Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey

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The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. In this paper 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. We indicate some problems for future research and include a selective bibliography.

References (149)

  • S.M. Johnson

    Optimal two- and three-stage production schedules with setup times included

    Naval Res. Logist. Quart.

    (1954)
  • E.L. Lawler and J. Labetoulle (1978). On preemptive scheduling of unrelated parallel processors, J. Assoc. Comput....
  • E.L. Lawler et al.

    A functional equation and its application to resource allocation and sequencing problems

    Management Sci.

    (1969)
  • D. Adolphson

    Single machine job sequencing with precedence constraints

    SIAM J. Comput.

    (1977)
  • D. Adolphson et al.

    Optimal linear ordering

    SIAM J. Appl. Math.

    (1973)
  • A.V. Aho et al.

    The transitive reduction of a directed graph

    SIAM J. Comput.

    (1972)
  • J.L. Baer

    Optimal scheduling on two processors with different speeds

  • K.R. Baker

    Introduction to Sequencing and Scheduling

    (1974)
  • K.R. Baker et al.

    Scheduling with parallel processors and linear delay costs

    Naval Res. Logist. Quart.

    (1973)
  • K.R. Baker et al.

    Finding an optimal sequence by dynamic programming: an extension to precedence-related tasks

    Operations Res.

    (1978)
  • K.R. Baker et al.

    Sequencing with due-dates and early start times to minimize maximum tardiness

    Naval Res. Logist. Quart.

    (1974)
  • M.S. Bakshi et al.

    The sequencing problem, Management Sci.

    (1969)
  • J.W. Barnes et al.

    An improved algorithm for scheduling jobs on identical machines

    AIIE Trans.

    (1977)
  • P. Bratley et al.

    Scheduling with earliest start and due date constraints on multiple machines

    Naval Res. Logist. Quart.

    (1975)
  • P. Brucker et al.

    Scheduling equal-length tasks under treelike precedence constraints to minimize maximum lateness

    Math. Operations Res.

    (1977)
  • J. Bruno et al.

    Scheduling independent tasks to reduce mean finishing time

    Comm. ACM

    (1974)
  • J. Bruno and T. Gonzalez (1976), Scheduling independent tasks with release dates and due dates on parallel machines,...
  • F. Burns and J. Rooker (1976), 3xn Flow-shops with convex external stage time dominance (unpublished...
  • A.K. Chandra et al.

    Worst-case analysis of a placement algorithm related to storage allocation

    SIAM J. Comput.

    (1975)
  • J.M. Charlton et al.

    A generalized machine scheduling algorithm

    Operational Res. Quart.

    (1970)
  • N.-F. Chen (1975), An analysis of scheduling algorithms in multiprocessing computing systems, Technical Report...
  • N.-F. Chen et al.

    On a class of scheduling algorithms for multiprocessors computing systems

  • E.G. Coffman, Jr., M.F. Garey and D.S. Johnson (1978), An application of bin-packing to multiprocessor scheduling, SIAM...
  • E.G. Coffman et al.

    Optimal scheduling for two-processor systems

    Acta Informat.

    (1972)
  • R.W. Conway et al.

    Theory of Scheduling

    (1967)
  • E.W. Davis

    Resource allocation in project network models ? a survey

    J. Indust. Engrg.

    (1966)
  • E.W. Davis

    Project scheduling under resource constraints ? historical review and categorization of procedures

    AIIE Trans.

    (1973)
  • J. Day et al.

    Review of scheduling research

    Naval Res. Logist. Quart.

    (1970)
  • P.J. Denning et al.

    A note on subexpression ordering in the execution of arithmetic expressions

    Comm. ACM

    (1973)
  • W.L. Eastman et al.

    Bounds for the optimal scheduling of n jobs on m processors

    Management Sci.

    (1964)
  • S.E. Elmaghraby et al.

    Scheduling jobs on a number of identical machines

    AIIE Trans.

    (1974)
  • M.L. Fisher

    Optimal solution of scheduling problems using Lagrange multipliers

    part I, Operations Res.

    (1973)
  • M.L. Fisher

    A dual algorithm for the one-machine scheduling problem

    Math. Programming

    (1976)
  • M. Fujii et al.

    Optimal sequencing of two equivalent processors

    SIAM J. Appl. Math.

    (1969)

    Erratum.

    (1971)
  • M.R. Garey (−),...
  • M.R. Garey et al.

    Bounds for multiprocessor scheduling with resource constraints

    SIAM J. Comput.

    (1975)
  • M.R. Garey et al.

    Performance guarantees for scheduling algorithms

    Operations Res.

    (1978)
  • M.R. Garey, R.L. Graham and D.S. Johnson (−), Unpublished. M.R. Garey, R.L. Graham, D.S. Johnson and A.C.-C. Yao...
  • M.R. Garey et al.

    Complexity results for multiprocessor scheduling under resource constraints

    SIAM J. Comput.

    (1975)
  • M.R. Garey et al.

    Scheduling tasks with nonuniform deadlines on two processors

    J. Assoc. Comput. Mach.

    (1976)
  • M.R. Garey et al.

    Approximation algorithms for combinatorial problems: an annotated bibliography

  • M.R. Garey et al.

    Two-processor scheduling with start-times and deadlines

    S1AM J. Comput.

    (1977)
  • M.R. Garey et al.

    The complexity of flowshop and jobshop scheduling

    Math. Operations Res.

    (1976)
  • L. Gelders et al.

    Coordinating aggregate and detailed scheduling decisions in the one-machine job shop: part I

    Theory, Operations Res.

    (1974)
  • L. Gelders et al.

    Coordinating aggregate and detailed scheduling in the one-machine job shop: II—computation and structure

    Operations Res.

    (1975)
  • W.S. Gere

    Heuristics in job shop scheduling

    Management Sci.

    (1966)
  • B. Giffler et al.

    Algorithms for solving production-scheduling problems

    Operations Res.

    (1960)
  • P.C. Gilmore et al.

    Sequencing a one-state variable machine: a solvable case of the traveling salesman problem

    Operations Res.

    (1964)
  • T. Gonzalez (1976), A note on open shop preemptive schedules, Technical Report 214, Computer Science Department,...
  • T. Gonzalez (1977), Optimal mean finish time preemptive schedules, Technical Report 220, Computer Science Department,...
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