本論文主要在探討當工作可分割時之等效平行機台排程問題。在本問題中，假設一個工作可以被分成許多的子工作，並且可將這些子工作指派到不同的機台上同時加工。每個工作具有已知的加工時間、準備時間以及交期。在機台加工過程中，當欲加工工作與前一加工工作不同時，必須耗費一相依整備時間方能進行加工。為最小化此問題之總延遲時間，本論文提出一個兩階段式方法來求解此問題。第一階段中，本論文提出五種初步排程產生方法。接著在第二階段中，將在第一階段產生的排程中有延遲的工作或子工作做進一步分割，並將分割後的子工作重新指派到機台上以減少總延遲時間。由實驗結果顯示，本論提出之方法表現優於前人所提出之方法。

This study focuses on the problem of scheduling jobs on identical parallel machines with job-splitting property. In this problem, it assumed that a job can be split into several sub-jobs, and these sub-jobs can be processed on different machines simultaneously. Each job has a processing time, a ready date and a due date. If a sub-job of a job is assigned after a sub-job of another job on a machine, a sequence-dependent setup time is incurred. A two-phase heuristic algorithm is proposed to minimize the total tardiness. In phase 1, five efficient heuristic methods are proposed. In phase 2, the sub-job of tardy jobs in the schedule provided by phase 1 are further split, and the split sub-jobs are rescheduled on the machines to reduce the total tardiness. Computer experiments show that the proposed algorithm outperforms a previously suggested algorithm.

Chen, B., Ye, Y. Y. and Zhang, J. W. (2006), “Lot-sizing scheduling with batch setup times”, Journal of Scheduling, Vol. 9, No. 3, pp. 299-310
Diaz-Santillan, E. and Malav□, C.O. (2004), “Simulated annealing for parallel machine scheduling with split jobs and sequence-dependent set-ups”, International Journal of Industrial Engineering-Theory Applications and Practice, Vol. 11, No. 1, pp. 43-53
Hurink, J. L., Kern W. and Nawijn W. (2000) “Scheduling Split-Jobs on Parallel Machines”, Memorandum No. 1530, University of Twente, Fac. of Mathematical Sciences
Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G. and Shmoys, D. B., “Sequencing and scheduling: algorithms and complexity”, in: Grave, S., Rinnooy Kan, A.H.G. and Zipkin P. (1993), Logistics of Production and Inventory, North-Holland, Amsterdam, pp. 445-522
Lee, Y. H. and Pinedo, M. (1997), “Scheduling jobs on parallel machines with sequence-dependent setup times”, European Journal of Operational Research, Vol. 100, No. 3, pp. 464-474
Logendran, R. and Subur, F. (2003), “Unrelated parallel machine scheduling with job splitting”, IIE Transactions, Vol. 36, No. 4, pp. 359-372
Koulamas, C. (1994), “The total tardiness problem: Review and extensions”, Operations Research, Vol. 42, No. 6, pp. 1025-1041
Koulamas, C. (1997), “Decomposition and hybrid simulated annealing heuristics for the parallel-machine total tardiness problem”, Naval Research Logistics, Vol. 44, No. 1, pp. 109-125
Kim, Y. D., Shim, S. O., Kim, S. B. and Choi, Y. C. (2004), “Parallel machine scheduling considering a job-splitting property”, International Journal of Production Research, Vol. 42, No. 21, pp. 4531-4546
Richard, P. and Proust, C. (2000), “Maximizing benefits in short-term planning in bottle-glass industry”, International Journal of Production Economics, Vol. 64, No. 1, pp. 11-19
Serafini, P. (1996), “Scheduling jobs on several machines with the job splitting property”, Operations Research, Vol. 44, No. 4, pp. 617-628
S□er, G. A., Pico, F. and Santiago, A. (1997), “Identical machine scheduling to minimize the number of tardy jobs when lot-splitting is allowed”, Computers and Industrial Engineering, Vol. 33, No. 1, pp. 277-280
Shim, S. O., Kim, Y. D. (2006), “A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property”, Computers and Operations Research, Vol. 35, No. 3, pp. 863-875
Tahar, D. N., Yalaoui, F., Chu, C. B. and Amodeo, L. (2006), “A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times”, International Journal of Production Economics, Vol. 99, No. 1, pp. 63-73
Xing, W. X. and Zhang, J.W. (2000), “Parallel machine scheduling with splitting jobs”, Discrete Applied Mathematics, Vol. 103, No. 1, pp. 259-269
Yalaoui, F. and Chu, C. B. (2003), “An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times”, IIE Transactions, Vol. 35, No. 2, pp. 183-190