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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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[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, () · 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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