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The Assignment Problem with Seniority and Job Priority Constraints

Author

Listed:
  • Gaétan Caron

    (Ecole Polytechnique de Montréal, Montréal, Québec, Canada)

  • Pierri Hansen

    (Ecole des Hautes Études Commerciales, Montréal, Québec, Canada)

  • Brigitte Jaumard

    (Ecole Polytechnique de Montréal, Montréal, Québec, Canada)

Abstract

Consider an assignment problem in which persons are qualified for some but usually not all of the jobs. Moreover, assume persons belong to given seniority classes and jobs have given priority levels. Seniority constraints impose that the solution be such that no unassigned person can be given a job unless an assigned person with the same or higher seniority becomes unassigned. Priority constraints specify that the solution must be such that no unassigned job can become assigned without a job with the same or higher priority becoming unassigned. It is shown that: (i) adding such constraints does not reduce and may even increase the number of assigned persons in the optimal solution; (ii) using a greedy heuristic for constrained assignment (as often done in practice) may reduce the number of assigned persons by half, and (iii) an optimal solution to the assignment problem with both types of constraints can be obtained by solving a classical assignment problem with adequately modified coefficients.

Suggested Citation

  • Gaétan Caron & Pierri Hansen & Brigitte Jaumard, 1999. "The Assignment Problem with Seniority and Job Priority Constraints," Operations Research, INFORMS, vol. 47(3), pages 449-453, June.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:3:p:449-453
    DOI: 10.1287/opre.47.3.449
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    References listed on IDEAS

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    1. Ronny Aboudi & George L. Nemhauser, 1991. "Some Facets for an Assignment Problem with Side Constraints," Operations Research, INFORMS, vol. 39(2), pages 244-250, April.
    2. Joseph B. Mazzola & Alan W. Neebe, 1986. "Resource-Constrained Assignment Scheduling," Operations Research, INFORMS, vol. 34(4), pages 560-572, August.
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    Cited by:

    1. Manion Anderson & Merve Bodur & Scott Rathwell & Vahid Sarhangian, 2023. "Optimization Helps Scheduling Nursing Staff at the Long-Term Care Homes of the City of Toronto," Interfaces, INFORMS, vol. 53(2), pages 133-154, March.
    2. Volgenant, A., 2002. "Solving some lexicographic multi-objective combinatorial problems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 578-584, June.
    3. Volgenant, A., 2004. "Solving the k-cardinality assignment problem by transformation," European Journal of Operational Research, Elsevier, vol. 157(2), pages 322-331, September.
    4. Mehran Hojati, 2010. "Near-optimal solution to an employee assignment problem with seniority," Annals of Operations Research, Springer, vol. 181(1), pages 539-557, December.
    5. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.
    6. Volgenant, A., 2004. "A note on the assignment problem with seniority and job priority constraints," European Journal of Operational Research, Elsevier, vol. 154(1), pages 330-335, April.

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