本研究以彈性製造系統(Flexible Manufacturing System, FMS)中同步機台與車輛排程問題為研究主題，在此問題下不同的系統特性將會影響著系統的績效表現，如FMS中的加工機台，多為CNC多功能加工機台，工件的同一個作業可以選擇替代機台進行加工，此特性更能增加排程的複雜性，替代機台會影響到總完工時間以及機台與車輛的利用率；在文獻中以數學規劃求解同步排程問題時，車輛搬運工件的時間都是以搬運距離除以車輛移動速度，並未考慮到車輛在搬運途中可能因為壅塞而延遲搬運時間或是車輛鎖死(Deadlock)等實際上會面臨到的問題，因此本研究在FMS同步機台與車輛排程問題下，建構以離散事件模擬來達到實務情況，並以區域控制(zone-control)處理車輛鎖死的問題。
由於研究中所考量的系統特性越多，系統的細緻度也隨之上升，在考量替代機台與區域控制的情況下，將會有兩個低細緻度模型與一個高細緻度模型，故本研究將引用MO2TOS(Multi-fidelity Optimization with Ordinal Transformation and Optimal Sampling)多細緻度模型最佳化架構，能有效利用低、高細緻度模型之間的關係對此FMS同步機台與車輛排程之問題進行求解。
MO2TOS最佳化架構下共有四種抽樣方法(Greedy、Random、Hybrid、Adaptive Sampling)，由於模型與模型之間具有一定之相關性，並非完全無相關(Independent)，採用Greedy Sampling可比其他抽樣方法使用較少的高細緻度模型抽樣資源與較高的抽樣成功率進行最佳方案的抽取，且Greedy Sampling亦可適用於其他不同的FMS環境。
在MO2TOS架構下，若好、壞方案歸於相同組別，將有可能使得該組之組平均績效因此而變差，而使得較少的抽樣資源分配至該組當中，將會有抽不到最佳方案的風險產生，故本研究進一步優化其抽樣資源分配之方法，利用各組之組最佳方案作為各組的特徵值，以進行後續抽樣資源的分配，可有效地將有限之抽樣資源分配到較為關鍵的組別，以節省整個MO2TOS架構中，抽樣過程所耗費的抽樣資源。

This research focuses on the problems of Simultaneous Scheduling of Machines and AGVs in FMS. According to the problem, different system characteristics will affect the performance of system. In FMS, there are most multi-functions CNC machines, so same process in one work can choose the alternative machines to do. This characteristic can increase the flexibility of scheduling more. Alternative machines affect the makespan and the using percentage of machines and AGVs. In past researches, when using Mathematical Programming to solve simultaneous scheduling problem, transportation time of AGVs is the transportation distance divided by the speed of the AGV. It didn’t consider the actual problems that AGVs will delay or be in Deadlock due to the congestion during the transportation. Therefore, for the problems of Simultaneous scheduling of Machines and AGVs in FMS, this research constructs the discrete event simulation to achieve actual conditions, and use zone-control to deal with the problems that lead to deadlock.
If the research considers more system characteristics, the fidelities of system will increase too. So, when considers the condition of alternative machines and zone control, there will be two low-fidelity models and one high-fidelity model. This research will cite the Multi-fidelity Optimization with Ordinal Transformation and Optimal Sampling (MO2TOS) optimization framework. It will effectively use the relationship between low-fidelity models and high-fidelity model to solve the problems of simultaneous machines and vehicles scheduling in FMS.
There are four sampling methods in MO2TOS framework (Greedy、Random、Hybrid、Adaptive Sampling). Because there are some relationships between models but not completely unrelated, using Greedy Sampling may consume less computing cost in high-fidelity model and have higher success rate to choose the best design than other methods. Greedy Sampling can also apply in other different FMS environments.
In the MO2TOS framework, if great and bad designs are included in the same group, it may lead the mean performance of group to be worse. In the consequence, less sampling resources will be allocated into the group, a risk that can’t choose the best design may happen. So, this research further optimize the allocation methods of sampling resources in high-fidelity model. Use the performance of the best design in every group to be eigenvalue to conduct the sampling resources allocation will effectively allocate the sampling resources to critical groups and saving the sampling resources.

[1] 林則孟(2001)。系統模擬理論與應用。台北市：滄海書局。
[2] 陳宏銘(2015)。多細緻度模型最佳化於彈性製造系統之探討(未出版之碩士論文)。國立清華大學工業工程與工程管理研究所，新竹市。
[3] 張祐翔(2013)。應用模擬最佳化於FMS之機台與車輛同步排程(未出版之碩士論文)。國立清華大學工業工程與工程管理研究所，新竹市。
[4] 許雅寧(2014)。粒子群聚演算法於FMS之機台與車輛同步排程(未出版之碩士論文)。國立清華大學工業工程與工程管理研究所，新竹市。
[5] 黎士賢(1999)。網路式移動區域控制無人搬運車系統(未出版之碩士論文)。國立中央大學工業管理研究所，桃園市。
[6] Abdelmaguid, T. F., Nassef, A. O., Kamal, B. A., & Hassan, M. F. (2004). A hybrid GA/heuristic approach to the simultaneous scheduling of machines and automated guided vehicles. International Journal of Production Research, 42(2), 267-281.
[7] Alessi, S. M. (2000). Simulation design for training and assessment. Aircrew training and assessment, 197-222.
[8] Anwar, M. F., & Nagi, R. (1998). Integrated scheduling of material handling and manufacturing activities for just-in-time production of complex assemblies. International Journal of Production Research, 36(3), 653-681.
[9] Balabanov, V., & Venter, G. (2004, August). Multi-fidelity optimization with high-fidelity analysis and low-fidelity gradients. In 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 4459.
[10] Bilge, Ü., & Ulusoy, G. (1995). A time window approach to simultaneous scheduling of machines and material handling system in an FMS. Operations Research, 43(6), 1058-1070.
[11] Browne, J., Dubois, D., Rathmill, K., Sethi, S. P., & Stecke, K. E. (1984). Classification of flexible manufacturing systems, The FMS magazine, 2(2), 114-117.
[12] Butler, K. W., Veltre, D. E., & Brady, D. (2009). Implementation of active learning pedagogy comparing low-fidelity simulation versus high-fidelity simulation in pediatric nursing education. Clinical Simulation in Nursing, 5(4), e129-e136.
[13] Buzacott, J. A., & Mandelbaum, M. (1985). Flexibility and productivity in manufacturing systems. In Proceedings of the annual IIE Conference, 404-413.
[14] Chan, F. T. S., Chaube, A., Mohan, V., Arora, V., & Tiwari, M. K. (2010). Operation allocation in automated manufacturing system using GA-based approach with multifidelity models. Robotics and Computer-Integrated Manufacturing, 26(5), 526-534.
[15] Chen, C. H. (2010). Stochastic simulation optimization: an optimal computing budget allocation (Vol. 1). World scientific.
[16] Coyette, A., Kieffer, S., & Vanderdonckt, J. (2007, September). Multi-fidelity prototyping of user interfaces. In IFIP Conference on Human-Computer Interaction, 150-164. Springer Berlin Heidelberg.
[17] Dahl, Y., Alsos, O. A., & Svanæs, D. (2010). Fidelity considerations for simulation-based usability assessments of mobile ICT for hospitals. Intl. Journal of Human–Computer Interaction, 26(5), 445-476.
[18] Davis, P. K., & Bigelow, J. H. (1998). Experiments in multiresolution modeling (MRM) (No. RAND/MR-1004-DARPA). RAND CORP SANTA MONICA CA.
[19] Dieckmann, P., Gaba, D., & Rall, M. (2007). Deepening the theoretical foundations of patient simulation as social practice. Simulation in Healthcare, 2(3), 183-193.
[20] Fanti, M. P. (2002). Event-based controller to avoid deadlock and collisions in zone-control AGVS. International Journal of Production Research, 40(6), 1453-1478.
[21] Forrester, A. I., Sóbester, A., & Keane, A. J. (2007, December). Multi-fidelity optimization via surrogate modelling. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 463(2088), 3251-3269. The Royal Society.
[22] Gano, S. E., Renaud, J. E., & Sanders, B. (2005). Hybrid variable fidelity optimization by using a kriging-based scaling function. Aiaa Journal, 43(11), 2422-2433.
[23] Gnanavel Babu, A., Jerald, J., Noorul Haq, A., Muthu Luxmi, V., & Vigneswaralu, T. P. (2010). Scheduling of machines and automated guided vehicles in FMS using differential evolution. International Journal of Production Research, 48(16), 4683-4699.
[24] Groover, M. P. (2007). Automation, production systems, and computer-integrated manufacturing. Prentice Hall Press.
[25] Han, M. H., & McGinnis, L. F. (1989). Control of material handling transporter in automated manufacturing. IIE transactions, 21(2), 184-190.
[26] Hao, W., Shaoping, W., & Tomovic, M. M. (2010). Modified sequential Kriging optimization for multidisciplinary complex product simulation. Chinese Journal of Aeronautics, 23(5), 616-622.
[27] Harmonosky, C. M. (1995, December). Simulation-based real-time scheduling: review of recent developments. In Proceedings of the 27th conference on Winter simulation, 220-225. IEEE Computer Society.
[28] Ho, Y. C., & Wang, C. R. (1997). A Shifting-Zone Control Strategy for Vehicle-Collision Prevention in a Multiple-Vehicle AGV System. In Proceedings of the 14th International Conference on Production Research, OSAKA, Japan.
[29] Huang, E., Xu, J., Zhang, S., & Chen, C. H. (2015). Multi-fidelity Model Integration for Engineering Design. Procedia Computer Science, 44, 336-344.
[30] Huang, D., Allen, T. T., Notz, W. I., & Miller, R. A. (2006). Sequential kriging optimization using multiple-fidelity evaluations. Structural and Multidisciplinary Optimization, 32(5), 369-382.
[31] Jerald, J., Asokan, P., Saravanan, R., & Rani, A. D. C. (2006). Simultaneous scheduling of parts and automated guided vehicles in an FMS environment using adaptive genetic algorithm. International Journal of Advanced Manufacturing Technology, 29(5-6), 584-589.
[32] Joseph, O. A., Sridharan, R. (2011). Evaluation of routing flexibility of a flexible manufacturing system using simulation modelling and analysis. International Journal of Advanced Manufacturing Technology, 56(1-4), 273-289.
[33] Kanazaki, M., Takagi, H., & Makino, Y. (2013). Mixed-fidelity efficient global optimization applied to design of supersonic wing. Procedia Engineering, 67, 85-99.
[34] Karabtik, S., & Sabuncuolu, I. (1993, May). A beam search based algorithm for scheduling machines and AGVs in an FMS. In Proceedings of the Second Industrial Engineering Research Conference, Los Angeles, 308-312.
[35] Kim, C. W., & Tanchoco, J. M. (1991). Conflict-free shortest-time bidirectional AGV routeing. International Journal of Production Research, 29(12), 2377-2391.
[36] Koziel, S., & Leifsson, L. Þ. (2013, December). Shape-Preserving Response Prediction for Engineering Design Optimization. In ICCS, 879-888.
[37] Kumar, M. S., Janardhana, R., & Rao, C. S. P. (2011). Simultaneous scheduling of machines and vehicles in an FMS environment with alternative routing. International Journal of Advanced Manufacturing Technology, 53(1-4), 339-351.
[38] Lacomme, P., Moukrim, A., & Tchernev*, N. (2005). Simultaneous job input sequencing and vehicle dispatching in a single-vehicle automated guided vehicle system: a heuristic branch-and-bound approach coupled with a discrete events simulation model. International Journal of Production Research, 43(9), 1911-1942.
[39] Lee, C. C., & Lin, J. T. (1995). Deadlock prediction and avoidance based on Petri nets for zone-control automated guided vehicle systems. International Journal of Production Research, 33(12), 3249-3265.
[40] Leifsson, L., Koziel, S., & Bekasiewicz, A. (2014). Fast Low-fidelity Wing Aerodynamics Model for Surrogate-based Shape Optimization. Procedia Computer Science, 29, 811-820.
[41] Li, W., Li, M., Chen, C. S., & Liu, X. (2015). Compactly supported radial basis functions for solving certain high order partial differential equations in 3D. Engineering Analysis with Boundary Elements, 55, 2-9.
[42] Madan, M., Son, Y. J., Cho, H., & Kulvatunyou, B. (2005). Determination of efficient simulation model fidelity for flexible manufacturing systems. International Journal of Computer Integrated Manufacturing, 18(2-3), 236-250.
[43] March, A., & Willcox, K. (2012). Provably convergent multifidelity optimization algorithm not requiring high-fidelity derivatives. AIAA journal, 50(5), 1079-1089.
[44] Mascarenhas, M. B. (1981). Planning for flexibility. Long Range Planning, 14(5), 78-82.
[45] Moon, I., & Lee, J. (2000). Genetic algorithm application to the job shop scheduling problem with alternative routings. Pusan National University.
[46] Nasr, N., & Elsayed, E. A. (1990). Job shop scheduling with alternative machines. International Journal of Production Research, 28(9), 1595-1609.
[47] Nageswararao, M., Narayanarao, K., & Ranagajanardhana, G. (2014). Simultaneous Scheduling of Machines and AGVs in Flexible Manufacturing System with Minimization of Tardiness Criterion. Procedia Materials Science, 5, 1492-1501.
[48] Nishi, T., Hiranaka, Y., & Grossmann, I. E. (2011). A bilevel decomposition algorithm for simultaneous production scheduling and conflict-free routing for automated guided vehicles. Computers & Operations Research, 38(5), 876-888.
[49] Ombuki, B. M., & Ventresca, M. (2004). Local search genetic algorithms for the job shop scheduling problem. Applied Intelligence, 21(1), 99-109.
[50] Ono, I., Yamamura, M., & Kobayashi, S. (1996, May). A genetic algorithm for job-shop scheduling problems using job-based order crossover. In Evolutionary Computation, 1996., Proceedings of IEEE International Conference on, 547-552.
[51] Paige, J. B., & Morin, K. H. (2013). Simulation fidelity and cueing: a systematic review of the literature. Clinical Simulation in Nursing, 9(11), e481-e489.
[52] Pandit, R., & Palekar, U. S. (1993). Job shop scheduling with explicit material handling considerations. Working paper, Iowa State University, Ames, Iowa.
[53] Park, S. C., Byoung K. C., and Namkyu P. (2011). Virtual FMS architecture for FMS prototyping. AIP Conference Proceedings, 628-637.
[54] Raman, N. (1986). Simultaneous scheduling of machines and material handling devices in automated manufacturing. In Proc. of the Second ORSA/TIMS Conference on Flexible Manufacturing Systems: Operations Research Models and Applications.
[55] Reddy, B. S. P., & Rao, C. S. P. (2006). A hybrid multi-objective GA for simultaneous scheduling of machines and AGVs in FMS. International Journal of Advanced Manufacturing Technology, 31(5-6), 602-613.
[56] Rehmann, A. J., Mitman, R. D., & Reynolds, M. C. (1995). A Handbook of Flight Simulation Fidelity Requirements for Human Factors Research. CREW SYSTEM ERGONOMICS INFORMATION ANALYSIS CENTER WRIGHT-PATTERSON AFB OH.
[57] Robinson, T. D., Eldred, M. S., Willcox, K. E., and Haimes, R., (2008). Surrogate-based optimization using multifidelity models with variable parameterization and corrected space mapping. AIAA Journal, 46(11), 2814-2822.
[58] Sawik, T. (1996). A multilevel machine and vehicle scheduling in a flexible manufacturing system. Mathematical and computer modelling, 23(7), 45-57.
[59] Satishkumar, M. V. (2011). Simultaneous scheduling of machines and Agvs using evolutionary optimization algorithms.
[60] Shivhare, M., & Bansal, S. (2014). Layout Optimization in Flexible Manufacturing System using Particle Swarm Optimization in Matlab. International Journal of Software Engineering and Its Application, 8(7), 55-64.
[61] Stecke, K. E. (1985). Design, planning, scheduling, and control problems of flexible manufacturing systems. Annals of Operations research, 3(1), 1-12.
[62] Subbaiah, K. V., Rao, M. N., & Rao, K. N. (2009). Scheduling of AGVs and machines in FMS with makespan criteria using sheep flock heredity algorithm. International Journal of Physical Sciences, 4(2), 139-148.
[63] Sun, G., Li, G., Zhou, S., Xu, W., Yang, X., Li, Q. (2011). Multi-fidelity optimization for sheet metal forming process. Structural and Multidisciplinary Optimization, 44(1), 111-124.
[64] Ulusoy, G., & Bilge, Ü. (1993). Simultaneous scheduling of machines and automated guided vehicles. International Journal of Production Research, 31(12), 2857-2873.
[65] Ulusoy, G., Sivrikaya-Şerifoǧlu, F., & Bilge, Ü. (1997). A genetic algorithm approach to the simultaneous scheduling of machines and automated guided vehicles. Computers & Operations Research, 24(4), 335-351.
[66] Vis, I. F. (2006). Survey of research in the design and control of automated guided vehicle systems. European Journal of Operational Research, 170(3), 677-709.
[67] Wang, F. K., & Lin, J. T. (2004). Performance evaluation of an automated material handling system for a wafer fab. Robotics and Computer-Integrated Manufacturing, 20(2), 91-100.
[68] Wilhelm, W. E., & Shin, H. M. (1985). Effectiveness of alternate operations in a flexible manufacturing system. International Journal of Production Research, 23(1), 65-79.
[69] Xu, J., Zhang, S., Huang, E., Chen, C. H., Lee, L. H., & Celik, N. (2014, August). An ordinal transformation framework for multi-fidelity simulation optimization. In 2014 IEEE International Conference on Automation Science and Engineering (CASE), 385-390.
[70] Xu, J., Zhang, S., Huang, E., Chen, C. H., Lee ,L. H., & Celik, N. (2016). MO2TOS: Multi-fidelity Optimization with Ordinal Transformation and Optimal Sampling. Asia-Pacific Journal of Operational Research.
[71] Yeh, M. S., & Yeh, W. C. (1998). Deadlock prediction and avoidance for zone-control AGVS. International Journal of Production Research, 36(10), 2879-2889.