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Recent Developments in Deterministic Sequencing and Scheduling: A Survey

  • Conference paper
Deterministic and Stochastic Scheduling

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 84))

Abstract

The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. We survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. This paper is a revised version of the survey by Graham et al. (Ann. Discrete Math. 5(1979) 287–326) , with emphasis on recent developments.

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References

  • N.R. Achuthan (1980) Flow-Shop Scheduling Problems, Ph.D. Thesis, Indian Statistical Institute, Calcutta.

    Google Scholar 

  • I. Adiri, N. Hefetz (1980) Subproblems of openshop — more than two machines — schedule length problem. Operations Research, Statistics and Economics Mimeograph Series 260, Technion, Haifa.

    Google Scholar 

  • D. Adolphson (1977) Single machine job sequencing with precedence constraints. SIAM J. Comput. 6, 40–54.

    MathSciNet  MATH  Google Scholar 

  • D. Adolphson, T.C. Hu (1973) Optimal linear ordering. SIAM J. Appl. Math. 25, 403–423.

    MathSciNet  MATH  Google Scholar 

  • K.R. Baker (1974) Introduction to Sequencing and Scheduling, Wiley, New York.

    Google Scholar 

  • K.R. Baker, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan (1982) Preemptive scheduling of a single machine to minimize maximum cost subject to release dates and precedence constraints. Oper. Res., to appear.

    Google Scholar 

  • K.R. Baker, L.E. Schrage (1978) Finding an optimal sequence by dynamic programming: an extension to precedence-related tasks. Oper. Res. 26, 111–120.

    MATH  Google Scholar 

  • K.R. Baker, Z.-S. Su (1974) Sequencing with due-dates and early start times to minimize maximum tardiness. Naval Res. Logist. Quart. 21, 171–176.

    MathSciNet  MATH  Google Scholar 

  • M.S. Bakshi, S.R. Arora (1969) The sequencing problem. Management Sci. 16, B247–B263.

    Google Scholar 

  • J.W. Barnes, J.J. Brennan (1977) An improved algorithm for scheduling jobs on identical machines. AIIE Trans. 9, 25–31.

    Google Scholar 

  • L. Bianco, S. Ricciardelli (1981) Scheduling of a single machine to minimize total weighted completion time subject to release dates. Istituto di Analisi dei Sistemi ed Informatica, CNR, Rome.

    Google Scholar 

  • J. Blazewicz, J.K. Lenstra, A.H.G. Rinnooy Kan (1980) Scheduling subject to resource constraints: classification and complexity. Report BW 127, Mathematisch Centrum, Amsterdam.

    MATH  Google Scholar 

  • P. Bratley, M. Florian, P. Robillard (1975) Scheduling with earliest start and due date constraints on multiple machines. Naval Res. Logist. Quart. 22, 165–173.

    MATH  Google Scholar 

  • P. Brucker, M.R. Garey, D.S. Johnson (1977) Scheduling equal-length tasks under tree-like precedence constraints to minimize maximum lateness. Math. Oper. Res. 2, 275–284.

    MathSciNet  MATH  Google Scholar 

  • J. Bruno, E.G. Coffman, Jr., R. Sethi (1974) Scheduling independent tasks to reduce mean finishing time. Comm. ACM 17, 382–387.

    MathSciNet  MATH  Google Scholar 

  • J. Bruno, T. Gonzalez (1976) Scheduling independent tasks with release dates and due dates on parallel machines. Technical Report 213, Computer Science Department, Pennsylvania State University.

    Google Scholar 

  • J. Carlier (1980) Problème à une machine. Manuscript, Institut de programmation, Université Paris VI.

    Google Scholar 

  • J.M. Charlton, C.C. Death (1970) A generalized machine scheduling algorithm. Oper. Res. Quart. 21, 127–134.

    MATH  Google Scholar 

  • N.-F. Chen (1975) An analysis of scheduling algorithms in multiprocessing computing systems. Technical Report UIUCDCS-R-75-724, Department of Computer Science, University of Illinois at Urbana-Champaign.

    Google Scholar 

  • N.-F. Chen, C.L. Liu (1975) On a class of scheduling algorithms for multiprocessors computing systems. In: T.-Y. Feng (ed.) (1975) Parallel Processing, Lecture Notes in Computer Science 24, Springer, Berlin, 1–16.

    Google Scholar 

  • Y. Cho, S. Sahni (1978) Preemptive scheduling of independent jobs with release and due times on open, flow and job shops. Technical Report 78-5, Computer Science Department, University of Minnesota, Minneapolis.

    Google Scholar 

  • E.G. Coffman, Jr. (ed.) (1976) Computer and Job-Shop Scheduling Theory, Wiley, New York.

    MATH  Google Scholar 

  • E.G. Coffman, Jr., M.R. Garey, D.S. Johnson (1978) An application of bin-packing to multiprocessor scheduling. SIAM J. Comput. 7, 1–17.

    MathSciNet  MATH  Google Scholar 

  • E.G. Coffman, Jr., R.L. Graham (1972) Optimal scheduling for two-processor systems. Acta Informat. 1, 200–213.

    MathSciNet  Google Scholar 

  • R.W. Conway, W.L. Maxwell, L.W. Miller (1967) Theory of Scheduling, Addison-Wesley, Reading, Mass.

    MATH  Google Scholar 

  • S.A. Cook (1971) The complexity of theorem-proving procedures. Proc. 3rd Annual ACM Symp. Theory of Computing, 151–158.

    Google Scholar 

  • E.W. Davis (1966) Resource allocation in project network models-a survey. J. Indust. Engrg. 17,177–188.

    Google Scholar 

  • E.W. Davis (1973) Project scheduling under resource constraints-historical review and categorization of procedures. AIIE Trans. 5, 297–313.

    Google Scholar 

  • J. Day, M.P. Hottenstein (1970) Review of scheduling research. Naval Res. Logist. Quart. 17, 11–39.

    MATH  Google Scholar 

  • D. Dolev (1981) Scheduling wide graphs. Unpublished manuscript.

    Google Scholar 

  • W.L. Eastman, S. Even, I.M. Isaacs (1964) Bounds for the optimal scheduling of njobs on m processors. Management Sci. 11, 268–279.

    MathSciNet  Google Scholar 

  • S.E. Elmaghraby, S.H. Park (1974) Scheduling jobs on a number of identical machines. AIIE Trans. 6,1–12.

    MathSciNet  Google Scholar 

  • H. Emmons (1969) One-machine sequencing to minimize certain functions of job tardiness. Oper. Res. 17,701–715.

    MathSciNet  MATH  Google Scholar 

  • M.L. Fisher (1976) A dual algorithm for the one-machine scheduling problem. Math. Programming 11, 229–251.

    MathSciNet  Google Scholar 

  • M.L. Fisher, B.J. Lageweg, J.K. Lenstra, A.H.G. Rinnooy Kan (1981) Surrogate duality relaxation for job shop scheduling. Report, Mathematisch Centrum, Amsterdam.

    MATH  Google Scholar 

  • M. Fujii, T. Kasami, K. Ninomiya (1969,1971) Optimal sequencing of two equivalent processors. SIAM J. Appl. Math. 17, 784–789; Erratum. 20, 141.

    MathSciNet  Google Scholar 

  • H.N. Gabow (1980) An almost-linear algorithm for two-processor scheduling. Technical Report CU-CS-169-80, Department of Computer Science, University of Colorado, Boulder.

    Google Scholar 

  • M.R. Garey (-) Unpublished.

    Google Scholar 

  • M.R. Garey, R.L. Graham, D.S. Johnson (1978) Performance guarantees for scheduling algorithms. Oper. Res. 26, 3–21.

    MathSciNet  MATH  Google Scholar 

  • M.R. Garey, D.S. Johnson (1976) Scheduling tasks with nonuniform deadlines on two processors. J. Assoc. Comput. Mach. 23, 461–467.

    MathSciNet  MATH  Google Scholar 

  • M.R. Garey, D.S. Johnson (1977) Two-processor scheduling with start-time s and deadlines, SIAM J. Comput. 6, 416–426.

    MathSciNet  MATH  Google Scholar 

  • M.R. Garey, D.S. Johnson (1979) Computers and Intractability: a Guide to the Theory of NP-Completeness, Freeman, San Francisco.

    MATH  Google Scholar 

  • M.R. Garey, D.S. Johnson (1981) Approximation algorithms for bin packing problems: a survey. In: G. Ausiello, M. Lucertini (eds.) (1981) Analysis and Design of Algorithms in Combinatorial Optimization, CISM Courses and Lectures 266, Springer, Vienna, 147–172.

    Google Scholar 

  • M.R. Garey, D.S. Johnson, R. Sethi (1976) The complexity of flow-shop and jobshop scheduling. Math. Oper. Res. 1,117–129.

    MathSciNet  MATH  Google Scholar 

  • M.R. Garey, D.S. Johnson, B.B. Simons, R.E. Tarjan (1981A) Scheduling unit-time tasks with arbitrary release times and deadlines. SIAM J. Comput. 10, 256–269.

    MathSciNet  MATH  Google Scholar 

  • M.R. Garey, D.S. Johnson, R.E. Tarjan, M. Yannakakis (1981B) Scheduling opposing forests. Unpublished manuscript.

    Google Scholar 

  • L. Gelders, P.R. Kleindorfer (1974) Coordinating aggregate and detailed scheduling decisions in the one-machine job shop: part I. Theory. Oper. Res. 22, 46–60.

    MathSciNet  MATH  Google Scholar 

  • L. Gelders, P.R. Kleindorfer (1975) Coordinating aggregate and detailed scheduling in the one-machine job shop: II — computation and structure. Oper. Res. 23, 312–324.

    MathSciNet  MATH  Google Scholar 

  • W.S. Gere (1966) Heuristics in job shop scheduling. Management Sci. 13,167–190.

    Google Scholar 

  • B. Giffler, G.L. Thompson (1960) Algorithms for solving production-scheduling problems. Oper. Res. 8, 487–503.

    MathSciNet  MATH  Google Scholar 

  • P.C. Gilmore, R.E. Gomory (1964) Sequencing a one-state variable machine: a solvable case of the traveling salesman problem. Oper. Res. 12, 655–679.

    MathSciNet  MATH  Google Scholar 

  • T. Gonzalez (1977) Optimal mean finish time preemptive schedules. Technical Report 220, Computer Science Department, Pennsylvania State University.

    Google Scholar 

  • T. Gonzalez (1979A) A note on open shop preemptive schedules. IEEE Trans. Computers C-28, 782–786.

    Google Scholar 

  • T. Gonzalez (1979B) NP-Hard shop problems. Report CS-79-35, Department of Computer Science, Pennsylvania State University, University Park.

    Google Scholar 

  • T. Gonzalez, O.H. Ibarra, S. Sahni (1977) Bounds for LPT schedules on uniform processors. SIAM J. Comput. 6, 155–166.

    MathSciNet  MATH  Google Scholar 

  • T. Gonzalez, D.B. Johnson (1980) A new algorithm for preemptive scheduling of trees. J. Assoc. Comput. Mach. 27, 287–312.

    MathSciNet  MATH  Google Scholar 

  • T. Gonzalez, E.L. Lawler, S. Sahni (1981) Optimal preemptive scheduling of a fixed number of unrelated processors in linear time. To appear.

    Google Scholar 

  • T. Gonzalez, S. Sahni (1976) Open shop scheduling to minimize finish time. J. Assoc. Comput. Mach. 23, 665–679.

    MathSciNet  MATH  Google Scholar 

  • T. Gonzalez, S. Sahni (1978A) Flowshop and jobshop schedules: complexity and approximation. Oper. Res. 26, 36–52.

    MathSciNet  MATH  Google Scholar 

  • T. Gonzalez, S. Sahni (1978B) Preemptive scheduling of uniform processor systems. J. Assoc. Comput. Mach. 25, 92–101.

    MathSciNet  MATH  Google Scholar 

  • D.K. Goyal (1977) Non-preemptive scheduling of unequal execution time tasks on two identical processors. Technical Report CS-77-039, Computer Science Department, Washington State University, Pullman.

    Google Scholar 

  • R.L. Graham (1966) Bounds for certain multiprocessing anomalies. Bell System Tech. J. 45, 1563–1581.

    Google Scholar 

  • R.L. Graham (1969) Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 263–269.

    Google Scholar 

  • R.L. Graham (-) Unpublished.

    Google Scholar 

  • R.L. Graham, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 5, 287–326.

    MathSciNet  MATH  Google Scholar 

  • J.N.D. Gupta, S.S. Reddi (1978) Improved dominance conditions for the three-machine flowshop scheduling problem. Oper. Res. 26, 200–203.

    MathSciNet  MATH  Google Scholar 

  • A.M.A. Hariri, C.N. Potts (1981) An algorithm for single machine sequencing with release dates to minimise total weighted completion time. Report BW 143, Mathematisch Centrum, Amsterdam.

    Google Scholar 

  • N. Hefetz, I. Adiri (1979) An efficient optimal algorithm for the two-machines, unit-time, job-shop, schedule-length, problem. Operations Research, Statistics and Economics Mimeograph Series 237, Technion, Haifa.

    Google Scholar 

  • W.A. Horn (1972) Single-machine job sequencing with treelike precedence ordering and linear delay penalties. SIAM J. Appl. Math. 23, 189–202.

    MathSciNet  MATH  Google Scholar 

  • W.A. Horn (1973) Minimizing average flow time with parallel machines. Oper. Res. 21, 846–847.

    MATH  Google Scholar 

  • W.A. Horn (1974) Some simple scheduling algorithms. Naval Res. Logist. Quart. 21, 177–185.

    MathSciNet  MATH  Google Scholar 

  • E. Horowitz, S. Sahni (1976) Exact and approximate algorithms for scheduling nonidentical processors. J. Assoc. Comput. Mach. 23, 317–327.

    MathSciNet  MATH  Google Scholar 

  • E.C. Horvath, S. Lam, R. Sethi (1977) A level algorithm for preemptive scheduling. J. Assoc. Comput. Mach. 24, 32–43.

    MathSciNet  MATH  Google Scholar 

  • N.C. Hsu (1966) Elementary proof of Hu’s theorem on isotone mappings. Proc. Amer. Math. Soc. 17, 111–114.

    MathSciNet  MATH  Google Scholar 

  • T.C. Hu (1961) Parallel sequencing and assembly line problems. Oper. Res. 9, 841–848.

    Google Scholar 

  • O.H. Ibarra, C.E. Kim (1976) On two-processor scheduling of one-or two-unit time tasks with precedence constraints. J. Cybernet. 5, 87–109.

    MathSciNet  Google Scholar 

  • O.H. Ibarra, C.E. Kim (1977) Heuristic algorithms for scheduling independent tasks on nonidentical processors. J. Assoc. Comput. Mach. 24, 280–289.

    MathSciNet  MATH  Google Scholar 

  • O.H. Ibarra, C.E. Kim (1978) Approximation algorithms for certain scheduling problems. Math. Oper. Res. 3,197–204.

    MathSciNet  MATH  Google Scholar 

  • E. Ignall, L. Schrage (1965) Application of the branch-and-bound technique to some flow-shop scheduling problem. Oper. Res. 13, 400–412.

    MathSciNet  Google Scholar 

  • J.R. Jackson (1955) Scheduling a production line to minimize maximum tardiness. Research Report 43, Management Science Research Project, University of California, Los Angeles.

    Google Scholar 

  • J.R. Jackson (1956) An extension of Johnson’s results on job lot scheduling. Naval Res. Logist. Quart. 3, 201–203.

    Google Scholar 

  • J.M. Jaffe (1979) Efficient scheduling of tasks without full use of processor resources. Report MIT/LCS/TM-122, Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge.

    Google Scholar 

  • J.M. Jaffe (1980) An analysis of preemptive multiprocessor job scheduling. Math. Oper. Res. 5, 415–421.

    MathSciNet  MATH  Google Scholar 

  • S.M. Johnson (1954) Optimal two-and three-stage production schedules with setup times included. Naval Res. Logist. Quart. 1, 61–68.

    Google Scholar 

  • S.M. Johnson (1958) Discussion: sequencing n jobs on two machines with arbitrary time lags. Management Sci. 5, 299–303.

    Google Scholar 

  • R.M. Karp (1972) Reducibility among combinatorial problems. In: R. E. Miller, J.W. Thatcher (eds.) (1972) Complexity of Computer Computations, Plenum Press, New York, 85–103.

    Google Scholar 

  • R.M. Karp (1975) On the computational complexity of combinatorial problems. Networks 5, 45–68.

    MathSciNet  MATH  Google Scholar 

  • L.G. Khachiyan (1979) A polynomial algorithm in linear programming. Soviet Math. Dokl. 20, 191–194.

    MATH  Google Scholar 

  • H. Kise, T. Ibaraki, H. Mine (1978) A solvable case of the one-machine scheduling problem with ready and due times. Oper. Res. 26, 121–126.

    MathSciNet  MATH  Google Scholar 

  • M. Kunde (1976) Beste Schranken beim LP-Scheduling. Bericht 7603, Institut für Informatik und Praktische Mathematik, Universität Kiel.

    Google Scholar 

  • J. Labetoulle, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan (1979) Preemptive scheduling of uniform machines subject to release dates. Report BW 99, Mathematisch Centrum, Amsterdam.

    Google Scholar 

  • B.J. Lageweg, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan (1981A) Computer aided complexity classification of combinatorial problems. Report BW 137, Mathematisch Centrum, Amsterdam.

    MATH  Google Scholar 

  • B.J. Lageweg, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan (1981B) Computer aided complexity classification of deterministic scheduling problems. Report BW 138, Mathematisch Centrum, Amsterdam.

    MATH  Google Scholar 

  • B.J. Lageweg, J.K. Lenstra, A.H.G. Rinnooy Kan (1976) Minimizing maximum lateness on one machine: computational experience and some applications. Statist. Neerlandica 30, 25–41.

    MathSciNet  MATH  Google Scholar 

  • B.J. Lageweg, J.K. Lenstra, A.H.G. Rinnooy Kan (1977) Job-shop scheduling by implicit enumeration. Management Sci. 24, 441–450.

    MathSciNet  MATH  Google Scholar 

  • B.J. Lageweg, J.K. Lenstra, A.H.G. Rinnooy Kan (1978) A general bounding scheme for the permutation flow-shop problem. Oper. Res. 26, 53–67.

    MATH  Google Scholar 

  • S. Lam, R. Sethi (1977) Worst case analysis of two scheduling algorithms. SIAM J. Comput. 6, 518–536.

    MathSciNet  MATH  Google Scholar 

  • E.L. Lawler (1973) Optimal sequencing of a single machine subject to precedence constraints. Management Sci, 19, 544–546.

    MATH  Google Scholar 

  • E.L. Lawler (1976A) Sequencing to minimize the weighted number of tardy jobs. RAIRO Rech. Opér. 10.5 Suppl. 27–33.

    MathSciNet  Google Scholar 

  • E.L. Lawler (1976B) Combinatorial Optimization: Networks and Ma-troids, Holt, Rinehart and Winston, New York.

    Google Scholar 

  • E.L. Lawler (1977) A “pseudopolynomial” algorithm for sequencing jobs to minimize total tardiness. Ann. Discrete Math. 1, 331–342.

    MathSciNet  Google Scholar 

  • E.L. Lawler (1978) Sequencing jobs to minimize total weighted completion time subject to precedence constraints. Ann. Discrete Math. 2, 75–90.

    MathSciNet  MATH  Google Scholar 

  • E.L. Lawler (1980) Preemptive scheduling of precedence-constrained jobs on parallel machines. Report BW 132, Mathematisch Centrum, Amsterdam.

    Google Scholar 

  • E.L. Lawler (1981) Preemptive scheduling of uniform parallel machines to minimize the number of late jobs. Report, Mathematisch Centrum, Amsterdam, to appear.

    Google Scholar 

  • E.L. Lawler (-) Unpublished.

    Google Scholar 

  • E.L. Lawler, J. Labetoulle (1978) On preemptive scheduling of unrelated parallel processors by linear programming. J. Assoc. Comput. Mach. 25, 612–619.

    MathSciNet  MATH  Google Scholar 

  • E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan (1981) Minimizing maximum lateness in a two-machine open shop. Math. Oper. Res. 6, 153–158.

    MathSciNet  MATH  Google Scholar 

  • E.L. Lawler, C.U. Martel (1980) Computing “polymatroidal” network flows. Research Memorandum ERL M80/52, Electronics Research Laboratory, University of California, Berkeley.

    Google Scholar 

  • E.L. Lawler, J.M. Moore (1969) A functional equation and its application to resource allocation and sequencing problems. Management Sci. 16,77–84.

    MATH  Google Scholar 

  • J.K. Lenstra (1977) Sequencing by Enumerative Methods, Mathematical Centre Tracts 69, Mathematisch Centrum, Amsterdam.

    MATH  Google Scholar 

  • J.K. Lenstra (-) Unpublished.

    Google Scholar 

  • J.K. Lenstra, A.H.G. Rinnooy Kan (1978) Complexity of scheduling under precedence constraints. Oper. Res. 26, 22–35.

    MathSciNet  MATH  Google Scholar 

  • J.K. Lenstra, A.H.G. Rinnooy Kan (1979) Computational complexity of discrete optimization problems. Ann. Discrete Math. 4, 121–140.

    MathSciNet  MATH  Google Scholar 

  • J.K. Lenstra, A.H.G. Rinnooy Kan (1980) Complexity results for scheduling chains on a single machine. European J. Oper. Res. 4, 270–275.

    MathSciNet  MATH  Google Scholar 

  • J.K. Lenstra, A.H.G. Rinnooy Kan, P. Brucker (1977) Complexity of machine scheduling problems. Ann. Discrete Math. 1, 343–362.

    MathSciNet  Google Scholar 

  • C.L. Liu (1972) Optimal scheduling on multi-processor computing systems. Proc. 13th Annual IEEE Symp. Switching and Automata Theory, 155-160.

    Google Scholar 

  • C.L. Liu (1976) Deterministic job scheduling in computing systems. Department of Computer Science, University of Illinois at Urbana-Champaign.

    Google Scholar 

  • J.W.S. Liu, C.L. Liu (1974A) Bounds on schedulling algorithms for heterogeneous computing systems. In: J.L. Rosenfeld (ed.) (1974) Information Processing 74, North-Holland, Amsterdam, 349–353.

    Google Scholar 

  • J.W.S. Liu, C.L. Liu (1974B) Bounds on scheduling algorithms for heterogeneous computing systems. Technical Report UIUCDCS-R-74-632, Department of Computer Science, University of Illinois at Urbana-Champaign, 68 pp.

    Google Scholar 

  • J.W.S. Liu, C.L. Liu (1974C) Performance analysis of heterogeneous multi-processor computing systems. In: E. Gelenbe, R. Mahl (eds.) (1974) Computer Architectures and Networks, North-Holland, Amsterdam, 331–343.

    Google Scholar 

  • C. Martel (1981) Scheduling uniform machines with release times, deadlines and due times. J. Assoc.Comput. Mach., to appear.

    Google Scholar 

  • G.B. Mcmahon (1969) Optimal production schedules for flow shops. Canad. Oper. Res. Soc. J. 7, 141–151.

    MathSciNet  Google Scholar 

  • G.B. McMahon (1971) A Study of Algorithms for Industrial Scheduling Problems, Ph.D. Thesis, University of New South Wales, Kensington.

    Google Scholar 

  • G.B. McMahon, M. Florian (1975) On scheduling with ready times and due dates to minimize maximum lateness. Oper. Res. 23, 475–482.

    MATH  Google Scholar 

  • R. McNaughton (1959) Scheduling with deadlines and loss functions. Management Sci. 6, 1–12.

    MathSciNet  MATH  Google Scholar 

  • L.G. Mitten (1958) Sequencing njobs on two machines with arbitrary time lags. Management Sci. 5, 293–298.

    MathSciNet  Google Scholar 

  • C.L. Monma (1980) Sequencing to minimize the maximum job cost. Oper. Res. 28, 942–951.

    MathSciNet  MATH  Google Scholar 

  • C.L. Monma, A.H.G. Rinnooy Kan (1981) Efficiently solvable special cases of the permutation flow-shop problem. Report 8105, Erasmus University, Rotterdam.

    Google Scholar 

  • C.L. Monma, J.B. Sidney (1979) Sequencing with series-parallel precedence constraints. Math. Oper. Res. 4, 215–224.

    MathSciNet  MATH  Google Scholar 

  • J.M. Moore (1968) An njob, one machine sequencing algorithm for minimizing the number of late jobs. Management Sci. 15, 102–109.

    MATH  Google Scholar 

  • R.R. Muntz, E.G. Coffman, Jr. (1969) Optimal preemptive scheduling on two-processor systems. IEEE Trans. Computers C-18, 1014–1020.

    Google Scholar 

  • R.R. Muntz, E.G. Coffman, Jr. (1970) Preemptive scheduling of real time tasks on multiprocessor systems. J. Assoc. Comput. Mach. 17, 324–338.

    MathSciNet  MATH  Google Scholar 

  • J.F. Muth, G.L. Thompson (eds.) (1963) Industrial Scheduling, Prentice-Hall, Englewood Cliffs, N.J., 236.

    Google Scholar 

  • I. Nabeshima (1963) Sequencing on two machines with start lag and stop lag. J. Oper. Res. Soc. Japan 5, 97–101.

    Google Scholar 

  • S.S. Panwalkar, W. Iskander (1977) A survey of scheduling rules. Oper. Res. 25, 45–61.

    MathSciNet  MATH  Google Scholar 

  • C.H. Papadimitriou, P.C. Kanellakis (1980) Flowshop scheduling with limited temporary storage. J. Assoc. Comput. Mach. 27, 533–549.

    MathSciNet  MATH  Google Scholar 

  • J. Piehler (1960) Ein Beitrag zum Reihenfolgeproblem. Unternehmensforschung 4, 138–142.

    Google Scholar 

  • C.N. Potts (1980A) An adaptive branching rule for the permutation flow-shop problem. European J. Oper. Res. 5, 19–25.

    MathSciNet  MATH  Google Scholar 

  • C.N. Potts (1980B) Analysis of a heuristic for one machine sequencing with release dates and delivery times. Oper. Res. 28,1436–1441.

    MathSciNet  MATH  Google Scholar 

  • C.N. Potts (-) Unpublished.

    Google Scholar 

  • S.S. Reddi, C.V. Ramamoorthy (1972) On the flow-shop sequencing problem with no wait in process. Oper. Res. Quart. 23, 323–331.

    MATH  Google Scholar 

  • G. Rinaldi, A. Sassano (1977) On a job scheduling problem with different ready times: some properties and a new algorithm to determine the optimal solution. Report R.77-24, Istituto di Automatica, Università di Roma.

    Google Scholar 

  • A.H.G. Rinnooy Kan (1976) Machine Scheduling Problems: Classification, Complexity and Computations, Nijhoff, The Hague.

    Google Scholar 

  • A.H.G. Rinnooy Kan, B.J. Lageweg, J.K. Lenstra (1975) Minimizing total costs in one-machine scheduling. Oper. Res. 23, 908–927.

    MathSciNet  MATH  Google Scholar 

  • P. Rosenfeld (-) Unpublished.

    Google Scholar 

  • M.H. Rothkopf (1966) Scheduling independent tasks on parallel processors. Management Sci. 12, 437–447.

    MathSciNet  Google Scholar 

  • B. Roy, B. Sussmann (1964) Les problèmes d’ordonnancement avec contraintes disjonctives. Note DS no. 9 bis, SEMA, Montrouge.

    Google Scholar 

  • S. Sahni (1976) Algorithms for scheduling independent tasks. J. Assoc. Comput. Mach. 23,116–127.

    MathSciNet  MATH  Google Scholar 

  • S. Sahni, Y. Cho (1979A) Complexity of scheduling jobs with no wait in process. Math. Oper. Res, 4, 448–457.

    MathSciNet  MATH  Google Scholar 

  • S. Sahni, Y. Cho (1979B) Nearly on line scheduling of a uniform processor system with release times. SIAM J. Comput. 8, 275–285.

    MathSciNet  MATH  Google Scholar 

  • S. Sahni, Y. Cho (1980) Scheduling independent tasks with due times on a uniform processor system. J. Assoc. Comput. Mach. 27, 550–563.

    MathSciNet  Google Scholar 

  • R. Sethi (1976A) Algorithms for minimal-length schedules. In: [Coffman 1976], 51-99.

    Google Scholar 

  • R. Sethi (1976B) Scheduling graphs on two processors. SIAM J. Comput. 5, 73–82.

    MathSciNet  Google Scholar 

  • R. Sethi (1977) On the complexity of mean flow time scheduling. Math. Oper. Res. 2, 320–330.

    MathSciNet  MATH  Google Scholar 

  • J. Shwimer (1972) On the N-job, one-machine, sequence-independent scheduling problem with tardiness penalties: a branch-and-bound solution. Management Sci. 18, B301–313.

    MathSciNet  Google Scholar 

  • J.B. Sidney (1973) An extension of Moore’s due date algorithm. In: S.E. Elmaghraby (ed.) (1973) Symposium on the Theory of Scheduling and its Applications, Lecture Notes in Economics and Mathematical Systems 86, Springer, Berlin, 393–398.

    Google Scholar 

  • J.B. Sidney (1975) Decomposition algorithms for single-machine sequencing with precedence relations and deferral costs. Oper. Res. 23, 283–298.

    MathSciNet  MATH  Google Scholar 

  • J.B. Sidney (1979) The two-machine maximum flow time problem with series parallel precedence relations. Oper. Res. 27, 782–791.

    MathSciNet  MATH  Google Scholar 

  • B. Simons (1978) A fast algorithm for single processor scheduling. Proc. 19th Annual IEEE Symp. Foundations of Computer Science, 246-252.

    Google Scholar 

  • B. Simons (1980) A fast algorithm for multiprocessor scheduling. Proc. 21st Annual IEEE Symp. Foundations of Computer Science, 50-53.

    Google Scholar 

  • M.L. Smith, S.S. Panwalkar, R.A. Dudek (1975) Flow shop sequencing with ordered processing time matrices. Management Sci. 21, 544–549.

    MathSciNet  MATH  Google Scholar 

  • M.L. Smith, S.S. Panwalkar, R.A. Dudek (1976) Flow shop sequencing problem with ordered processing time matrices: a general case. Naval Res. Logist. Quart. 23, 481–486.

    MathSciNet  MATH  Google Scholar 

  • W.E. Smith (1956) Various optimizers for single-stage production. Naval Res. Logist. Quart. 3, 59–66.

    MathSciNet  Google Scholar 

  • H.I. Stern (1976) Minimizing makespan for independent jobs on non-identical parallel machines—an optimal procedure. Working Paper 2/75, Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva.

    Google Scholar 

  • W. Szwarc (1968) On some sequencing problems. Naval Res. Logist. Quart. 15, 127–155.

    MATH  Google Scholar 

  • W. Szwarc (1971) Elimination methods in the m×n sequencing problem. Naval Res. Logist. Quart. 18, 295–305.

    MathSciNet  MATH  Google Scholar 

  • W. Szwarc (1973) Optimal elimination methods in the m×n sequencing problem. Oper. Res. 21, 1250–1259.

    MathSciNet  MATH  Google Scholar 

  • W. Szwarc (1978) Dominance conditions for the three-machine flow-shop problem. Oper. Res. 26, 203–206.

    MathSciNet  MATH  Google Scholar 

  • J.D. Ullman (1975) ZVP-Complete scheduling problems. J. Comput. System Sci. 10, 384–393.

    MathSciNet  MATH  Google Scholar 

  • J.D. Ullman (1976) Complexity of sequencing problems. In: [Coffman 1976], 139-164.

    Google Scholar 

  • M.K. Warmuth (1980) M Processor unit-execution-time scheduling reduces to M-1 weakly connected components. M.S. Thesis, Department of Computer Science, University of Colorado, Boulder.

    Google Scholar 

  • D.A. Wismer (1972) Solution of the flowshop-scheduling problem with no intermediate queues. Oper. Res. 20, 689–697.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University of California, Berkeley, USA

    E. L. Lawler

  2. Mathematisch Centrum, Amsterdam, The Netherlands

    J. K. Lenstra

  3. Erasmus University, Rotterdam, The Netherlands

    A. H. G. Rinnooy Kan

Authors
  1. E. L. Lawler
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  2. J. K. Lenstra
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  3. A. H. G. Rinnooy Kan
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada

    M. A. H. Dempster

  2. Balliol College, Oxford, England

    M. A. H. Dempster

  3. Mathematisch Centrum, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands

    J. K. Lenstra

  4. Econometric Institute H2-11, Erasmus University, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    A. H. G. Rinnooy Kan

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© 1982 D. Reidel Publishing Company

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Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G. (1982). Recent Developments in Deterministic Sequencing and Scheduling: A Survey. In: Dempster, M.A.H., Lenstra, J.K., Rinnooy Kan, A.H.G. (eds) Deterministic and Stochastic Scheduling. NATO Advanced Study Institutes Series, vol 84. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7801-0_3

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  • DOI: https://doi.org/10.1007/978-94-009-7801-0_3

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