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研究生： 陳思齊
Sz-Chi Chen
論文名稱： 巡邏車輛途程問題
The Patrol Car Routing Problem
指導教授： 陳惠國
Huey-Kuo Chen
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
畢業學年度： 95
語文別： 中文
論文頁數： 103
中文關鍵詞： 時窗限制 、中國信差問題 、車輛途程問題 、即時性
外文關鍵詞： Time Windows Constraints, Vehicle Routing Problem, Chinese Postman Problem, Real Time
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    • 巡邏車輛途程問題(Patrol Car Routing Problem, PCRP)係指巡邏車從總部出發，依照預先設定之目標繞行管轄範圍內之節點或路段，然後回到總部結束勤務謂之。PCRP依照問題之性質可以概分成三類：(1)節點之車輛途程問題(Vehicle Routing Problem, VRP)，(2)節線之中國信差問題(Chinese Postman Problem, CPP)，(3)前兩者之混合，為一般性車輛途程問題。本研究針對第一類與第二類問題深入探討，納入即時性(犯罪案件隨時隨地發生)與時窗限制(特定時間與地點為犯罪熱點)之可能性，並以增設虛擬節點與虛擬節線的方式將節線之中國信差問題轉換成節點之車輛途程問題，相較於以往文獻，將虛擬點之間距離合理轉換，並建構為混合整數規劃模型。針對含即時性之巡邏車輛途程問題，利用滾動時間之概念，在關鍵時點上，納入即時性需求考量，對所建構之數學模型重複求算其初始路線與進行路線改善，以獲得近似最佳解。
    本研究產生30組測試例題作為測試分析，歸納出巡守時間長短影響線上巡邏車數，線上巡邏車數進一步影響巡邏車到案發現場的反應時間。而隨機案件的產生，擾動了原先規劃的路線，進一步影響了總使用車輛數及巡邏班次，同時巡邏車支援案發點亦造成總旅行時間的變長。最後本研究與巡邏實務運作方式比較，以驗證模型與演算法之正確性。

    The patrol car routing problem (PCRP) is the problem of finding a minimum cost route for the patrol cars, subject to the condition that the patrol cars cruise certain nodes or links of a network. The PCRP can be regarded as an extension of the conventional vehicle routing problem with time windows (VRPTW) and Chinese postman problem with time windows (CPPTW). In this paper we approximate the PCRP by adopting the time rolling horizon approach in which a mixed integer optimization subproblem, is repetitively formed and solved so as to take into account the incoming real-time information. A heuristic comprising route construction and route improvement is developed. Thirty numerical problems and real applications are provided for demonstration.

    摘要................................................................................................................................I Abstract....................................................................................................................... II 目錄..............................................................................................................................VI 圖目錄.......................................................................................................................VIII 表目錄...........................................................................................................................X 第一章 緒論................................................................................................................1 1.1 研究背景與動機.............................................................................................1 1.2 研究目的.........................................................................................................2 1.3 研究範圍與假設.............................................................................................2 1.3.1 研究內容..............................................................................................3 1.3.2 研究假設..............................................................................................3 1.4 研究內容與流程.............................................................................................5 第二章 文獻回顧........................................................................................................8 2.1 巡邏勤務與巡邏方式.....................................................................................8 2.1.1 巡邏勤務..............................................................................................8 2.2 車輛途程問題與相關問題...........................................................................10 2.2.1 時窗限制車輛途程問題....................................................................11 2.2.2 時窗限制車輛途程問題之求解方法................................................11 2.2.3 含依時性旅行成本之即時車輛途程問題........................................16 2.2.4 小結....................................................................................................17 2.3 中國信差問題...............................................................................................17 2.3.1 中國信差問題之分類........................................................................17 2.3.2 完全方向性之中國信差問題............................................................19 2.3.3 節線途程問題轉換成節點途程問題................................................26 2.3.4 小結....................................................................................................32 第三章 模型建構......................................................................................................33 3.1 節點途程問題模型建構...............................................................................33 3.1.1 模型假設............................................................................................34 3.1.2 符號說明............................................................................................35 3.1.3 數學模型............................................................................................36 3.1.4 巡邏情境分析....................................................................................38 3.2 節線途程問題...............................................................................................40 3.2.1 模型假設............................................................................................40 3.2.2 符號說明............................................................................................41 3.2.3 數學模型............................................................................................43 3.2.4 對應轉換............................................................................................45 第四章 求解演算法..................................................................................................55 4.1 車輛途程問題求解方法...............................................................................55 4.1.1 依時性旅行時間................................................................................55 4.1.2 時空網路與臨界點............................................................................56 4.2 路線建構.......................................................................................................57 4.3 综和求解流程...............................................................................................59 4.4 節線途程問題求解流程...............................................................................61 第五章 範例測試與分析..........................................................................................63 5.1 節點途程問題之範例測試...........................................................................63 5.1.1 範例題庫的建立................................................................................63 5.1.2 範例(1)測試的結果...........................................................................65 5.1.3 線上巡邏車數對平均反應時間之影響.............................................69 5.1.4 測試問題大小與求解時間之關係....................................................71 5.1.5 小結....................................................................................................72 5.2 實務運作資料與模型求解結果之比較......................................................73 5.3 節線問題之數例分析...................................................................................78 第六章 結論與建議..................................................................................................82 6.1 結論...............................................................................................................82 6.2 建議...............................................................................................................83 參考文獻......................................................................................................................86 附錄一 說明溫玉彬(2001)時窗限制下之中國信差問題.......................................90 附錄二 詳細資料......................................................................................................93 附錄三 針對無方向性路段後續研究方向.............................................................99 附錄四 針對即時案件處理以及VRP 與實際路網之轉換.................................102

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