Earliness-tardiness minimization on scheduling a batch processing machine with non-identical job sizes

Minimize earlinesstardiness (E/T) on a single batch processing machine.Consider jobs with a common due date and non-identical sizes.Formulate a mathematical model and derive optimal properties.Develop algorithms and conduct computational experiments. This paper considers the scheduling problem of minimizing earlinesstardiness (E/T) on a single batch processing machine with a common due date. The problem is extended to the environment of non-identical job sizes. First, a mathematical model is formulated, which is tested effectively under IBM ILOG CPLEX using the constraint programming solver. Then several optimal properties are given to schedule batches effectively, and by introducing the concept of ARB (Attribute Ratio of Batch), it is proven that the ARB of each batch should be made as small as possible in order to minimize the objective, designed as the heuristic information for assigning jobs into batches. Based on these properties, a heuristic algorithm MARB (Minimum Attribute Ratio of Batch) for batch forming is proposed, and a hybrid genetic algorithm is developed for the problem under study by combining GA (genetic algorithm) with MARB. Experimental results demonstrate that the proposed algorithm outperforms other algorithms in the literature, both for small and large problem instances.

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

[2]  Rui Xu,et al.  Makespan minimization on single batch-processing machine via ant colony optimization , 2012, Comput. Oper. Res..

[3]  George Q. Huang,et al.  Scheduling a batch processing machine with non-identical job sizes: a clustering perspective , 2011 .

[4]  Yoshiro Ikura,et al.  Efficient scheduling algorithms for a single batch processing machine , 1986 .

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

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

[7]  John W. Fowler,et al.  Production Planning and Control for Semiconductor Wafer Fabrication Facilities - Modeling, Analysis, and Systems , 2013, Operations research / computer science interfaces series.

[8]  T. C. Edwin Cheng,et al.  Common due date assignment and scheduling with a rate-modifying activity to minimize the due date, earliness, tardiness, holding, and batch delivery cost , 2012, Comput. Ind. Eng..

[9]  John W. Fowler,et al.  A survey of problems, solution techniques, and future challenges in scheduling semiconductor manufacturing operations , 2011, J. Sched..

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

[11]  Krassimir T. Atanassov,et al.  Modelling of a Roulette Wheel Selection Operator in Genetic Algorithms Using Generalized Nets , 2009 .

[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]  Kuo-Ching Ying,et al.  Minimizing earliness-tardiness penalties for common due date single-machine scheduling problems by a recovering beam search algorithm , 2008, Comput. Ind. Eng..

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

[15]  Guojun Li,et al.  Batch Scheduling with a Common Due Window on a Single Machine , 2006, FSKD.

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

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

[18]  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..

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

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

[21]  Lars Mönch,et al.  Decomposition heuristics for minimizing earliness-tardiness on parallel burn-in ovens with a common due date , 2007, Comput. Oper. Res..

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

[23]  Purushothaman Damodaran,et al.  Minimizing makespan on a batch-processing machine with non-identical job sizes using genetic algorithms , 2006 .