良好的船隊排程與船期表規劃攸關航商的經營成效甚巨，直接影響航商本身的獲利能力、服務水準與市場競爭力。目前航商在船隊排程與船期表的制訂上，都是依照人工經驗進行試誤法反覆調整，缺乏效率且無法確保得到良好的結果。以往針對定期貨櫃船舶運輸的研究多偏向中長期的航線選擇及規劃，而在短期班次表建立的研究甚少有相關研究。緣此，本研究站在航商的立場，以航商最大利潤為目標，根據中長期規劃的航線結果，並考量定期貨櫃船舶運輸的相關營運限制與資料，發展一短期船隊排程與船期表規劃模式。本研究期能於未來實務應用上，提供航商一有效的工具，以幫助航商有效規劃船隊排程及建立船期表。
本研究利用網路流動技巧構建多航線船隊排程模式，此模式包含多重船流時空網路及多重物流時空網路，以定式船舶及貨物在時空中流動之情況。其中船流時空網路則以整數流動方式定式船隊的週期排程；物流時空網路則根據不同時效性之貨物需求，構建多重起迄時對（OD-time pair）時空網路。在物流時空網路與船流時空網路中，再加上實務的營運限制，以符合實際的作業。此模式可定式為一整數多重網路流動問題，屬NP-hard問題。本研究利用拉氏鬆弛法暨次梯度法配合數學規劃軟體CPLEX進行模式求解。最後，為測試本研究模式與解法的實用績效，本研究以國內一航商之營運資料為例，進行實例測試與分析，進而提出結論與建議。

A good ship routing and shipment scheduling is more important for shipping carriers. They are essential to shipping carriers’ profitability, level of service and competitive capability in the market. However, most of the shipping carriers in Taiwan currently adopt a trial-and-error process for ship routing and shipment scheduling practices. Such an approach is considered to be less efficient, and can possibly result in an inferior feasible solution. In the past, most research on container liner was mainly focused on port selecting and ship routing planning, which was typically in the stage of long-term operations. Since shipment scheduling on the short-term operations are quite lacking, therefore, on the basis of the shipping carriers perspective, we base on the result of the long-term operations to develop a ship routing and shipment scheduling model on short-term operations with the objective of maximizing the operating profit, subject to the related operating constraints. The model is expected to be an effective tool for the shipping carriers to establish their ship schedule.
We employ network flow techniques to construct the model, which include multiple ship-flow networks and multiple cargo-flow networks in order to formulate the flows of ships and cargos in the dimensions of time and space. In the ship-flow networks, we use an integer flow network to formulate the periodical ship routes. In the cargo-flow networks, we construct multiple OD-time-pair time-space networks on the base of cargos’ timeliness. Some side constraints set between the ship- and cargo -flow networks according to the real operating requirements. The model formulated as a multiple commodity network flow program that is characterized as an NP-hard problem. We employ a mathematical programming solver and develop the Lagrangian
relaxation-based algorithm, coupled with a subgradient method, to solve the problem. Finally, to evaluate the model in practice, we perform a case study using real operation data from a Taiwan marine transport company. Conclusions and suggestions then be given.

1.余秀梅，「多元商品模式應用在動態貨櫃調度問題之研究」，國立成功大學交通管理科學研究所碩士論文 (1994)。
2.陳世欽，「多時效性貨物需求下貨機飛航排程暨班次表建立之研究」，國立中央大學土木研究所碩士論文 (2003)。
3.張永昌、陳春益，「選擇定期貨櫃航線舶靠港之探討」，中華民國運輸學會第九屆論文研討會，頁309-316 (1994)。
4.陳弘輝，「定期貨櫃船繞航模式之比較」，國立海洋大學航運管理研究所碩士論文 (1999)。
5.陳宇軒，「整合航空客運與貨運之飛航排程暨班次表建立之研究」，國立中央大學土木研究所碩士論文 (2004)。
6.陳妙珍、顏上堯、張珮璇，「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 (2000)。
7.陳春益、邱明琦，「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，頁267-298 (2002)。
8.黃望修，「貨櫃運輸船隊長程航次逐港灣靠與穿梭地區中心灣靠營運方式之財務效益比較分析」，國立交通大學管理科學研究所碩士論文 (1990)。
9.郭塗城、朱經武，「定期船停靠港口模式之探討」，中華民國第五屆運輸網路研討會，頁317-326 (2000)。
10.彭信坤，「貨櫃船隊船型配置及航線選擇方案之研究」，國立成功大學交通管理科學研究所碩士論文 (1982)。
11.董孝行，「貨櫃船最適船型之研究」，運輸計劃季刊，第十五卷，第三期，頁435-459， (1986)。
12.廖于慧、盧華安、曹壽民、廖國勛，「定期貨櫃航線之船期安排」，運輸學刊，第十六卷，第三期，頁203-226 （2004）。
13.廖于慧、盧華安、曹壽民，「轉運航線之船期安排」，運輸學刊，第十七卷，第一期，頁1-26 （2005）。
14.劉中平，「定期貨櫃船之船隊部署」，國立海洋大學航運技術研究所碩士論文 (1999)。
15.賴俊宏，「國際快遞業飛航排程暨班次表建立之研究」，國立中央大學土木研究所碩士論文 (2004)。
16.盧華安，「定期貨櫃航線設計之研究」，運輸計劃季刊，第三十一卷，第一期，頁121-142 (2002)。
17.盧華安、徐育彰，「定期貨櫃航線選擇與船隊部署之研究」，運輸計劃季刊，第三十卷，第三期，頁577-602 (2001)。
18.顏上堯、王中瑞，「飛航網路定線與班次頻次數之規劃」，中華民國運輸學會第十屆論文研討會論文集 (1995)。
19.顏上堯、何淑萍，「飛航排程暨班次表之建立」，運輸計劃季刊，第二十三卷，第一期，頁73-90 (1994)。
20.顏上堯、翁綵穗，「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，頁891-922 (2001)。
21.顏上堯、曾志煌，「單機種機隊排程與班次整合之研究」，運輸計劃季刊，第二十八卷，第四期，頁635-658 (1999)。
22.顏上堯、楊慧華，「多機種飛航排程規劃」，運輸計劃季刊，第二十四卷，第二期，頁195-220 (1995)。
23.顏上堯、齊志仁、湯慶輝，「隨機需求下多目標長途客運排程模式之研究」，運輸計劃季刊，第三十四卷，第一期，頁93-118 (2005)。
24.顏上堯、藍世宗，「定期貨櫃船舶航線規劃模式與求解演算法之研究」，運輸計劃季刊，第三十二卷，第一期，頁47-74 (2003)。
25.Abara, J., “Applying Integer Linear Programming to the Fleet Assignment Problem,” Interfaces, Vol. 19, pp. 20-28 (1989).
26.Agin, N. and Cullen, D., “An Algorithm for Transportation Routing and Vehicle Loading,” in Geisler, M. (Ed.), Logistics, pp.1-20, North Holland, Amsterdam (1975).
27.Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P. and Vance, P. H., “Branch-and-Price: Column Generation for Solving Huge Integer Programs,” Operations Research, Vol. 46, pp.316-329 (1998).
28.Benders J. F., “Partitioning procedures for solving mixed-variables programming problems,” Numerische Mathematik, Vol.4, pp. 238-252 (1962).
29.Camerini, P. K., Fratta, L. and Maffioli, F., “On Improving Relaxation Methods by Modified Gradient Techniques,” Mathematical Programming Study, Vol. 3, pp. 6-25 (1975).
30.Chen, C. Y. and Kornhauser, A. L., ”Decomposition of Convex Mulitcommodity Network Flow Problem,” Report SOR-90-19, Dept. of Civil Engineering and Operations Research, Princeton University, Princeton, NJ (1990).
31.Chih, K. C. K., “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 (1986).
32.Cho, S. C. and Perakis, A. N., “Optimal Liner Fleet Routing Strategies,” Maritime Policy and Management, Vol.23, pp.249-259 (1996).
33.Clarke, L. W., Hane, C. A., Johnson, E. L. and Nemhauser, G. L., “Maintenance and Crew Considerations in Fleet Assignment, ” Transportation Science, Vol.30, pp. 249-260 (1996).
34.Desaulniers, G., Desrosiers, J., Dumas, Y., Solomon, M.M. and Soumis, F., “Daily Aircraft Routing and Scheduling”, Management Science, Vol. 43, pp. 841-855 (1997).
35.Fisher, M. L., “The Lagrangian Relaxation Method for Solving Integer Programming Problem,” Management Science, Vol. 27, pp. 1-18 (1981).
36.Hane, C. A., Barnhart, C., Johnson, E. L., Marsten, R., Nemhauser, G. L. and Sigismondi, G., “The Fleet Assignment Problem: Solving a Large-Scale Integer Program,” Mathematical Programming Study, Vol. 70, pp. 211-232 (1995).
37.Kennington, J. L. and Helgason, R. V., “Algorithms for Network Programming,” Wiley, NJ, (1980).
38.Kennington, J. L. and Shalby, M., “An Effective Subgradient Procedure for Minimum Cost Multicommodity Flow Problem,” Management Science, Vol.23, pp.994-1004 (1977).
39.Lamatsch, A, “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 (1992).
40.Lane, D.E., Heaver, T.D. and Uyeno. D., “Planning and scheduling for efficiency in liner shipping,” Maritime Policy and Management, Vol. 14, pp.109-125 (1987).
41.Lee, B. C., “Routing Problem With Service Choices, Flight Transportation Laboratory,” Report R86-4, Massachusetts Institute of Technology, MA (1986).
42.Levin, A., “Scheduling and Fleet Routing Models for Transportation Systems,” Transportation Science, Vol. 5, pp. 232-255 (1971).
43.Levin, A., “Some Fleet Routing and Scheduling Problems for Air Transportation Systems,” Flight Transportation Laboratory Report R68-5, Massachusetts Institute of Technology, MA (1969).
44.Mesquita, M. and Paixao, J., “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 (1992).
45.Perakis, A.N. and Jaramillo, D.I., “Fleet deployment optimization for liner shipping. Part 1: Background, problem formulation and solution approaches,” Maritime Policy and Management,Vol. 18, pp.183-200 (1991).
46.Powell, B. and Perakis, A.N., “Fleet deployment optimization for liner shipping: An integer programming model, ” Maritime Policy and Management,Vol. 24, pp.183-192 (1997).
47.Powell, W. B. and Ioannis, A. K., “Shipment Routing Algorithms with Tree Constraints,” Transportation Science, Vol. 26, pp. 230-245 (1992).
48.Rana, K. and Vickson, R.G., “A model and solution algorithm for optimal routing of a time-chartered containership,” Transportation Science,Vol. 22, pp.83-95 (1988).
49.Rana, K. and Vickson, R.G., “Routing container ships using Lagrangean relaxation and decomposition,” Transportation Science ,Vol.25, pp.201-214 (1991).
50.Ronen, D., “Ship scheduling：The last decade,” European Journal of Operational Research,Vol. 71, pp.325-333 (1993).
51.Shan, Y. S., “A Dynamic Mulitcommodity Network Flow Model for Real Time Optimal Real Freight Car Management,” Ph.D. Dissertation, Princeton University, Princeton, NJ (1985).
52.Simpson, R.W., “A Review of Scheduling and Routing Model for Airline Scheduling,” IX AGIFORS Symposium, Broadway, England (1969).
53.Subramanian, R., Scheff, R. P., Quillinan, J. D., Wiper, D. S. and Marsten, R. E., “Coldstart: Fleet Assignment at Delta Air Lines,” Interface, Vol. 24, pp.104-120 (1994).
54.Teodorovic, D., “Airline Operations Research,” Gordon and Breach Science Publishers, New York (1988).
55.Teodorovic, D. and Guberinic, S., “Optimal Dispatching Strategy on an Airline Network after a Schedule Perturbation,” European Journal of Operational Research Vol.15, pp.178-182 (1984).
56.Yan, S., “Approximating reduced costs under degeneracy in a network flow problem with side constraints,” Networks Vol.27, pp.267-278 (1996).
57.Yan, S. and Chen, H. L., “A Scheduling Model and a Solution Algorithm for Inter-city Bus Carriers,” Transportation Research, Vol. 36A, pp. 805-825 (2002).
58.Yan, S., Tang, T. T., and Tu, Y. P., “Optimal construction of airline individual crew pairings,” Computers and Operations Research, Vol. 29, pp. 341-363 (2002).
59.Yan, S. and Tu, Y., “Multi-Fleet Routing and Multi-Stop Flight Scheduling for Schedule Perturbation,” European Journal of Operational Research, Vol.103,pp. 155-169 (1997).
60.Yan, S. and Young, H. F., “A Decision Support Framework for Multi-Fleet Routing and Multi-Stop Flight Scheduling,” Transportation Research, Vol. 30A, pp. 379-398 (1996).