A branch-and-bound algorithm for the early/tardy machine scheduling problem with a common due-date and sequence-dependent setup time

The single-machine early/tardy (E/T) scheduling problem is addressed in this research. The objective of this problem is to minimize the total amount of earliness and tardiness. Earliness and tardiness, are weighted equally and the due date is common and large (unrestricted) for all jobs. Machine setup time is included and is considered sequence-dependent. When sequence-dependent setup times are included, the complexity of the problem increases significantly and the problem becomes NP-hard. In the literature, only mixed integer programming formulation is available to optimally solve the problem at hand. In this paper, a branch-and-bound algorithm (B&B) is developed to obtain optimal solutions for the problem. As it will be shown, the B&B solved problems three times larger than what has been reported in the literature.

[1]  W. Szwarc.  Single-machine scheduling to minimize absolute deviation of completion times from a common due date , 1989 .

[2]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[3]  Nagraj Balakrishnan,et al.  Early/tardy scheduling with sequence dependent setups on uniform parallel machines , 1999, Comput. Oper. Res..

[4]  Michel Gendreau,et al.  A divide and merge heuristic for the multiprocessor scheduling problem with sequence dependent setup times , 2001, Eur. J. Oper. Res..

[5]  Ching-Fang Liaw,et al.  A branch-and-bound algorithm for the single machine earliness and tardiness scheduling problem , 1999, Comput. Oper. Res..

[6]  Meral Azizoglu,et al.  Scheduling job families about an unrestricted common due date on a single machine , 1997 .

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

[8]  G HallNicholas,et al.  Earliness-tardiness scheduling problems , 1991 .

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

[10]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

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

[12]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[13]  B. Alidaee,et al.  A note on minimizing the weighted sum of tardy and early completion penalties in a single machine: A case of small common due date , 1997 .

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

[15]  Zhi-Long Chen.  Scheduling with batch setup times and earliness-tardiness penalties , 1997 .

[16]  Anup K. Sen,et al.  Single machine weighted earliness-tardiness penalty problem with a common due date , 2001, Comput. Oper. Res..

[17]  Suresh P. Sethi,et al.  Earliness-Tardiness Scheduling Problems, II: Deviation of Completion Times About a Restrictive Common Due Date , 1991, Oper. Res..

[18]  Wlodzimierz Szwarc.  The weighted common due date single machine scheduling problem revisited , 1996, Comput. Oper. Res..

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

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

[21]  Jatinder N. D. Gupta,et al.  A review of scheduling research involving setup considerations , 1999 .

[22]  Ghaith Rabadi.  Minimizing the total earliness and tardiness for a single-machine scheduling problem with a common due date and sequence-dependent setup times , 1999 .