Scheduling on identical parallel machines to minimize total completion time with deadline and machine eligibility constraints

This study addresses the identical parallel machine scheduling problem with job deadlines and machine eligibility constraints to minimize total job completion time. Jobs must be completed before or at a deadline and preemptions are not allowed. Every job is allowed to be processed on a specified subset of machines. This problem is NP-hard. A heuristic and a branch and bound algorithm are developed to solve the problem. For the branch and bound algorithm, a lower bound based on the dual solution of the assignment problem is proposed and the heuristic serves as the initial upper bound. Many dominance rules are developed to curtail the branching nodes during the search procedure. Computational results indicate that the lower bound improves the performance of those in the literature in terms of execution time, and heuristic consistently generates a good quality schedule.

[1]  Grissele Centeno,et al.  Minimizing makespan on parallel machines with release time and machine eligibility restrictions , 2004 .

[2]  Joseph Y.-T. Leung,et al.  Minimizing total completion time on uniform machines with deadline constraints , 2006, TALG.

[3]  Meral Azizoglu.  Preemptive scheduling on identical parallel machines subject to deadlines , 2003, Eur. J. Oper. Res..

[4]  David S. Johnson,et al.  Scheduling Tasks with Nonuniform Deadlines on Two Processors , 1976, J. ACM.

[5]  Po-Chieng Hu,et al.  Minimizing total flow time for the worker assignment scheduling problem in the identical parallel-machine models , 2005 .

[6]  Chun-Yuan Cheng,et al.  Scheduling unrelated parallel machines to minimize total weighted tardiness , 2003, 2006 IEEE International Conference on Service Operations and Logistics, and Informatics.

[7]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[8]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[9]  Marc E. Posner,et al.  Minimizing Weighted Completion Times with Deadlines , 1985, Oper. Res..

[10]  Po-Chieng Hu,et al.  Further study of minimizing total flowtime for the worker assignment scheduling problem in the identical parallel-machine models , 2006 .

[11]  Hyun Joon Shin,et al.  Scheduling jobs on parallel machines: a restricted tabu search approach , 2003 .

[12]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[13]  Joseph Y.-T. Leung,et al.  Minimizing Total Completion Time on Parallel Machines with Deadline Constraints , 2003, SIAM J. Comput..

[14]  Uttarayan Bagchi,et al.  Technical Note - An Improved Lower Bound for Minimizing Weighted Completion Times with Deadlines , 1987, Oper. Res..

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

[16]  Grisselle Centeno,et al.  Parallel machine scheduling with release time and machine eligibility restrictions , 1997 .

[17]  Chung-Lun Li,et al.  Scheduling unit-length jobs with machine eligibility restrictions , 2006, Eur. J. Oper. Res..

[18]  Chandrasekharan Rajendran,et al.  A performance analysis of dispatching rules and a heuristic in static flowshops with missing operations of jobs , 2001, Eur. J. Oper. Res..

[19]  B. Bavarian,et al.  Job scheduling on parallel machines using simulated annealing , 1991, Conference Proceedings 1991 IEEE International Conference on Systems, Man, and Cybernetics.