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Dynamic Generalized Assignment Problems with Stochastic Demands and Multiple Agent--Task Relationships

Author

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  • Konstantin Kogan
  • Eugene Khmelnitsky
  • Toshihide Ibaraki

Abstract

The assignment problem is a well-known operations research model. Its various extensions have been applied to the design of distributed computer systems, job assignment in telecommunication networks, and solving diverse location, truck routing and job shop scheduling problems. This paper focuses on a dynamic generalization of the assignment problem where each task consists of a number of units to be performed by an agent or by a limited number of agents at a time. Demands for the task units are stochastic. Costs are incurred when an agent performs a task or a group of tasks and when there is a surplus or shortage of the task units with respect to their demands. We prove that this stochastic, continuous-time generalized assignment problem is strongly NP-hard, and reduce it to a number of classical, deterministic assignment problems stated at discrete time points. On this basis, a pseudo-polynomial time combinatorial algorithm is derived to approximate the solution, which converges to the global optimum as the distance between the consecutive time points decreases. Lower bound and complexity estimates for solving the problem and its special cases are found. Copyright Springer Science+Business Media New York 2005

Suggested Citation

  • Konstantin Kogan & Eugene Khmelnitsky & Toshihide Ibaraki, 2005. "Dynamic Generalized Assignment Problems with Stochastic Demands and Multiple Agent--Task Relationships," Journal of Global Optimization, Springer, vol. 31(1), pages 17-43, January.
    • Handle: RePEc:spr:jglopt:v:31:y:2005:i:1:p:17-43
    DOI: 10.1007/s10898-004-4273-3
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    Cited by:

    1. Monnerat, Filipe & Dias, Joana & Alves, Maria João, 2019. "Fleet management: A vehicle and driver assignment model," European Journal of Operational Research, Elsevier, vol. 278(1), pages 64-75.
    2. Joseph B. Mazzola & Alan W. Neebe, 2012. "A generalized assignment model for dynamic supply chain capacity planning," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 470-485, September.

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