Research on the Scheduling of Single Batching Machine with Non-identical Job Size

N jobs,each job j with a processing time pj and height sj,being partitioned into batches,are to be processed on a single batching machine with a certain height B.The jobs can be processed by the machine simultaneously only when the sum of the jobs' height is not larger than B.The processing time of a batch is equal to the longest processing of the job among the batch.The spare space of a batch is the difference between the machine height and the sum of the jobs' height.The objective function,to minimize the sum of the total spare space of the machine and the total completion time of the jobs,is NP-hard.The research is inspired by the scheduling of bell type annealing furnace in the steel making industry,a machine that can anneal several jobs simultaneously if the sum of the jobs' height is not larger than the height of itself.A greedy algorithm is proposed based on the quality of some jobs,and dynamic programming is applied to obtain the optimal partitioned batches for the SPT ordered jobs.To give a more detailed comparison of the algorithms,dynamic programming is also applied to the total completion time of all jobs with non-identical job size,which is compared with the heuristic algorithms proposed by Uzsoy.Another quality is used to improve the solution obtained by the dynamic programming.Based on the rule,a local search,named DPLS,is carried out and it is very efficient for the problem through the experiment.