced in terms of the numbers of inbound and outbound containers. As a result, the relocation of empty containers has become one of the major problems faced by liner operators. In this paper, we consider the dynamic empty container allocation problem where we need to reposition empty containers and to determine the number of leased containers needed to meet customers' demand over time. We formulate this problem as a two-stage stochastic network: in stage one, the parameters such as supplies, demands, and ship capacities for empty containers are deterministic; whereas in stage two, these parameters are random variables. We need to make decisions in stage one such that the total of the stage one cost and the expected stage two cost is minimized. By taking advantage of the network structure, we show how a stochastic quasi-gradient method and a stochastic hybrid approximation procedure can be applied to solve the problem. In addition, we propose some new variations of these methods that seem to work faster in practice. We conduct numerical tests to evaluate the value of the two-stage stochastic model over a rolling horizon environment and to investigate the behavior of the solution methods with different implementations.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:32:y:1998:i:2:p:142-162
    DOI: 10.1287/trsc.32.2.142
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    References listed on IDEAS

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    1. Warren B. Powell, 1986. "A Stochastic Model of the Dynamic Vehicle Allocation Problem," Transportation Science, INFORMS, vol. 20(2), pages 117-129, May.
    2. 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.
    3. Warren B. Powell, 1989. "A Review of Sensitivity Results for Linear Networks and a New Approximation to Reduce the Effects of Degeneracy," Transportation Science, INFORMS, vol. 23(4), pages 231-243, November.
    4. 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.
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