Abstract
We consider the problem of minimizing the weighted number of tardy jobs on a single machine where each job is also subject to a deadline that cannot be violated. We propose an exact method based on a compact integer linear programming formulation of the problem and an effective reduction procedure that allows to solve to optimality instances with up to 30,000 jobs in size, and up to 50,000 jobs in size for the special deadline-free case.
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Baptiste, Ph., Le Pape, C., & Péridy, L. (1998). Global constraints for partial CSPs: a case-study of resource and due date constraint. In LNCS (Proc. of CP) (Vol. 1520, pp. 87–101).
Dauzère-Pérès, S., & Sevaux, M. (2003). Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine. Naval Research Logistics, 50, 273–288.
Dauzère-Pérès, S., & Sevaux, M. (2004). An exact method to minimize the number of tardy jobs in single machine scheduling. Journal of Scheduling, 7, 405–420.
Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annuals of Discrete Mathematics, 5, 287–326.
Hariri, A. M. A., & Potts, C. N. (1994). Single machine scheduling with deadlines to minimize the weighted number of tardy jobs. Management Science, 40(12), 1712–1719.
Karp, R. M. (1972). Reducibility among combinatorial problems. In R. E. Miller & J. W. Thatcher (Eds.), Complexity of Computations (pp. 85–103). New York: Plenum.
Lawler, E. L. (1983). Scheduling a single machine to minimize the number of late jobs (Report CSD-83-139). EECS Department, University of California, Berkeley. Available from http://techreports.lib.berkeley.edu.
Lenstra, J. K., Rinnooy Kan, A. H. G., & Brucker, P. (1977). Complexity of machine scheduling problems. Annals of Discrete Mathematics, 1, 343–362.
Linderoth, J. T., & Savelsbergh, M. W. P. (1999). A computational study of search strategies for mixed integer programming. INFORMS Journal on Computing, 11(2), 173–187.
Martello, S., & Toth, P. (2003). An exact algorithm for the two-constraint 0–1 knapsack problem. Operations Research, 51, 826–835.
M’Hallah, R., & Bulfin, R. L. (2003). Minimizing the weighted number of tardy jobs on a single machine. European Journal of Operational Research, 145(1), 45–56.
M’Hallah, R., & Bulfin, R. L. (2007). Minimizing the weighted number of tardy jobs on a single machine with release dates. European Journal of Operational Research, 176, 727–744.
Moore, J. M. (1968). An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Science, 15, 102–109.
Potts, C. N., & Van Wassenhove, L. M. (1988). Algorithms for scheduling a single machine to minimize the weighted number of late jobs. Management Science, 34(7), 843–858.
T’kindt, V., Della Croce, F., & Bouquard, J.-L. (2007). Enumeration of Pareto optima for a flowshop scheduling problem with two criteria. INFORMS Journal on Computing, 19(1), 64–72.
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Baptiste, P., Della Croce, F., Grosso, A. et al. Sequencing a single machine with due dates and deadlines: an ILP-based approach to solve very large instances. J Sched 13, 39–47 (2010). https://doi.org/10.1007/s10951-008-0092-6
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DOI: https://doi.org/10.1007/s10951-008-0092-6