隨機性擾動下規劃問題求解演算法之研究

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湯慶輝(Ching-Hui Tang) 查詢紙本館藏

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土木工程學系

論文名稱

隨機性擾動下規劃問題求解演算法之研究
(A Solution Approach for Planning Problems under Stochastic Disturbances)

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摘要(中)

過去學者在處理規劃問題時，大多以預測之平均值構建數學模式求算最佳解。然而在運輸系統的實務營運中，隨時可能遭遇許多隨機性因素的干擾，例如旅次需求、車輛旅行時間、班機到離延誤等。此等隨機性因素對規劃的最佳化結果可能產生相當的影響，甚至可能使其在實際營運時失去最佳性。另外，以往研究多將靜態時期規劃與即時性擾動規劃兩者分開單獨處理，且在面對隨機性擾動時，多著重於處理即時性擾動規劃。因此，本研究針對隨機問題之特性，發展一整合規劃與即時階段之求解架構，將規劃與即時兩不同階段之規劃問題在隨機擾動下做一整合性之分析。期能於未來實務應用上，提供有效的工具，以處理隨機環境中的規劃問題。
為測試所發展的求解架構之可行性，本研究以機門指派與長途客運排程問題為應用對象。本研究可分成三個部分：第一個部分在機門指派問題方面，考量班機隨機到離延誤之特性，整合靜態機門指派與即時性機門指派，求得一較符合班機隨機延誤下之機門指派結果。第二部份則以長途客運排程問題為對象，考量車輛旅行時間之隨機特性，除在規劃階段發展一隨機性旅行時間長途客運排程模式外，並進一步考量因車輛旅行時間延誤之即時調整問題，建立一套整體性之求解架構，求得一較符合車輛旅行時間隨機擾動下之排程結果。第三部份同樣利用本研究發展之求解架構，同時考量市場旅客需求之隨機性、變動的市場佔有率與車輛旅行時間之隨機特性，發展一多隨機因素之長途客運排程模式，同時亦考量即時階段之調整問題，以幫助業者有效規劃車隊排程與班次表。此三部份皆使用實際營運資料加上適當的假設，利用C程式語言，配合CPLEX數學規劃軟體進行求解。最後，根據此三部份的研究結果，提出結論與建議。

摘要(英)

There are many stochastic factors that will affect the performance of the planning results in a passenger transportation system, such as passenger demands, vehicular travel times and flight delays. Past traditional deterministic models have been established based on the average values of factors such as input to obtain optimal solutions. However, such stochastic factors during the operational stage could have a significant influence on the planning results. An optimal plan might therefore lose its optimality when applied in real world operations where stochastic disturbances occur. In addition, most stochastic disturbance planning problems have been handled in two separate stages, the planning and the real-time stages. Most past research on these types of problems has focused on improving real-time adjustments to stochastic disturbances. In this research however we try to develop an integrated framework that combines both the planning and the simulated real-time stages together. The framework is expected to be useful for solving for better planning solutions to stochastic disturbance problems.
To evaluate how the proposed framework performs in practice, we perform applications to both gate assignment and inter-city bus scheduling problems. The dissertation includes three essays. In the first, we consider the stochastic characteristics of flight delays in actual operations; we integrate both the planning and the simulated real-time stages together to solve for gate assignment plans flexible enough to meet stochastic disturbances. In the second essay, we consider the bus scheduling planning problem with stochastic bus travel times. We develop an integrated framework that can systematically analyze planned bus scheduling and simulated real-time schedule adjustment problems in order to help the inter-city bus carriers plan suitable bus routes/schedules. The third essay considers the stochastic passenger demands, the variable market shares and the stochastic bus travel times of real world operations to develop a multi-stochastic bus scheduling model. Simulated real-time schedule adjustment is also incorporated into the framework. The result is to produce a better bus route/schedule plan. We performed these applications using real operational data, with reasonable simplifications. We used the C computer language to write the necessary programs, coupled with the CPLEX mathematical programming solver, to solve the problems. Finally, conclusions and suggestions are given.

關鍵字(中)

★ 隨機性擾動
★ 機門指派
★ 班機隨機到離延誤
★ 隨機車輛旅行時間
★ 隨機需求
★ 變動市場佔有率
★ 長途客運排程

關鍵字(英)

★ Stochastic disturbances
★ Stochastic bus travel times
★ Variable market shares
★ Stochastic passenger demands
★ Stochastic flight delays
★ Inter-city bus scheduling
★ Gate assignment

論文目次

Contents
摘要 I
Abstract II
List of Tables VI
List of Figures VII
Chapter 1 Introduction 1
Chapter 2 Essay1: A Heuristic Approach for Airport Gate Assignments for Stochastic Flight Delays 5
2.1 Introduction 5
2.2 The framework 7
2.2.1 The solution process and assumptions 8
2.2.2 The planned gate assignments 11
2.2.2.1 The gate-flow network 11
2.2.2.2 The model formulation 15
2.2.2.3 The extension and the deterministic flight delay gate assignment model (DFDGAM) 17
2.2.3 The simulated reassignment 18
2.2.4 The MAMs 21
2.2.4.1 MAM1 22
2.2.4.2 MAM2 22
2.3 Numerical tests 24
2.3.1 Data analyses 24
2.3.2 Test results 24
2.3.3 Sensitivity analysis 28
2.3.4 The flight delay patterns 32
2.4 Discussion and conclusions 33
Appendix: 34
A. The model formulation of the DFDGAM 34
B. The flight delay distributions 35
References 35
Chapter 3 Essay 2: An Integrated Framework for Inter-City Bus Scheduling under Stochastic Bus Travel Times 38
3.1 Introduction 38
3.2 Integrated framework 40
3.2.1 Solution process 40
3.2.2 Planned bus schedules 42
3.2.2.1 Fleet-flow network 42
3.2.2.2 Multiplier “u” and robustness 44
3.2.2.3 Model formulation 47
3.2.3 Simulated real-time schedule adjustments 48
3.2.4 MAMs 52
3.2.4.1 MAM1 52
3.2.4.2 MAM2 53
3.3 Issues related to the framework 54
3.3.1 Lower bounds 54
3.3.2 Comparison with Lagrangian Multipliers 57
3.3.3 Comparison with the deterministic travel time scheduling model 59
3.3.4 Evaluation method 60
3.4 Numerical tests 61
3.4.1 Data analyses and test results 61
3.4.2 Sub-gradient method results 64
3.4.3 Comparisions with expectation model 65
3.4.4 Weighting value 66
3.4.5 Number of Scenarios 67
3.4.6 Problem scales 68
3.5 Conclusions 70
Appendix: Bus travel time distribution 72
References 73
Chapter 4 Essay 3: A Scheduling Framework Incorporating Real-time Schedule Adjustments for Inter-City Bus Carriers under Stochastic Travel Times and Demands 76
4.1 Introduction 76
4.2 The framework 79
4.2.1 The solution process 79
4.2.2 The planned bus routes/schedules 80
4.2.2.1 The fleet-flow network 81
4.2.2.2 The passenger choice model 84
4.2.2.3 The mathematical formulation 89
4.2.2.4 The extension and the DTTDSM 93
4.2.3. Simulated real-time schedule adjustments 94
4.2.4 MAMs 97
4.2.4.1 MAM1 97
4.2.4.2 MAM2 98
4.3 Numerical tests 99
4.3.1 Data analyses 99
4.3.2 Test results 100
4.3.3 Evaluation results 104
4.3.4 The number of scenarios 105
4.3.5 The bus travel time and passenger demand distribution 106
4.4 Conclusions 109
Appendix 109
A. The calculation of the , and 109
B. The model formulation of the DTTDSM 111
C. The solution method for the DTTDSM 113
D. Average market demand for each OD pair for each time interval 115
References 116
Chapter 5 Conclusions, Suggestions and Contributions 119
5.1 Conclusions 119
5.2 Suggestions 120
5.3 Contributions 122

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Kenyon, A.S. and Morton, D.P., 2003. Stochastic vehicle routing with random travel times, Transportation Science 37, 69-82.
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Mulvey, J.M., Vanderbei, R.J., Zenios, S.A., 1995. Robust optimization of large-scale systems, Operations Research 43, 254–281.
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Essay 3
Berkhout, J., 1985. Structure method for vehicle scheduling, Computer Scheduling of Public Transport 2, 199–208.
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Ceder, A. and Wilson, N.H.M., 1986. Bus network design, Transportation Research B 20, 331–344.
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Kuah, G.K. and Perl, J., 1988. Optimization of feeder bus routes and bus stop spacing, Journal of Transportation Engineering 114, 341–354.
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 E 39, 209–227.
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Paraskevopoulos, D., Karakitsos, E., and Rustem, B., 1991. Robust capacity planning under uncertainty, Management Science 37, 787–800.
Pattnaik, S.B., Mohan, S., and Tom, V.M., 1998. Urban bus transit route network design using genetic algorithm, Journal of Transportation Engineering 124, 368–375.
Rosenberger, J.M., Johnson, E.L., and Nemhauser, G.L., 2004. A robust fleet-assignment model with hub isolation and short cycles, Transportation Science 38, 357–368.
Prakash, S., Balaji, B.V., and Tuteja, D., 1999. Optimizing dead mileage in urban bus routes through a nondominated solution approach, European Journal of Operational Research 114, 465–473.
Ruszczynski, A. and Shapiro, A., 2003., Stochastic Programming. Elsevier, Amsterdam.
Salzborn, F.J.M. 1980., Scheduling bus systems with interchanges, Transportation Science 14, 211–231.
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Sinclair, M. and van Oudheusden, D.L., 1997. Network approach to trip frequency scheduling for bus routes in heavily congested cities, European Journal of Operational Research 103, 18–27.
Soteriou, A.C. and Chase, R.B., 2000. A robust optimization approach for improving service quality, Manufacturing & Service Operations Management 2, 264–286.
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van Nes, R., Hamerslag, R., and Immer, B.H., 1988. Design of public transport networks, Transportation Research Record 1202, 74–83.
Wen, C.H., Lan, L.W., and Chen, C.H., 2005. Passengers perception on service quality and their choice for intercity bus services. Transportation Research Board, 84th Annual Meeting, Washington, DC.
Yan, S. and H. L. Chen. 2002. A scheduling model and a solution algorithm for inter-city bus carriers, Transportation Research A 36, 805–825.
Yan, S. and Young, H.F., 1996. A decision support framework for multi-fleet routing and multi-stop flight scheduling, Transportation Research A 30, 379–398.
Yan, S., Shieh, C.W., and Chen, M., 2002. A simulation framework for evaluating airport gate assignments, Transportation Research A 36, 885–898.
Yu, C. and Li, H., 2000. A robust optimization model for stochastic logistic problems, International Journal of Production Economics 64, 385–397.

指導教授

顏上堯(Shangyao Yan)

審核日期

2006-6-30

推文