M-stage scheduling problem—a critical appraisal

Abstract The deterministic M-stage scheduling problem is reviewed and critically appraised from the points of view of variety, contents, assumptions, recent solution procedures and criteria of optimality. The complications of practical problems are discussed to explore the true nature of the problem formulation. Several implications of the present formulation of scheduling problem are discussed and directions for future research in scheduling theory are suggested.

[1]  L. G. Mitten.  Sequencing n Jobs on Two Machines with Arbitrary Time Lags , 1959 .

[2]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[3]  Richard D. Smith,et al.  A General Algorithm for Solution of the n-Job, M-Machine Sequencing Problem of the Flow Shop , 1967, Oper. Res..

[4]  G. B. McMahon,et al.  Flow-Shop Scheduling with the Branch-and-Bound Method , 1967, Oper. Res..

[5]  Richard A. Dudek,et al.  Development of M-Stage Decision Rule for Scheduling N Jobs Through M Machines , 1964 .

[6]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[7]  Henri Louis Beenhakker,et al.  THE DEVELOPMENT OF ALTERNATE CRITERIA FOR OPTIMALITY IN THE MACHINE SEQUENCING PROBLEM , 1963 .

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

[9]  Alan S. Manne,et al.  On the Job-Shop Scheduling Problem , 1960 .

[10]  Linus Schrage,et al.  Solving Resource-Constrained Network Problems by Implicit Enumeration - Nonpreemptive Case , 1970, Oper. Res..

[11]  Said Ashour,et al.  INVESTIGATION OF VARIOUS BOUNDING PROCEDURES FOR PRODUCTION SCHEDULING PROBLEMS , 1968 .

[12]  Don Lloyd Spencer.  An investigation of the relationships between the sequencing and scheduling problems , 1969 .

[13]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

[14]  E. H. Bowman.  THE SCHEDULE-SEQUENCING PROBLEM* , 1959 .

[15]  E. Ignall,et al.  Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems , 1965 .

[16]  Z. A. Lomnicki,et al.  Some Applications of the “Branch-and-Bound” Algorithm to the Machine Scheduling Problem , 1966 .

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

[18]  Ashour Said.  A Branch-and-Bound Algorithm for Flow Shop Scheduling Problems , 1970 .

[19]  S. Pandit.  The Loading Problem , 1962 .

[20]  Salah E. Elmaghraby,et al.  The machine sequencing problem – review and extensions , 1968 .

[21]  Sant Arora,et al.  The Sequencing Problem , 1969 .

[22]  John M. Charlton,et al.  A GENERAL METHOD FOR MACHINE SCHEDULING , 1968 .

[23]  Harvey M. Wagner,et al.  An integer linear‐programming model for machine scheduling , 1959 .

[24]  Egon Balas,et al.  Discrete Programming by the Filter Method , 1967, Oper. Res..