Decomposition heuristics for minimizing earliness-tardiness on parallel burn-in ovens with a common due date

This paper considers a scheduling problem for parallel burn-in ovens in the semiconductor manufacturing industry. An oven is a batch processing machine with restricted capacity. The batch processing time is set by the longest processing time among those of all the jobs contained in the batch. All jobs are assumed to have the same due date. The objective is to minimize the sum of the absolute deviations of completion times from the due date (earliness-tardiness) of all jobs. We suggest three decomposition heuristics. The first heuristic applies the exact algorithm due to Emmons and Hall (for the nonbatching problem) in order to assign the jobs to separate early and tardy job sets for each of the parallel burn-in ovens. Then, we use job sequencing rules and dynamic programming in order to form batches for the early and tardy job sets and sequence them optimally. The second proposed heuristic is based on genetic algorithms. We use a genetic algorithm in order to assign jobs to each single burn-in oven. Then, after forming early and tardy job sets for each oven we apply again sequencing rules and dynamic programming techniques to the early and tardy jobs sets on each single machine in order to form batches. The third heuristic assigns jobs to the m early job sets and m tardy jobs sets in case of m burn-in ovens in parallel via a genetic algorithm and applies again dynamic programming and sequencing rules. We report on computational experiments based on generated test data and compare the results of the heuristics with known exact solution for small size test instances obtained from a branch and bound scheme.

[1]  C. S. Sung,et al.  Minimizing makespan on a single burn-in oven in semiconductor manufacturing , 2000, Eur. J. Oper. Res..

[2]  Hamilton Emmons,et al.  Scheduling to a common due date on parallel uniform processors , 1987 .

[3]  Reha Uzsoy,et al.  A genetic algorithm to minimize maximum lateness on a batch processing machine , 2002, Comput. Oper. Res..

[4]  Chris N. Potts,et al.  Scheduling with batching: A review , 2000, Eur. J. Oper. Res..

[5]  Xiangtong Qi,et al.  Earliness and Tardiness Scheduling Problems on a Batch Processor , 1999, Discret. Appl. Math..

[6]  Reha Uzsoy,et al.  A review of production planning and scheduling models in the semiconductor industry , 1994 .

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

[8]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

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

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

[11]  J. A. Hoogeveen,et al.  Scheduling a batching machine , 1998 .

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

[13]  John W. Fowler,et al.  Genetic algorithm based scheduling of parallel batch machines with incompatible job families to minimize total weighted tardiness , 2004 .

[14]  Chung-Lun Li,et al.  Scheduling with agreeable release times and due dates on a batch processing machine , 1997 .

[15]  Lars Mönch,et al.  A Genetic Algorithm Approach for Minimizing Earliness and Tardiness on a Burn-In Oven with a Common Due Date , 2003 .

[16]  Kenneth R. Baker,et al.  Scheduling Groups of Jobs on a Single Machine , 1995, Oper. Res..

[17]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[18]  Dorit S. Hochbaum,et al.  Scheduling Semiconductor Burn-In Operations to Minimize Total Flowtime , 1997, Oper. Res..

[19]  Reha Uzsoy,et al.  Efficient Algorithms for Scheduling Semiconductor Burn-In Operations , 1992, Oper. Res..

[20]  Reha Uzsoy,et al.  Minimizing total completion time on a batch processing machine with job families , 1993, Oper. Res. Lett..

[21]  Y. H. Kim,et al.  Minimizing makespan on a single burn-in oven with job families and dynamic job arrivals , 2002, Comput. Oper. Res..

[22]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[23]  M. Mathirajan,et al.  Scheduling of Batch Processors in Semiconductor Manufacturing – A Review , 2003 .

[24]  J. I. Min,et al.  Scheduling in a two-machine flowshop with batch processing machine(s) for earliness/tardiness measure under a common due date , 2001, Eur. J. Oper. Res..

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

[26]  Haldun Aytug,et al.  Use of genetic algorithms to solve production and operations management problems: A review , 2003 .

[27]  Reha Uzsoy,et al.  Minimizing total completion time on batch processing machines , 1993 .

[28]  R. Uzsoy.  Scheduling a single batch processing machine with non-identical job sizes , 1994 .

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

[30]  Lars Mönch,et al.  Minimizing earliness–tardiness on a single burn-in oven with a common due date and maximum allowable tardiness constraint , 2006, OR Spectr..

[31]  J. A. Hoogeveen,et al.  Scheduling a batching machine , 1997 .

[32]  Michael E. Wall,et al.  Galib: a c++ library of genetic algorithm components , 1996 .

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

[34]  Lars Mönch.  Minimizing Earliness-Tardiness of Jobs with a Common Due Date on Parallel Burn-In Ovens , 2004 .

[35]  R. Gunst.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .