近年來台灣地區交通量成長迅速，個人小客車擁有比例與使用頻率亦日益增加，透過共乘制度除了可提高小客車之乘載率，紓解都會區交通雍塞與停車問題，並且可降低因全球油價上漲造成旅行成本增加所帶來的衝擊，以及達到節能減碳等優點。然而，目前實務上小客車的共乘配對上，多採用人工經驗進行排程規劃，不僅費時且缺乏系統分析，使得共乘的績效降低。過去小客車共乘的研究多以平均旅行時間為依據，進行共乘配對與排程，此作法未考量實際旅行時間的隨機性。在實際共乘進行時若隨機旅行時間造成之擾動過大，將使原規劃的配對與排程結果失去最佳性。因此，考量隨機性旅行時間之影響，建構一隨機性小客車共乘配對模式，期能提供一有效的規劃輔助工具，以幫助決策者有效地進行規劃。
本研究利用時空網路流動技巧建立一此隨機模式，模式中包含供車群車流、供車群人流與不供車群人流網路，以定式共乘群在時空中的流動與配對。本研究進一步修改隨機模式之旅行時間為平均旅行時間，建立一確定性模式。此兩模式可定式為特殊之整數多重貨物網路流動問題，屬NP-hard問題。為面臨實務之大型問題難以在有限時間內僅用數學規劃軟體求解，本研究發展一啟發式演算法以有效地求解問題。此外，本研究亦發展一模擬評估方法，以評估兩模式於實際共乘進行時之績效。最後為評估本研究中模式與演算法之實用績效，以實際狀況資料及合理假設產生測試例，進行本研究之範例測試並針對不同參數進行敏感度分析，結果顯示本模式與演算法在實用上可有效的運用，並進一步提出結論與建議。

Respecting traffic volume has significantly grown and private cars become more popular than before in Taiwan. Therefore, carpool that enhances the car occupancy rate can not only relieve traffic congestion, but also reduce the travel cost which comes from the price of global petroleum going up, even save energy. As regards in Taiwan, carpool matching is manually performed by planning personnels with experience in current practice, without a systematic analysis. Such a manual approach is considered to be inefficient and ineffective. In other words, stochastic disturbances arising from variations in car travel times in actual operations are neglected. In the worst scenario, where car travel times fluctuate wildly during operations, the planned schedule could be disturbed enough to lose its optimality. Therefore, focusing on many-to-many origin-destination (OD), we constructed a stochastic carpool matching model that considers the influence of stochastic travel times. The matching model is expected to be an effective tool for the planner to solve carpool members matching.
We employed network flow techniques to construct the stochastic carpool matching model, including multiple CVG (a carpool member group who can provide a vehicle) vehicle-flow networks, CVG passenger-flow networks and multiple CNG (a carpool member group who cannot provide any vehicle) passenger-flow networks to formulate the flows of CVGs and CNGs in the dimensions of time and space. Then, we modified the stochastic travel times in the stochastic carpool matching model as an average travel time to develop a deterministic scheduling model. The two models are formulated as special integer multiple commodity network flow problems, which are characterized as NP-hard. Since the problem sizes are expected to be huge in real practice, the models are difficult to be solved in a reasonable time. Therefore, we also developed a heuristic algorithm for efficiently solving matching problems. In addition, to evaluate the stochastic and deterministic carpool matching models, we also developed a simulation-based evaluation method. The performance of the solution method in practice is evaluated by carrying out a case study using real data and suitable assumptions, and then sensitive analysis is performed for different parameters. The test results show the model to be good and that the solution method could be useful in practice.

1. Carpool共乘網，網址 http://www.carpool.com.tw/，(2010)。
2. 交通部全球資訊網，網址 http://www.motc.gov.tw/，(2010)。
3. 何依栖 (1989)，「都會區計程車共乘制度實施及管理之探討」，運輸計劃季刊，第十八卷，第四期，第507-518頁。
4. 余秀梅 (1994)，「多元商品模式應用在動態貨櫃調度問題之研究」，碩士論文，國立成功大學交通管理科學研究所。
5. 吳沛儒 (2004)，「任務型共乘接駁計程車之規劃與設計」，碩士論文，私立逢甲大學交通工程與管理學研究所。
6. 吳逸祥(2009)，「隨機旅行時間下計程車共乘及乘客配對整合模式與求解演算法之研究」，碩士論文，國立中央大學土木工程學系。
7. 吳權哲 (2007)，「都會區計程車共乘配對模式暨求解演算法之研究」，碩士論文，國立中央大學土木工程學系。
8. 呂英志 (2002)，「即時資訊下車輛路線問題之研究」，碩士論文，逢甲大學交通工程與管理研究所。
9. 辛孟鑫 (2005)，「撥召運輸系統路線規劃問題之研究－以台北市復康巴士為例」，碩士論文，國立成功大學交通管理科學研究所。
10. 林士鈞 (2004)，「定期貨櫃運輸船舶排程暨船期表建立之研究」，碩士論文，國立中央大學土木工程學系。
11. 林瑜芳(2008)，「小汽車共乘公平性配對模式暨求解演算法之研究」，碩士論文，國立中央大學土木工程學系。
12. 林益生 (1998)，「隨機環境下多商品、多車種派車問題之研究」，碩士論文，中原大學工業工程研究所。
13. 邱明琦、陳春益、林佐鼎 (2002)，「海運貨櫃排程模式之研究」，運輸計劃季刊，第三十一卷，第三期，第495-522頁。
14. 侯育周 (2007)，「隨機性班機到離延誤下動態機門指派之研究」，碩士論文，國立中央大學土木工程學系。
15. 苑鳳萍 (2001)，「客運車輛擾動下調度系統之研究」，碩士論文，國立交通大學運輸工程與管理研究所。
16. 唐存寬 (1999)，「在顧客需求為隨機之假設下多種貨品儲運分配系統設計」，碩士論文，國防管理學院資源管理研究所。
17. 桃北北宜基共乘網，網址 http://carpool.tpc.gov.tw/carpool/，(2010)。
18. 寇世傑(1998)，「以習慣領域理論探討推動通勤者共乘行為之契機」，碩士論文，國立交通大學交通運輸研究所。
19. 張有恆 (1994)，「都市公共運輸」，華泰書局。
20. 曹智翔 (2007)，「短期需求擾動下動態醫療物資輸配送之研究」，碩士論文，國立中央大學土木工程學系。
21. 許采蘋 (2005)，「計程車共乘與撥召計程車可行條件之研究」，碩士論文，國立交通大學交通運輸研究所。
22. 陳妙珍、顏上堯、張珮璇 (2000)，「航空公司資產與負債管理模式之建立」，第四屆海峽兩岸會計與管理學術研討會論文集，武漢。
23. 陳信諺 (2008)，「計程車共乘及旅客配對整合模式暨求解演算法之研究」，碩士論文，國立中央大學土木工程學系。
24. 陳俊豪 (2005)，「因應臨時事件變動租用數機場共用櫃檯即時指派之研究」，碩士論文，中央大學土木工程學系。
25. 陳春益、邱明琦 (2002)，「貨櫃航線網路設計模式之研究」，運輸計劃季刊，第三十一卷，第二期，第267-298頁。
26. 陳昱彰 (2006)，「區位分析應用於任務型共乘接駁計程車之派遣規劃」，碩士論文，私立逢甲大學交通工程與管理學研究所。
27. 陶治中、張勝雄等人(2005)，「智慧型運輸系統應用於高乘載計畫之示範與建置-都會區共乘系統之示範與建置(1/2)」，交通部科技顧問室。
28. 曾國雄(1982a)，「合車用乘(Car pool)在臺灣地區之可行性」，能源季刊，第十二卷，第三期，頁13-19。
29. 曾國雄(1982b)，「合租用乘(Van pool)在臺灣地區之可行性」，能源季刊，第十二卷，第三期，頁20-29。
30. 游俊雄、丁國樑 (1998)，「需求反應旅次運載模擬模式應用於捷運營運班表之評估」，運輸計劃季刊，第二十七卷，第三期，第489-508頁。
31. 黃漢瑄 (2006)，「撥召服務最佳化指派作業之研究」，碩士論文，私立淡江大學運輸管理學系運輸科學研究所。
32. 楊大輝、李綺容 (2007)，「需求變動下之航空貨運網路規劃」，運輸學刊，第十九卷，第二期，第169-189頁。
33. 楊淑芳 (2006)，「以巨集啟發式演算法求解即時資訊下之中型車共乘問題」，碩士論文，私立淡江大學運輸管理學系運輸科學研究所。
34. 廖建韋 (2007)，「醫療物資訂購及配送排程規劃之研究」，碩士論文，中央大學土木工程學系。
35. 賴淑芬(1990)，「工業區實施車輛共乘之可行性研究與規劃-以高雄市楠梓加工出口區為例」，碩士論文，國立成功大學交通管理學系。
36. 顏上堯、杜宇平、陳怡妃 (2004)，「因應臨時事件機場共用櫃檯即時指派之研究」，運輸計劃季刊，第三十三卷，第一期，第59- 81頁。
37. 顏上堯、翁綵穗 (2001)，「季節轉換間緩衝期飛航排程之研究」，運輸計劃季刊，第三十卷，第四期，第891- 922頁。
38. 顏上堯、齊志仁、湯慶輝 (2005)，「隨機需求下多目標長途客運排程模式之研究」，運輸計畫季刊，第 34 卷第 1 期，第93-118頁。
39. 顏上堯、羅智騰 (1996)，「因應預期性航具維修之系統性飛航排程」，中國土木水利工程學刊，第八卷，第三期， 第447-456頁。
40. 羅敏綺 (1998)，「隨機需求下捷運系統營運模擬模式之構建-以台北市木柵線為例」，碩士論文，國立成功大學交通管理科學研究所。
41. Aldaihani, M. and Dessouky, M.M. (2003), “Hybrid scheduling methods for para transit operations,” Computers and Industrial Engineering, Vol. 45, pp. 75-96.
42. Attanasio, A., Cordeau, J.F., Ghiani, G. and Laporte, G. (2004), “Parallel Tabu search heuristics for the dynamic multi-vehicle dial-a-ride problem,” Parallel Computing, Vol. 30, pp.377-387.
43. Baldacci, R., Maniezzo, V. and Mingozzi, A. (2004), “An exact method for the car pooling problem based on Lagrangean column generation,” Operations Research, Vol. 52(3), pp. 422-439.
44. Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P. and Vance, P. H. (1998). “Branch-and-price: column generation for solving huge integer programs,” Operations Research, Vol. 46, pp. 316-329.
45. Benders, J. F. (1962). “Partitioning procedures for solving mixed-variables programming problems,” Numerische Mathematik, Vol. 4, pp. 238-252.
46. Bodin, L.D. and Sexton, T. (1986), “The multi-vehicle subscriber dial-a-ride problem,” TIMS Studies in Management Science, Vol. 2, pp. 73-86.
47. Calvo, R. W., Luigi, F. L., Haastrup, P., and Maniezzo, V., “A distributed geographic information system for the daily car pooling problem,” Computers and Operations Research, Vol. 31, pp 2263- 2278 (2004).
48. Camerini, P. K., Fratta, L., and Maffioli, F. (1975). “On improving relaxation methods by modified gradient techniques,” Mathematical Programming Study, Vol. 3, pp. 6-25.
49. Chen, C. Y. and Kornhauser, A. L. (1990). “Decomposition of convex mulitcommodity network flow problem,” Report SOR-90-19, Dept. of Civil Engineering and Operations Research, Princeton University, Princeton, NJ.
50. Chih, K. C. K. (1986). “A real time dynamic optimal freight car management simulation model of multiple railroad, mulitcommodity temporal spatial flow problem,” Ph.D. Dissertation, Princeton University, Princeton, NJ.
51. Cordeau, J.F. (2006), “A branch-and-cut algorithm for the dial-a-ride problem,” Operations Research, Vol. 54, pp. 573-586.
52. Cordeau, J.F. and Laporte, G. (2003a), “A tabu search heuristic for the static multi-vehicle dial-a-ride problem,” Transportation Research Part B, Vol. 37, pp. 579-594.
53. Cordeau, J.F. and Laporte, G. (2003b), “The dial-a-ride Problem (DARP): variants, modeling issues and algorithms,” 4OR: A Quarterly Journal of Operations Research, Vol. 1, pp. 89–101.
54. Coslovich, L., Pesenti, R. and Ukovich, W. (2006), “A two-phase insertion technique of unexpected customers for a dynamic dial-a-ride problem,” European Journal of Operational Research, Vol. 175, pp. 1605-1615.
55. Desaulniers, G., Desrosiers, J., Dumas, Y., Solomon, M. M. and Soumis, F. (1997).“Daily aircraft routing and scheduling,” Management Science, Vol. 43, pp. 841-855.
56. Desrosiers, J., Dumas, Y. and Soumis, F. (1986), “A dynamic programming solution of the large-scale single vehicle dial-a-ride problem with time windows,” American Journal of Mathematical and Management Sciences, Vol. 6, pp. 301-325.
57. Diana M., and Dessouky, M.M. (2004), “A new regret insertion heuristic for solving large-scale dial-a-ride problems with time windows,” Transportation Research Part B, Vol.38, pp.539–557.
58. Fisher, M. L. (1981). “The Lagrangian relaxation method for solving integer programming problem,” Management Science, Vol. 27, pp. 1-18.
59. Fu, L. (2002a). “A simulation model for evaluating advanced dial-a-ride paratransit systems,” Transportation Research Part A, Vol. 36, pp. 291-307.
60. Fu, L. (2002b). “Scheduling dial-a-ride paratransit under time-varying, stochastic congestion,” Transportation Research Part B, Vol. 36, pp. 485-506.
61. Gendreau, M., Laporte, G. and Semet, F. (2001), “A dynamic model and parallel Tabu search algorithm for real-time ambulance relocation,” Parallel Computing, Vol. 27, pp. 1641-1653.
62. Hart, S.M. (1996), “The modeling and solution of a class of dial-a-ride problems using sumulated annealing,” Control and Cybernetics, Vol. 25, No. 1, pp. 1-27.
63. Horn, M.E.T. (2002), “Fleet scheduling and dispatching for demand-responsive passenger services,” Transportation Research Part C, Vol. 10, pp. 35-63.
64. Jaw, J.J., Odoni, A.R., Psaraftis, H.N. and Wilson, N.H.M. (1986), “A heuristic algorithm for the multi-vehicle advance-request dial-a-ride problem with time windows,” Transportation Research Part B, Vol. 20, pp. 243-257.
65. Jørgensen, R.M., Larsen, J. and Bergvinsdottir, K.B. (2008), “Solving the dial-a-ride problem using genetic algorithms,” Journal of the Operational Research Society (in press).
66. Kennington, J. L. and Shalby, M. (1977). “An effective subgradient procedure for minimum cost multicommodity flow problem,” Management Science, Vol. 23, pp.994-1004.
67. Kenyon, A. S. and Morton, D. P. (2003). “Stochastic vehicle routing with random travel times,” Transportation Science, Vol. 37, pp. 69-82.
68. Lai, M. F. and Lo, H. K. (2004). “Ferry service network design: Optimal fleet size, routing, and scheduling,” Transportation Research Part A, Vol. 38, pp. 305-328.
69. Lamatsch, A. (1992). “An approach to vehicle scheduling with depot capacity constraints,” in Desrochers, M. and Rousseau, J. M.(eds.), Computer Aided Transit Scheduling, Lecture Notes in Economics and Mathematical System 386, Springer Verlag, Berlin, Heidelberg, pp. 181-195.
70. Lee, B. C. (1986). “Routing problem with service choices, flight transportation laboratory,” Report R86-4, Massachusetts Institute of Technology, MA.
71. Levin, A. (1969). “Some fleet routing and scheduling problems for air transportation systems flight transportation laboratory,” Report R68-5, Massachusetts Institute of Technology, MA.
72. Levin, A. (1971). “Scheduling and fleet routing models for transportation systems,” Transportation Science, Vol. 5, pp. 232-255.
73. Li, X., Tian, P. and Leung, C. H. (2010). “Vehicle routing problems with time windows and stochastic travel and service times: Models and algorithm,” Int. J. Production Economics, Vol. 125, pp. 137-145.
74. List, G. F., Wood, B., Nozick, L. K., Turnquist, M. A., Jones, D. A., Kjeldgaard, E. A., and Lawton, C. R. (2003). “Robust optimization for fleet planning under uncertainty,” Transportation Research Part E, Vol. 39, pp. 209-227.
75. Madsen, O.B.G., Ravn, H.F. and Rygaard, J.M. (1995), “A heuristic algorithm for a dial-a-ride problem with time windows, multiple capacities, and multiple objectives,” Annals of Operations Research, Vol. 60, pp. 193-208.
76. Melachrinoudis, E., Ilhan, A.B. and Min, H. (2007), “A dial-a-ride problem for client transportation in a healthcare organization,” Computers and Operations Research, Vol. 34, pp. 742-759.
77. Mesquita, M. and Paixao, J. (1992). “Multiple depot vehicle scheduling problem: a new heuristic based on quasi-assignment algorithm,” in Desrochers, M. and Rousseau, J. M.(eds.), Computer Aided Transit Scheduling, Lecture Notes in Economics and Mathematical System 386, Springer Verlag, Berlin, Heidelberg, pp. 181-195.
78. Mulvery, J. M. and Ruszczynski, A. (1995). “A new scenario decomposition method for large-scale stochastic optimization,” Operations Research, Vol. 43, pp. 477-490.
79. Mulvery, J. M., Vanderbei, R. J., Zenios, S. A. (1995). “Robust optimization of large-scale systems,” Operations Research, Vol. 43, pp. 254-281.
80. Pearlstein, A. (1986), “A study of staff and fraculty commuters at the university of California, Los Angeles,” Transportation Research Record, No. 1082, pp. 26-33.
81. Powell, W. B. and Ioannis, A. K. (1992). “Shipment routing algorithms with tree constraints,” Transportation Science, Vol. 26, pp. 230-245.
82. Psaraftis, H.N. (1980), “A dynamic programming approach to the single-vehicle, many-to-many immediate request dial-a-ride problem,” Transportation Science, Vol. 14, pp. 130-154.
83. Psaraftis, H.N. (1983), “An exact algorithm for the single-vehicle many-to-many dial-a-ride problem with time windows,” Transportation Science, Vol. 17, pp. 351-357.
84. Rekiek, B., Delchambre, A. and Saleh, H.A. (2006), “Handicapped person transportation: an application of the grouping genetic algorithm,” Engineering Application of Artificial Intelligence, Vol. 19, pp. 511-520.
85. Ropke, S., Cordeau, J.F. and Laporte, G. (2007), “Models and branch-and-cut algorithms for pickup and delivery problems with time windows,” Networks, Vol. 49, pp. 258-272.
86. Ropke, S., Cordeau, J.F. and Laporte, G. (2007), “Models and branch-and-cut algorithms for pickup and delivery problems with time windows,” Networks, Vol. 49, pp. 258-272.
87. Rose G. (2002), “Providing premium carpool parking using a low-tech ITS initiative”, ITE Journal Institute of Transportation Engineers, Vol.72, pp.32-36. (Rose,2002)
88. Samuel, W.L. (1998), “Autonomous dial-a-ride transit benefit-cost evaluation,” Volpe National Transportation Systems Center, August.
89. Sexton, T. (1979), “The single vehicle many-to-many routing and scheduling problem,” Ph.D. dissertation, SUNY at Stony Brook.
90. Sexton, T. and Bodin, L.D. (1985a), “Optimizing single vehicle many-to-many operations with desired delivery times: I. scheduling,” Transportation Science, Vol. 19, pp. 378-410.
91. Sexton, T. and Bodin, L.D. (1985b), “Optimizing single vehicle many-to-many operations with desired delivery times: II. routing,” Transportation Science, Vol. 19, pp. 411-435.
92. Shan, Y.S. (1985). “A dynamic mulitcommodity network flow model for real time optimal real freight car management,” Ph.D. Dissertation, Princeton University, Princeton, NJ.
93. Simpson, R.W. (1969). “A review of scheduling and routing model for airline scheduling,” IX AGIFORS Symposium, Broadway, England.
94. Stancu Minasian, I. M. (1984). Stochastic Programming with Multiple Objective Functions, Editura Academiei, Bucharest.
95. Teodorovic, D. (1988). Airline Operations Research, Gordon and Breach Science Publishers, New York.
96. Teodorovic, D. and Guberinic, S. (1984). “Optimal dispatching strategy on an airline network after a schedule perturbation,” European Journal of Operational Research, Vol. 15, pp. 178-182.
97. Thengvall, B. G., Bard, J. F., and Yu, G. (2000). “Balancing user preferences for aircraft schedule recovery during airline irregular operations,” IIE Transactions on Operations Engineering, Vol. 32, pp.181-193.
98. Thengvall, B. G., Yu, G., and Bard, J. F. (2001). “Multiple fleet aircraft schedule recovery following hub closure,” Transportation Research Part A, Vol. 35, pp. 289-308.
99. Toth, P. and Vigo, D. (1996), “Fast local search algorithms for the handicapped persons transportation problem,” In I. H. Osman and J. P. Kelly (Eds.), Meta-heuristics: Theory and Applications, Kluwer Academic Publishers, Boston, pp. 677-690.
100. Toth, P. and Vigo, D. (1997), “Heuristic algorithms for the handicapped persons transportation problem,” Transportation Science, Vol. 31, pp. 60-71.
101. Xiang, Z., Chu, C. and Chen, H. (2006), “A fast heuristic for solving a large-scale static dial-a-ride problem under complex constraints,” European Journal of Operational Research, Vol. 174, pp. 1117-1139.
102. Yan, S. and Chen, C. H. (2007). “Coordinated flight scheduling models for allied airlines,” Transportation Research Part C, Vol. 15, pp. 246-264.
103. Yan, S. and Chen, H. L. (2002). “A scheduling model and a solution algorithm for inter-city bus carriers,” Transportation Research Part A, Vol. 36, pp. 805-825.
104. Yan, S. and Lai, W. S. (2007). “An optimal scheduling model for ready mixed concrete supply with overtime considerations,” Automation in Construction, Vol. 16, pp. 734-744.
105. Yan, S. and Lin, C. (1997). “Airline scheduling for the temporary closure of airports,” Transportation Science, Vol.31, pp. 72-82.
106. Yan, S. and Shih, Y. L. (2007). “A time-space network model for work team scheduling after a major disaster”, Journal of the Chinese Institute of Engineers, Vol. 30, pp. 63-75.
107. Yan, S. and Tseng, C. H. (2002). “A passenger demand based model for airline flight scheduling and fleet routing,” Computers and Operations Research, Vol. 29, pp. 1559-1581.
108. Yan, S. and Tu, Y. (1997). “Multi-fleet routing and multi-stop flight scheduling for schedule perturbation,” European Journal of Operational Research, Vol. 103, pp. 155-169.
109. Yan, S. and Yang, D. H. (1996). “A decision support framework for handling schedule perturbation”, Transportation Research Part B, Vol. 30, pp. 405-419.
110. Yan, S. and Young, H. F. (1996). “A decision support framework for multi-fleet routing and multi-stop flight scheduling,” Transportation Research Part A, Vol. 30, pp. 379-398.
111. Yan, S., Chen, C. H., and Chen, C. K. (2006). “Long-term manpower supply planning for air cargo terminals,” Journal of Transport Management, Vol. 12, Issue 4, pp. 175-181.
112. Yan, S., Chi, C. J., and Tang, C. H. (2006). “Inter-city bus routing and timetable setting under stochastic demands,” Transportation Research Part A, Vol. 40, pp. 572-586.
113. Yan, S., Chi, C. J., and Tang, C. H. (2006). “Inter-city bus routing and timetable setting under stochastic demands,” Transportation Research Part A, Vol. 40, pp. 572-586.
114. Yan, S., Lai, W., and Chen, M. (2008b). “Production scheduling and truck dispatching of ready mixed concrete,” Transportation Research, Part E, Vol. 44, Issue 1, pp. 164-179.
115. Yan, S., Shieh, C. W., and Chen, M. (2002). “A simulation framework for evaluating airport gate assignments, ”Transportation Research Part A, Vol. 36, pp. 885-898.
116. Yan, S., Tang, C. H., and Fu, T.C. (2008a). “An airline scheduling model and solution algorithms under stochastic demands,” European Journal of Operational Research, Vol. 190, pp. 22-39.
117. Yan, S., Tang, C. H., and Shieh, C.N. (2005). “a simulation framework for evaluating airline temporary schedule adjustments following incidents,” Transportation Planning and Technology, Vol. 28, pp. 189-211.