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Dynamic programming and decomposition approaches for the single machine total tardiness problem. (English) Zbl 0627.90055

The problem of sequencing jobs on a single machine to minimize total tardiness is considered. General precedence constrained dynamic programming algorithms and special-purpose decomposition algorithms are presented. Computational results for problems with up to 100 are given.

MSC:

90B35 Deterministic scheduling theory in operations research
90C39 Dynamic programming
65K05 Numerical mathematical programming methods
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References:

[1] Elmaghraby, S. E., The one-machine sequencing problem with delay costs, Journal of Industrial Engineering, 19, 105-108 (1968)
[2] Emmons, H., One-machine sequencing to minimize certain functions of job tardiness, Operations Research, 17, 701-715 (1969) · Zbl 0176.50005
[3] Fisher, M. L., A dual algorithm for the one-machine scheduling problem, Mathematical Programming, 11, 229-251 (1976) · Zbl 0359.90039
[4] Kao, E. P.C.; Queyranne, M., On dynamic programming methods for assembly line balancing, Operations Research, 30, 375-390 (1982) · Zbl 0481.90043
[5] Lawler, E. L., A ‘pseudopolynomial’ algorithm for sequencing jobs to minimize total tardiness, Annals of Discrete Mathematics, 1, 331-342 (1977) · Zbl 0353.68071
[6] Lawler, E. L., Efficient implementation of dynamic programming algorithms for sequencing problems, (Report BW 106 (1979), Mathematisch Centrum: Mathematisch Centrum New York) · Zbl 0416.90036
[7] Lawler, E. L., A fully polynomial approximation scheme for the total tardiness problem, Operations Research Letters, 1, 207-208 (1982) · Zbl 0511.90074
[8] Picard, J. C.; Queyranne, M., The time dependent traveling salesman problem and applications to the tardiness problem in one-machine sequencing, Operations Research, 26, 88-110 (1978) · Zbl 0371.90066
[9] Pots, C. N.; Van Wassenhove, L. N., A decomposition algorithm for the single machine total tardiness problem, Operations Research Letters, 1, 177-181 (1982) · Zbl 0508.90045
[10] Rinnooy Kan, A. H.G.; Lageweg, B. J.; Lenstra, J. K., Minimizing total costs in one-machine scheduling, Operations Research, 23, 908-927 (1975) · Zbl 0324.90039
[11] Schrage, L.; Baker, K. R., Dynamic programming solution of sequencing problems with precedence constraints, Operations Research, 26, 444-449 (1978) · Zbl 0383.90054
[12] Sen, T. T.; Austin, L. N.; Ghandforoush, P., An algorithm for the single-machine sequencing problem to minimize total tardiness, IEE Transactions, 15, 363-366 (1983)
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