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A Guaranteed-Accuracy Round-off Algorithm for Cyclic Scheduling and Set Covering

Author

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  • John J. Bartholdi

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

The problem of cyclic staff scheduling is solved by a linear programming round-off heuristic for which a bound on the absolute error is established. The quality of the bound is independent of the resource requirements. Moreover, the quality of the bound improves as the matrix of resource availability approximates the property of consecutive ones. The appropriateness of the heuristic is further established by showing that cyclic staff scheduling is NP -complete.

Suggested Citation

  • John J. Bartholdi, 1981. "A Guaranteed-Accuracy Round-off Algorithm for Cyclic Scheduling and Set Covering," Operations Research, INFORMS, vol. 29(3), pages 501-510, June.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:3:p:501-510
    DOI: 10.1287/opre.29.3.501
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    Cited by:

    1. Giovanni Felici & Claudio Gentile, 2004. "A Polyhedral Approach for the Staff Rostering Problem," Management Science, INFORMS, vol. 50(3), pages 381-393, March.
    2. Saravanan Kesavan & Susan J. Lambert & Joan C. Williams & Pradeep K. Pendem, 2022. "Doing Well by Doing Good: Improving Retail Store Performance with Responsible Scheduling Practices at the Gap, Inc," Management Science, INFORMS, vol. 68(11), pages 7818-7836, November.
    3. Brusco, Michael J. & Johns, Tony R., 1996. "A sequential integer programming method for discontinuous labor tour scheduling," European Journal of Operational Research, Elsevier, vol. 95(3), pages 537-548, December.
    4. Shane N. Hall & Sheldon H. Jacobson & Edward C. Sewell, 2008. "An Analysis of Pediatric Vaccine Formulary Selection Problems," Operations Research, INFORMS, vol. 56(6), pages 1348-1365, December.
    5. Hua Ni & Hernán Abeledo, 2007. "A branch-and-price approach for large-scale employee tour scheduling problems," Annals of Operations Research, Springer, vol. 155(1), pages 167-176, November.
    6. Mesquita, Marta & Moz, Margarida & Paias, Ana & Pato, Margarida, 2015. "A decompose-and-fix heuristic based on multi-commodity flow models for driver rostering with days-off pattern," European Journal of Operational Research, Elsevier, vol. 245(2), pages 423-437.
    7. Cai, X. & Li, K. N., 2000. "A genetic algorithm for scheduling staff of mixed skills under multi-criteria," European Journal of Operational Research, Elsevier, vol. 125(2), pages 359-369, September.
    8. Easton, Fred F. & Mansour, Nashat, 1999. "A distributed genetic algorithm for deterministic and stochastic labor scheduling problems," European Journal of Operational Research, Elsevier, vol. 118(3), pages 505-523, November.
    9. Victor Reyes & Ignacio Araya, 2021. "A GRASP-based scheme for the set covering problem," Operational Research, Springer, vol. 21(4), pages 2391-2408, December.
    10. Casado Yusta, S. & Pacheco Bonrostro, J., 2003. "Estudio comparativo de diferentes estrategias metaheurísticas para la resolución del labor scheduling problem./Analisys of different methauristas for solving labor scheduling," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 21, pages 537-554, December.
    11. Michael J. Brusco & Larry W. Jacobs, 1998. "Personnel Tour Scheduling When Starting-Time Restrictions Are Present," Management Science, INFORMS, vol. 44(4), pages 534-547, April.
    12. De Bruecker, Philippe & Van den Bergh, Jorne & Beliën, Jeroen & Demeulemeester, Erik, 2015. "Workforce planning incorporating skills: State of the art," European Journal of Operational Research, Elsevier, vol. 243(1), pages 1-16.
    13. Broos Maenhout & Mario Vanhoucke, 2017. "A resource type analysis of the integrated project scheduling and personnel staffing problem," Annals of Operations Research, Springer, vol. 252(2), pages 407-433, May.
    14. S Casado & M Laguna & J Pacheco, 2005. "Heuristical labour scheduling to optimize airport passenger flows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 649-658, June.
    15. Brusco, Michael J. & Jacobs, Larry W., 1995. "Cost analysis of alternative formulations for personnel scheduling in continuously operating organizations," European Journal of Operational Research, Elsevier, vol. 86(2), pages 249-261, October.
    16. Kumar, Sameer & Arora, Sant, 1999. "Efficient workforce scheduling for a serial processing environment: a case study at Minneapolis Star Tribune," Omega, Elsevier, vol. 27(1), pages 115-127, February.
    17. Lagodimos, A. G. & Leopoulos, V., 2000. "Greedy heuristic algorithms for manpower shift planning," International Journal of Production Economics, Elsevier, vol. 68(1), pages 95-106, October.
    18. Eyjólfur Ingi Ásgeirsson & Guðríður Lilla Sigurðardóttir, 2016. "Near-optimal MIP solutions for preference based self-scheduling," Annals of Operations Research, Springer, vol. 239(1), pages 273-293, April.
    19. Zeger Degraeve & Linus Schrage, 1999. "Optimal Integer Solutions to Industrial Cutting Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 11(4), pages 406-419, November.

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