根據交通部頒訂之公路養護手冊規定，台灣地區橋樑每年必須在規定期程內進行定期檢測，且需要針對橋樑所有的構件進行全面性的檢測。因此，管養單位需要花費龐大的人力、經費與時間來進行全面性的公路橋樑養護工作。而目前橋樑檢測作業排程主要是透過人工指派的方式來進行，此方式主要是仰賴相關決策人員之經驗與主觀判斷，導致缺乏整體系統性的分析與考量，而當面臨龐大的橋樑檢測工作排程時，此人工指派方式可能不具規劃效率，且會造成資源之浪費。有鑑於此，本研究構建一公路橋樑檢測作業排程之模式，以橋樑檢測作業總成本最小化為目標，考量實際橋樑檢測之狀況以及檢測時間限制，並以系統性最佳化之觀點構建一橋樑檢測作業排程規劃之模式。
　　本研究利用時空網路流動技巧建立此模式，以定式橋樑檢測工作小組於時空中流動之情況，本研究模式為一大型含額外限制之整數網路流動問題，屬NP-Hard問題。在求解方法上，利用C++程式語言配合數學規劃軟體CPLEX進行模式求解，當面臨實務上大型問題時，難以在有限時間內利用數學規劃軟體求得最佳解。緣此，本研究發展一啟發式演算法以有效地求解問題。最後，為評估模式及演算法之實用績效，本研究以苗栗地區橋樑資料以及合理之假設進行範例測試，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務上可有效的運用，可提供橋樑管養單位做為橋樑檢測作業規劃之參考。

　　Based on the road maintenance manual announced by the Ministry of Transportation and Communications in Taiwan, the bridge check must be regularly performed in Taiwan each year. Each bridge check contains the check of all structure components of the bridge. In general, it takes a long period of time and requires a lot of maintenance manpower to perform the bridge check. This means that bridge check scheduling is very complicated. In practice, bridge check scheduling is made mainly based on the personal experience of the decision maker, which lacks the perspective of system optimization and makes formulated bridge check scheduling inefficient. Therefore, the aim of this study is to construct a bridge check scheduling model where the actual bridge check constraints are taken into consideration and the objective is to minimize the total bridge check cost.

　　In this study, a bridge check scheduling model is developed, where the time-space network flow technique is utilized to formulate the potential movements of bridge check working teams among all bridge check points in the dimensions of time and space. Mathematically, the model is formulated as an integer multiple-commodity network flow problem and is characterized as NP-hard. The C computer language, coupled with the CPLEX mathematical programming software, is employed to solve the problem. Since the problem size is expected to be huge, a solution algorithm based on a problem decomposition/collapsing technique is thus developed to efficiently solve the problem. The numerical tests are performed using the bridge check data associated with Miaoli County, Taiwan. The test results show that the proposed model and solution algorithm could be useful for assigning complicated bridge check and used as a reference for the assignment of the bridge check.

［1］ 交通部公路總局，公路養護手冊，交通部公路總局，2011。
［2］ 邱明琦，陳春益，林佐鼎，「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，2002。
［3］ 吳秋木，「橋樑目視檢測系統安全因子篩選之研究」，國立嘉義大學，碩士論文，2006。
［4］ 延允中，「橋樑維護管理機制、成效查核與經費編列探討-以公路總局為例」，國立中央大學，碩士論文，2004。
［5］ 姜蔚宗，「公路橋樑檢測最佳化模式分析」，國立中央大學，碩士論文，2013。
［6］ 柴志傑，「臺灣地區橋樑目視檢測行程最佳化之研究」，國立中央大學，碩士論文，2009。
［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，第267-298頁，2002。
［8］ 曾志煌、許書耕、巫柏蕙、姚乃嘉、陳明正、葉啟章、蔡欣局、廖先格，「橋樑目視檢測評估手冊（草案）」，交通部運輸研究所，委託研究成果期末報告，2011。
［9］ 湯慶輝、黃新達，「救災直升機汰換與駕駛員換裝訓練時程之研究」，運輸學刊，第二十六卷，第一期，第1-33頁，2014。
［10］ 劉慧燕，「不定期船運船舶排程問題之研究」，國立成功大學，博士論文，2011。
［11］ 盧華安，「因應班機延遲之最佳化即時機門指派」，運輸計劃季刊，第三十卷，第四期，第849-869頁，2001。
［12］ 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，第891-921頁，2001。
［13］ 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，第635-658頁，1999。
［14］ Bodin L. and Golden B., “Classification in vehicle routing and scheduling,” Networks, Vol. 11, pp.97-108, 1981.
［15］ Bodin, L., Golden B., A. Assad and M. Ball, “Routing and Scheduling of Vehicles and Crews, The State of the Art,” Computer & Operations Research, Vol. 10 Issue2, pp.63-211, 1983.
［16］ Dai, K. H., B. Smith, Chen, S. E. and Sun, L. M., “Comparative study ofbridge management programmes and practices in the USA and China” ,Structure and Infrastructure Engineering , Vol. 4 ,pp. 1-12, 2013.
［17］ Lu, H. A. and Chen, C. Y., “A time-space network model for unit load device stock planning in international airline services,” Journal of Air Transport Management, Vol. 17 Issue 2, pp. 94-100, 2011.
［18］ Matos, A. C. and Oliveira R. C., “An Experimental Study of the Ant Colony System for the Period Vehicle Routing Problem,” Lecture Notes in Computer Science, Vol. 3172 LNCS, pp. 286-293, 2004.
［19］ Simpson, R. W., “A Review of Scheduling and Routing Model for Airline Scheduling,” IX AGIFORS Symposium, Broadway, England, 1969.
［20］ Wen, M., Cordeau, J. F., Laporte, G. and Larsen, J., “The dynamic multi-period vehicle routing problem,” Computers and Operations Research, Vol. 37 Issue 9, pp.1615-1623, 2010.
［21］ 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.
［22］ Yan, S. and Shih, Y. L., “A Time-Space Network Model for Work Team Scheduling after a Major Disaster”, submitted to Journal of the Chinese Institute of Engineers, 2006.
［23］ Yan, S. and Tseng, C. H., “A passenger demand based model for airline flight scheduling and fleet routing,” Computers and Operations Research, Vol. 29, pp. 1559-1581 , 2002.
［24］ Yan, S., Chen, C. Y. and Chang, S. C., “A carpooling model and solution method with stochastic vehicle travel times,” IEEE Transactions on Intelligent Transportation Systems, Vol. 15 Issue 1, pp. 47-61, 2014.
［25］ Yan, S., Chen, S. C. and Chen, C. H., “Air Cargo Fleet Routing and Timetable Setting with Multiple On-Time Demands,” Transportation Research Part E: Logistics and Transportation Review, Vol. 42, Issue 5, pp. 409-430, 2006.
［26］ Yan, S., Ho, S. P. and Yang, H. T., “An integrated model for fleet routing, flight scheduling and aircraft rental planning,” Journal of the Chinese Institute of Industrial Engineers, Vol. 14 Issue 3, pp.247-256, 1997.
［27］ Yan, S., Tang, C. H. and Shieh, C.N., “A Simulation Framework for Evaluating Airline Temporary Schedule Adjustments Following Incidents,” Transportation Planning and Technology, Vol. 28, No. 3, pp. 189-211 , 2005.
［28］ Yan, S., Wang, S. S. and Wu, M. W., “A model with a solution algorithm for the cash transportation vehicle routing and scheduling problem,” Computers & Industrial Engineering, Vol.63 Issue 2, pp. 464-473, 2012.
［29］ Yan, S., Wang, S. S. and Chang, Y. H., “Cash transportation vehicle routing and scheduling under stochastic travel times,” Engineering Optimization, Vol. 46 Issue 3, pp.289-307, 2014.
［30］ Yan, S., Hsiao, F. Y., Guo, J. J. and Chen, Y. C., “Effective Aircraft Maintenance Schedule Adjustment Following Incidents,” Transportation Planning and Technology, Vol. 34, No. 8, pp. 727-745, 2011.
［31］ Yu, B. and Yang, Z. Z., “An ant colony optimization model: The period vehicle routing problem with time windows.” Transportation Research Part E: Logistics and Transportation Review, Vol. 47 Issue 2, pp. 166–181, 2011.