A differential evolution approach for the common due date early/tardy job scheduling problem

The problem of scheduling multiple jobs on a single machine so that they are completed by a common specified date is addressed in this paper. This type of scheduling set costs depend on whether a job is finished before (earliness) or after (tardiness) the specified due date. The objective is to minimize a summation of earliness and tardiness penalty costs. Minimizing these costs pushes the completion time of each job as close as possible to the due date. The use of differential evolution as the optimization heuristic to solve this problem is investigated in this paper. Computational experiments over multiple (280 in total) public benchmark problems with up to 1000 jobs to be scheduled show the effectiveness of the proposed approach. The results obtained are of high quality putting new upper bounds to 60% of the benchmark instances.

[1]  Chengbin Chu,et al.  A survey of the state-of-the-art of common due date assignment and scheduling research , 2002, Eur. J. Oper. Res..

[2]  Maria Teresa Almeida,et al.  A composite heuristic for the single machine early/tardy job scheduling problem , 1998, Comput. Oper. Res..

[3]  Martin Feldmann,et al.  Single-machine scheduling for minimizing earliness and tardiness penalties by meta-heuristic approaches , 2003 .

[4]  Ivan Zelinka,et al.  Mechanical engineering design optimization by differential evolution , 1999 .

[5]  M. Montaz Ali,et al.  Population set-based global optimization algorithms: some modifications and numerical studies , 2004, Comput. Oper. Res..

[6]  H. G. Kahlbacher,et al.  A proof for the longest‐job‐first policy in one‐machine scheduling , 1991 .

[7]  Godfrey C. Onwubolu,et al.  New optimization techniques in engineering , 2004, Studies in Fuzziness and Soft Computing.

[8]  M. M. Ali,et al.  A numerical study of some modified differential evolution algorithms , 2006, Eur. J. Oper. Res..

[9]  Dr. Zbigniew Michalewicz,et al.  How to Solve It: Modern Heuristics , 2004 .

[10]  D. Biskup,et al.  Single-machine scheduling for minimizing earliness and tardiness penalties by metaheuristic approaches , 2002 .

[11]  Nicholas G. Hall.  Single- and multiple-processor models for minimizing completion time variance , 1986 .

[12]  S. S. Panwalkar,et al.  Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem , 1982, Oper. Res..

[13]  Martin Feldmann,et al.  Benchmarks for scheduling on a single machine against restrictive and unrestrictive common due dates , 2001, Comput. Oper. Res..

[14]  Godfrey C. Onwubolu,et al.  Optimizing CNC Drilling Machine Operations: Traveling Salesman Problem-Differential Evolution Approach , 2004 .

[15]  Yih-Long Chang,et al.  MINIMIZING MEAN ABSOLUTE DEVIATION OF COMPLETION TIMES ABOUT A COMMON DUE DATE. , 1986 .

[16]  Mansooreh Mollaghasemi,et al.  A branch-and-bound algorithm for the early/tardy machine scheduling problem with a common due-date and sequence-dependent setup time , 2004, Comput. Oper. Res..

[17]  Godfrey C. Onwubolu,et al.  Scheduling flow shops using differential evolution algorithm , 2006, Eur. J. Oper. Res..

[18]  Chae Y. Lee,et al.  Parallel genetic algorithms for the earliness-tardiness job scheduling problem with general penalty weights , 1995 .

[19]  Andreas C. Nearchou,et al.  Meta-heuristics from nature for the loop layout design problem , 2006 .

[20]  Yih-Long Chang,et al.  Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date , 1987 .

[21]  Marc E. Posner,et al.  Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date , 1991, Oper. Res..

[22]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[23]  J. J. Kanet.  Minimizing the average deviation of job completion times about a common due date , 1981 .

[24]  G. Rand.  Sequencing and Scheduling: An Introduction to the Mathematics of the Job-Shop , 1982 .

[25]  Ross J. W. James.  Using tabu search to solve the common due date early/tardy machine scheduling problem , 1997, Comput. Oper. Res..

[26]  Qi Hao,et al.  Common due-date determination and sequencing using tabu search , 1996, Comput. Oper. Res..

[27]  T.C.E. Cheng,et al.  Survey of scheduling research involving due date determination decisions , 1989 .

[28]  Gary D. Scudder,et al.  Sequencing with Earliness and Tardiness Penalties: A Review , 1990, Oper. Res..

[29]  Riccardo Poli,et al.  New ideas in optimization , 1999 .