Job-Shop Scheduling by Implicit Enumeration

The classical combinatorial optimization problem of minimizing maximum completion time in a general job-shop has been the subject of extensive research. In this paper we review and extend this work. A general bounding approach is developed which includes all previously presented lower bounds as special cases. The strongest bound obtainable in this way is combined with two enumeration schemes, the relative merits of which are discussed. The results of some computational experiments and a large bibliography are included as well.

[1]  G. Thompson,et al.  Algorithms for Solving Production-Scheduling Problems , 1960 .

[2]  Harold H. Greenberg,et al.  A Branch-Bound Solution to the General Scheduling Problem , 1968, Oper. Res..

[3]  Egon Balas,et al.  Machine Sequencing Via Disjunctive Graphs: An Implicit Enumeration Algorithm , 1969, Oper. Res..

[4]  John M. Charlton,et al.  A Generalized Machine-Scheduling Algorithm , 1970 .

[5]  Ichiro Nabeshima.  GENERAL SCHEDULING ALGORITHMS WITH APPLICATIONS TO PARALLEL SCHEDULING AND MULTIPROGRAMMING SCHEDULING , 1971 .

[6]  Michael Florian,et al.  An Implicit Enumeration Algorithm for the Machine Sequencing Problem , 1971 .

[7]  Marshall L. Fisher,et al.  Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I , 1973, Oper. Res..

[8]  K. Y. Chiu,et al.  An optimal schedule time of a job shop-like disjunctive graph , 1973, Networks.

[9]  M. Florian,et al.  On sequencing with earliest starts and due dates with application to computing bounds for the (n/m/G/Fmax) problem , 1973 .

[10]  Kenneth R. Baker,et al.  Sequencing with due-dates and early start times to minimize maximum tardiness , 1974 .

[11]  T. E. Moore,et al.  An Implicit Enumeration Algorithm for the Nonpreemptive Shop Scheduling Problem , 1974 .

[12]  B. J. Lageweg,et al.  Minimizing maximum lateness on one machine : Computational experience and some applications , 1976 .

[13]  Graham McMahon,et al.  On Scheduling with Ready Times and Due Dates to Minimize Maximum Lateness , 1975, Oper. Res..

[14]  A. Kan.  Machine Scheduling Problems: Classification, Complexity and Computations , 1976 .