
系統識別號 
U00261008201521020600 
論文名稱(中文) 
多旅行商問題模型應用於機隊指派問題 
論文名稱(英文) 
Multiple Traveling Salesman Problem Model for Fleet Assignment 
校院名稱 
成功大學 
系所名稱(中) 
民航研究所 
系所名稱(英) 
Institute of Civil Aviation 
學年度 
103 
學期 
2 
出版年 
104 
研究生(中文) 
莊偉志 
研究生(英文) 
WeiChih Chuang 
學號 
Q46024054 
學位類別 
碩士 
語文別 
英文 
論文頁數 
68頁 
口試委員 
指導教授王大中 口試委員袁曉峰 口試委員林東盈

中文關鍵字 
航空公司班表排程
機隊指派
多旅行商問題

英文關鍵字 
airline planning
fleet assignment
multiple traveling salesman problem

學科別分類 

中文摘要 
機隊指派為航空公司排班的四個主要步驟之一。其主要目的即在航線已知及機隊規模固定的情況下，將適當的機型及數量安排至適當的航線上營運，使得航空業者的總收益最大化或總營運成本最小化，而這種大型規劃問題的求解效率與品質通常隨著複雜度增加而有所下降，所以大部分的研究都著重於使用啟發式演算法(heuristic algorithm)，以尋求近似解作為最佳解來取代精確解，目的在於能夠較有效率地以較少的時間求解出滿意的結果。
本篇研究應用多旅行商問題模型(MTSP Model)，用以描述機隊指派各航段的狀況及排序固定的航班。不同於時空網路模型(TimeSpace Network)，此模型將航班離到場時間和機場轉化成點，並將可能航班點連接成線，根據限制式來直接求解出最小的距離成本，且考量限制條件及最小化距離成本來達成航班最佳化排序的目的，並達到機隊指派後能有最大化的獲利。多旅行商這類的規劃問題已經有許多的研究，其技術也已發展成熟，本篇研究透過轉換此種模式來求解機隊指派問題，其問題規模大小跟機隊指派問題是相同的，也有較好的問題求解程序可以加以修改。
本篇的研究提出一個二階段的方法求解機隊指派問題。首先，我們應用基因演算法(Genetic Algorithm)來求解出應用多旅行商問題模型的機隊指派問題， 考量到更多彈性時間，在機隊指派問題中加入了返回節線(backward arc)，在允許時間逆流的情況下，尋找一個符合限制且最小距離成本的最佳解，並找出每架飛機應該飛哪些航班，求解出每架飛機有最小距離成本的飛行路徑。接著，根據第一階段的解，我們使用一個線性規劃的數學式取代傳統的時間窗(time window)方式，去調整班表。此方法也像有時間窗的方法一樣能夠允許在航班離開時間有變動下，指派各航段應使用的機型。

英文摘要 
Fleet assignment is one of four main steps in airline planning. The objective is to determine which type of aircraft should fly on each flight leg while considering the different features and costs with different fleet types. The main purpose of the fleet assignment problem (FAP) is to maximize total profits or minimize total operating costs. The problem is usually formulated as an integer linear programming problem. The solving efficiency and quality of the massive programming problem will drop with complexity increasing. Due to the size of the FAP, various heuristic algorithms or methods for solving this problem have been studied. The purpose of finding the heuristic solutions for the optimal feasible solution is to find the satistied results more efficient for less time.
This thesis proposes a multiple traveling salesman problem model(MTSP Model) to solve the FAP, and determine which type of aircraft should fly on each flight arc and flights which has the optimal order. It’s different to TimeSpace Network model, this model drawing the flight dots by the departure time, departure airport, arrival time and arrival airport, and joining the flight dots to calculate the minimal costs by following the relative constraints. The perpose is to obtain optimal flight order by considering constraints and minimal the costs of distance to get the maximum total profits after fleet assignment procedure. In this thesis, the MTSP Model is choosen because the MTSP is a wellknown problem which is solved by many kinds of solver with good solving quality. The MTSP not only has the roughly same problem size comparing to the FAP but also has welldeveloped technique to be solved.
This thesis proposes a twophase approach to solving the FAP. First, genetic algorithm is applied to solve MTSP model for FAPs. Cosidering more feasible time, backward arcs are used to solve this problem. By allowing backward time, the optimal feasible solution with the minimum number of rescheduled flight is sought. Some routes, which have minimal costs of distance, are found. Finally, the continuously adjustable flight schedule problem is solved using a integer linear programming model instead of using a time window to change flight schedules. Our method has a similar level of flexibility as the fleet assignment model with time window (FAMTW), and solves the problem in shorter time than the FAMTW. An approach for solving the aircraft routing problem is also proposed.

論文目次 
CONTENTS
ABSTRACT i
摘要 iii
誌謝 v
CONTENTS vi
LIST OF TABLES viii
LIST OF FIGURES ix
LIST OF NOTATIONS x
Chapter 1 Introduction 1
1.1 Preface 1
1.2 Motivation and Objective 2
1.3 Fleet Assignment Problem Literature Review 6
1.4 Outline of this Research 7
Chapter 2 FAP Integer Programming 8
2.1 Combinatorial Optimization 8
2.2 Fleet Assignment Problem 9
2.2.1 Basic Fleet Assignment Problem 9
2.2.2 TimeSpace Network 9
2.2.3 Mathematical Formulation of the Fleet Assignment Problem 11
2.2.4 Fleet Assignment with TimeWindow 19
2.2.5 Backward Arc Technique 26
2.3 Methods for Solving the Fleet Assignment Problem 28
2.3.1 Exact Procedures 28
2.3.2 Approximation Algorithms 31
2.4 Summary 35
Chapter 3 Multiple Traveling Salesman Problem Model for Fleet Assignment 36
3.1 Multiple Traveling Salesman Problem 36
3.2 Multiple Traveling Salesman Problem Model for Fleet Assignment 39
3.3 Using Backward Arc Technique 44
3.4 Summary 46
Chapter 4 Solve MTSP Model for FAP 47
4.1 Appling GA to the MTSP Model for FAP 47
4.2 Adjustiment for Using Backward Arc 51
Chapter 5 Simulation Results 58
5.1 Simulation Data 58
5.2 Simulation Results 59
Chapter 6 Conclusions 65
6.1 Conclusions 65
6.2 Future Reseaech 65
Reference 66
LIST OF TABLES
Table 1: An example of extra connection opportunity if time windows are allowed. 21
Table 2: Method types for solving the FAP. 28
Table 3: Data in an example 51
Table 4: The schedule data sets 59
Table 5: The results of 7 different schedules using the MTSP model for FAP comparing to optimal solution obtained by using LPSolve. 59
Table 6: The results for compared with adding backward arcs 63
LIST OF FIGURES
Figure 1: The trend of oil prices (data from U.S. Energy Information Administration) 1
Figure 2: The plan schedule of airline business 3
Figure 3: Timespace network. 10
Figure 4: Two stations example for flight coverage constraint 13
Figure 5: Two stations example for aircraft balance constraint 13
Figure 6: Six stations example for fleet size constraint 14
Figure 7: Example of passenger spill 16
Figure 8: The demand distribution [20] 17
Figure 9: Example of a time window timespace network for two airports. 20
Figure 10: Node consolidation preprocessing technique 23
Figure 11: Deleted redundant flight arc preprocessing technique. 24
Figure 12 Island preprocessing technique 25
Figure 13: Backward connection arcs 27
Figure 14: The example of multiple traveling salesman problem model for fleet assignment 39
Figure 15: Three situation of distance definition. 41
Figure 16: The distance definition with exponential function. 45
Figure 17: The example of multichromosome representation for the number of flight (n = 13) and the number of aircraft (m = 3) 48
Figure 18: The flow chart of using GA. 50
Figure 19: The timespace before/after the adjustable phase. 52
Figure 20: The timespace before/after the adjustable phase for the example. 56
Figure 21: The computation procedure. 58
Figure 22: The profit with compared. 61
Figure 23: The computational time with compared. 61
Figure 24: The profit for compared with adding backward arcs. 64

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