本研究從理論方法與實作角度切入，考慮實務上高科技製造產業製造管理中生產排程問題的複雜性，在一般性生產排程(GPS)系統下，提出一針對一般性非等效平行機台排程問題(GUPMSP)之管理與求解架構。所謂GUPMSP，係指具有：非等效平行機台環境、動態工件到達、工件加工不可中斷性、不可分割順序相依前置時間、多重資源需求、一般性加工順序限制，以及迴流製程等特性之排程問題。首先，本研究提出一個具優化機制之排程產生器(OptSG)，以求解GUPMSP的最佳解或近似最佳解。OptSG由彩色時間性裴氏圖(CTPN)、三階段模擬邏輯(Three-phase simulation logics)，以及遺傳演算法(GA)所構成。透過模式結構與模式組態的分離架構，使得OptSG具有結構獨立性，使其無論在問題求解或問題分析上均具有強健性與便利性。此外，本研究另提出一個混合整數線性規劃(MILP)模式，以求解GUPMSP的最佳解。MILP模式的角色，主要在提供GUPMSP的最佳解作為標竿(benchmark)，以評估OptSG的求解效度。MILP模式中，其同時考慮不可分割順序相依前置時間與多重資源需求兩項排程特性，為文獻中所未有。本研究最後進行實驗，以實際數據比較MILP、OptSG，以及單一派工法則(DRBH)的求解品質與求解時間。實驗結果驗證本研究提出之模式在理論上之求解最佳性與實務上之實作可行性。

In this study, considering the complex problem nature in practical high-tech manufacturing environment from the viewpoints of both theoretical approaches and on-line implementation, a managerial framework in a generic production scheduling (GPS) system from which the generalized unrelated parallel machine scheduling problem (GUPMSP) arises was proposed. GUPMSP is characterized by the following characteristics: unrelated parallel machine environment, dynamic job arrival, non-preemption, inseparable sequence-dependent setup time, multiple resources requirement, general precedence constraint, and job re-circulation. We proposed the optimization-based schedule generator (OptSG) for the approximation of GUPMSP. Separation of model structure and model configuration in OptSG contributes to the structural independence, which makes OptSG robust and convenient in analysis and problem solving of GUPMSP in real settings with changing properties. Meanwhile, we proposed a mixed-integer-linear-programming (MILP) model for the optimization of GUPMSP. This MILP model was developed as a benchmark to estimate the validity of OptSG. Inseparable sequence-dependent setup time and multiple resources requirement that have not been addressed simultaneously in the literature were considered in the MILP model. Finally, we conducted several experiments to compare the solutions of MILP model, OptSG, and dispatching rule-based heuristics (DRBH). The results validated the practical viability of this study.

References
Al-Jaar, R. Y. and A. A. Desrochers (1990), “Performance evaluation of automated manufacturing systems using generalized stochastic Petri nets”, IEEE Transactions on Robotics and Automation, Vol. 6, No. 6, pp. 621-639.
Allahverdi, A., J. N. D. Gupta and T. Aldowaisan (1999), “A review of scheduling research involving setup considerations”, Omega: The International Journal of Management Science, Vol. 27, pp. 219-239
Baker, K. R. (1974), Introduction to Sequencing and Scheduling, John Wiley & Sons, New York.
Bautista, J., A. Lusa, R. Suarez, M. Mateo, R. Pastor and A. Corominas (1999), “Application of genetic algorithms to assembly sequence planning with limited resources”, Proceedings of the 1999 IEEE International Symposium on Assembly and Task Planning, pp. 411-416.
Beasley, J. E. and P. C. Chu (1996), “A genetic algorithm for the set covering problem”, European Journal of Operational Research, Vol. 94, pp. 392-404.
Chen, C., V. Vempati and N. Aljaber (1995), “An application of genetic algorithms for flow shop problems”, European Journal of Operational Research, Vol. 80, pp. 389-396.
Chen, J. H., L. C. Fu, M. H. Lin and A. C. Huang (2001), “Petri-net and GA-based approach to modeling, scheduling, and performance evaluation for wafer fabrication”, IEEE Transactions on Robotics and Automation, Vol. 17, No. 5, pp. 619-636.
Chen, T. R. and T. C. Hsia (1994), “Job shop scheduling with multiple resources and an application to a semiconductor testing facility”, Proceedings on the 33rd Conference on Decision and Control, pp. 1564-1570.
Cheng, R., M. Gen and Y. Tsujimura (1996), “A tutorial survey of job-shop scheduling problems using genetic algorithms: part I. Representation”, International Journal of Computers and Industrial Engineering, Vol. 30, No. 4, pp. 983-997.
Cheng, R., M. Gen and Y. Tsujimura (1999), “A tutorial survey of job-shop scheduling problems using genetic algorithms: part II. Hybrid genetic search strategies”, International Journal of Computers and Industrial Engineering, Vol. 36, No. 2, pp. 343-364.
Cheng, T. C. E. and C. C. S. Sin (1990), “A state-of-the-art review of parallel-machine scheduling research”, European Journal of Operational Research, Vol. 47, pp. 271-292.
Desrochers, A. A. and R. Y. Al-Jaar (1995), Applications of Petri Nets in Manufacturing Systems, IEEE Press, New York.
Dillenberger, C., L. F. Escudero, A. Wollensak and W. Zhang (1994), “On practical resource allocation for production planning and scheduling with period overlapping setups”, European Journal of Operational Research, Vol. 75, pp. 275-286.
Dorndorf, U. and E. Pesch (1995), “Evolution based learning in a job shop scheduling environment”, Computers and Operations Research, Vol. 22, pp. 25-40.
Evans, J. B. (1988), Structures of discrete event simulation: An introduction to the engagement strategy, Ellis Horwood Limited, England.
Evans, J. B. (1993), “The Devnet: a Petri net for discrete event simulation”, Lecture Notes in Computer Science: Advances in Petri Nets 1993, Vol. 674, pp. 91-125.
Garey, M. R. and D. S. Johnson (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, Bell Laboratories, New Jersey.
Gen, M. and R. Cheng (1997), Genetic Algorithms and Engineering Design, John Wiley & Sons, New York.
Gen, M. and R. Cheng (2000), Genetic Algorithms and Engineering Optimization, John Wiley & Sons, New York.
Ghedjati, F. (1999), “Genetic algorithms for the job-shop scheduling problem with unrelated parallel constraints: heuristic mixing method machines and precedence”, Computers & Industrial Engineering, Vol. 37, pp. 39-42.
Glover, F. and M. Laguna (1997), Tabu Search, Kluwer Academic Publishers, Boston.
Herrmann, J., J. M. Proth and N. Sauer (1997), “Heuristics for unrelated machine scheduling with precedence constraints”, European Journal of Operational Research, Vol. 102, pp. 528-537.
Hinterding, R. (1998), “Mapping, order-independent genes and the knapsack problem”, Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 13-17.
Jeng, M. D., X. L. Xie and S. W. Chou (1998), “Modeling, qualitative analysis, and performance evaluation of the etching area in an IC wafer fabrication system using Petri nets”, IEEE Transactions on Semiconductor Manufacturing, Vol. 11, No. 3, pp. 358-373.
Jensen, K., (1981), “Coloured Petri nets and the invariant-method”, Theoretical Computer Science, Vol. 14, pp. 317-336.
Kempf, K., R. Uzsoy, S. Smith and K. Gary (2000), “Evaluation and comparison of production schedules”, Computers in Industry, Vol. 42, pp. 203-220.
Lee, C. C. (1995), “Three-phase discrete event simulation of timed Petri nets”, Ph.D. Dissertation, Department of Industrial Engineering and Engineering Management, National Tsing Hua University.
Lin, J. T. and C. C. Lee (1996), “Three-phase discrete event simulation of timed Petri nets”, Journal of the Chinese Institute of Industrial Engineers, Vol. 13, No. 1, pp. 11-22.
Lin, S. Y. and H. P. Huang (1998), “Modeling and emulation of a furnace in IC fab based on colored-timed Petri net”, IEEE Transactions on Semiconductor Manufacturing, Vol. 11, No. 3, pp. 410-420.
McNaughton, R. (1959), “Scheduling with deadlines and loss functions”, Management Science, Vol. 6, No. 1, pp. 1-12.
Mori, M. and C. T. Ching (1997), “A genetic algorithm for multi-mode resource constrained project scheduling problem”, European Journal of Operational Research, Vol. 100, pp. 134-141.
Odrey, N. G., J. D. Green and A. Appello (2001), “A generalized Petri net modeling approach for the control of re-entrant flow semiconductor wafer fabrication”, Robotics and Computer Integrated Manufacturing, Vol. 17, pp. 5-11.
Palmer, C. and A. Kershenbaum (1995), “An approach to a problem in network design using genetic algorithms”. Networks, Vol. 26, pp. 151-163.
Panwalker, S. S. and W. Iskander (1977), “A survey of scheduling rules”, Operations Research, Vol. 25, No. 1, pp. 45-61.
Pearn, W. L., S. H. Chung and M. H. Yang (2002), “A case study on the wafer probing scheduling problem”, Production Planning and Control, Vol. 13, No. 1, pp. 66-75.
Pearn, W. L., S. H. Chung and M. H. Yang (2002), “Minimizing the total machine workload for the wafer probing scheduling problem”, IIE Transactions, Vol. 34, pp. 211-220.
Piersma, N. and W. V. Dijk (1996), “A local search heuristic for unrelated parallel machine scheduling with efficient neighborhood search”, Mathematical and Computer Modeling, Vol. 24, No. 9, pp. 1-19.
Pinedo, M. and X. Chao (1999), Operations Scheduling with Applications in Manufacturing and Services, McGraw-Hill, New York.
Pritsker, A. A. B. (1995), Introduction to Simulation and SLAM II, John Wiley & Sons, New York.
Proth, J. M. and X. L. Xie (1996), Petri Nets: A Tool for Design and Management of Manufacturing Systems, John Wiley & Sons, New York.
Reeves, C. (1995), “A genetic algorithm for flow shop sequencing”, Computers and Operations Research, Vol. 22, pp. 5-13.
Sipser, M. (1997), Introduction to the Theory of Computation, PWS Publishing Company, Boston.
Tate, D. and A. Smith (1995), “A genetic approach to the quadratic assignment problem”, Computers and Operations Research, Vol. 22, pp. 73-83.
Viswanadham, N. and Y. Narahari (1992), Performance Modeling of Automated Manufacturing Systems, Prentice Hall, New Jersey.
Weng, M. X., J. Lu and H. Y. Ren (2001), “Unrelated parallel machine scheduling with setup consideration and a total weighted completion time objective”, International Journal of Production Economics, Vol. 70, pp. 215-226.
Wu, J. Z. (2001), “Modeling the scheduling for semiconductor final test and an algorithm for solving the empirical problem”, Master Thesis, Department of Industrial Engineering and Engineering Management, National Tsing Hua University.
Xiong, H. H. and M. C. Zhou (1998), “Scheduling of semiconductor test facility via Petri nets and hybrid heuristic search”, IEEE Transactions on Semiconductor Manufacturing, Vol. 11, No. 3, pp. 384-393.
Yang, W. H. and C. J. Liao (1999), “Survey of scheduling research involving setup times”, International Journal of Systems Science, Vol. 30, No. 2, pp. 143-155.
Zuberek, W. M., (1991), “Timed Petri nets: definitions, properties, and applications”, Microelectronics and Reliability: Special Issues on Petri Nets and Related Graph Models, Vol. 31, No. 4, pp. 627-644.