Abstract
This paper considers a problem of scheduling N jobs on a single machine to minimize the maximum lateness. A partitioning of the jobs into F families is given. A set-up time is required at the start of each batch, where a batch is a largest set of contiguously scheduled jobs from the same family. We propose a single-batch heuristic in which all jobs of a family form a batch, and a double-batch heuristic in which each family is partitioned into at most two batches according to the due dates of its jobs. Both heuristics require O(N log N) time. It is shown that the single-batch heuristic has a worst-case performance ratio of 2 -1/F, whereas a composite heuristic which selects the better of the schedules generated by the single- and double-batch heuristics has a worst-case performance ratio of 5/3 for arbitrary F. Lower bounds are derived and are incorporated in a branch and bound algorithm. This algorithm uses a procedure to reduce the size of the problem, and employs a branching rule which forces pairs of jobs to lie in the same batch or in different batches. Computational tests show that the algorithm is effective in solving problems with up to 50 jobs.
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References
J. Bruno and P. Downey, Complexity of task sequencing with deadlines, set-up times and changeover costs, SIAM Journal on Computing 7(1978)393–404.
J.R. Jackson, Scheduling a production line to minimize maximum tardiness, Research Report 43, Management Science Research Project, University of California, Los Angeles, CA, 1955.
C.L. Monma and C.N. Potts, On the complexity of scheduling with batch setup times, Operations Research 37(1989)798–804.
C.N. Potts, Scheduling two job classes on a single machine, Computers and Operations Research 18(1991)411–415.
C.N. Potts and L.N. Van Wassenhove, Integrating scheduling with batching and lot-sizing: A review of algorithms and complexity, Journal of the Operational Research Society 43(1992)395–406.
J.M.J. Schutten, S.L. van de Velde and W.H.M. Zijm, Single-machine scheduling with release dates, due dates and family setup times, Management Science 42(1996)1165–1174.
S. Zdrzałka, Approximation algorithms for single-machine sequencing with delivery times and unit batch set-up times, European Journal of Operational Research 51(1991)199–209.
S. Zdrzałka, Single machine sequencing with delivery times and equal batch set-up times: 3/2-approximation algorithm, Report, Institute of Engineering Cybernetics, Technical University of Wrocław, Poland, 1991.
S. Zdrzałka, Analysis of approximation algorithms for single-machine scheduling with delivery times and sequence independent batch setup times, European Journal of Operational Research 80 (1995)371–380.
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Hariri, A., Potts, C. Single machine scheduling with batch set-up times to minimize maximum lateness. Annals of Operations Research 70, 75–92 (1997). https://doi.org/10.1023/A:1018903027868
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DOI: https://doi.org/10.1023/A:1018903027868