250ST Optimization Models of Transport Networks

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1 Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: ETSEIB - Barcelona School of Industrial Engineering EIO - Department of Statistics and Operations Research MASTER'S DEGREE IN STATISTICS AND OPERATIONS RESEARCH (Syllabus 2013). (Teaching unit Optional) MASTER'S DEGREE IN SUPPLY CHAIN, TRANSPORT AND MOBILITY MANAGEMENT (Syllabus 2014). (Teaching unit Optional) MASTER'S DEGREE IN INDUSTRIAL ENGINEERING (Syllabus 2014). (Teaching unit Optional) 5 Teaching languages: English Teaching staff Coordinator: Codina Sancho, Esteve Opening hours Timetable: To be defined at the beginning of the semester Prior skills Prior knowledge of real analysis and algebra. Using programming languages??oriented computing * Technical / scientific (* MATLAB and / or * Python) or equivalent. Basic knowledge of Operational Research Degree competences to which the subject contributes Specific: CETM3. Knowledge for planning, management and operation of transportation systems and mobility, ability to analyze service levels to users, operating costs and environmental and social such as mass transit, and private vehicle traffic impacts, air transport, sea transport, intermodal transport and urban mobility. CESC4. Know and apply the techniques of modeling, simulation and optimization to solve the problems involved the design and management of supply chains. CETM2. Understanding and quantifying capacity fundamentals transport systems and mobility determine the safety, quality and sustainability of transport infrastructure and optimizing the operation of these systems. Teaching methodology The teaching method will combine classic exhibition content sessions (theory) and laboratory sessions / problems to reinforce / complement the theory sessions. The teaching method requires specific training materials by monitoring the subject and conducting practice sessions. The theoretical sessions concerning paragraphs 1 and 2 of the agenda will be mostly with the help of slides, while concerning paragraphs 3,4,5 preferably incorporate the use of slate. Throughout the course you will be presenting and following one or more case studies to illustrate the application in practice of the cone of the course taken. Learning objectives of the subject Know the main equilibrium models used in planning and design of passenger transportation systems (road networks and public transport) and its relationship with the optimization problems in networks and optimization algorithms that are used in practice. Know the main elements and principles of modeling to create instances of the previous models. Perform iterations manually and with the aid of suitable software of algorithms: a) Frank-Wolfe, b) Spiess. Integration, use and 1 / 5

2 role of the previous models in the planning tools of passenger transport. Study load Total learning time: 125h Hours large group: 0h 0.00% Hours medium group: 30h 24.00% Hours small group: 15h 12.00% Guided activities: 0h 0.00% Self study: 80h 64.00% 2 / 5

3 Content Non-linear Optimization Basics Learning time: 25h Theory classes: 6h Practical classes: 3h Laboratory classes: 0h Guided activities: 0h Self study : 16h Elements of an optimization problem, objective function and constraints. Convexity. Introduction to linear programming and linear programming models. Problems of nonlinear unconstrained optimization. Local and Global Solutions. Conditions 1er order and gradient method. Line searches. Optimization problems with linear constraints. First order conditions or Karush-Kuhn and Tucker. Introduction to non-linear network flows. Shortest path problems (recall). Concept of variational inequality in Rn. Introduction to AMPL modeling languages Delivery of an exercise in problem solving for nonlinear flows on networks with an analysis of the solution. Verification of 1storder conditions. Solve small linear optimization problems using AMPL. Apply manually shortest path algorithms on small networks. State the conditions of Karush-Kuhn and Tucker for a nonlinear problem and check whether the solution verifies them or not. Perform steps of the gradient method manually. Perform a line search. Traffic Network Models. Wardrop Equilibrium Learning time: 29h 10m Theory classes: 7h Practical classes: 3h 30m Self study : 18h 40m The four-stage process in transportation planning studies (review). Modelling passenger flows and traffic in urban transport networks. Basic elements: supply, demand and behavioural elements. Concept mapping. Modeling elements: zoning and origin-destination matrix; representation of a network of private transport; capabilities and functions of delay. The principle of Wardrop user equilibrium on a general network of private transport with inelastic demand: separability and formulation as optimization problem over networks. Optimization based solution algorithms and heuristics: incremental assignment. Characteristics of the solutions. Terms of uniqueness in total flows. Description of Professional software packages incorporating equilibrium models. Exercise: calculate equilibrium flows in networks of small size Know the elements of network traffic modeling used in transportation planning and equilibrium models. Perform iterations with the algorithm of Frank-Wolfe and MSA. Meet the convergence criteria of the Frank-Wolfe algorithm 3 / 5

4 Models for public transportation networks Learning time: 29h 10m Theory classes: 7h Practical classes: 3h 30m Self study : 18h 40m Modeling elements: lines, segments, stops and transfers. Models based on times tables based on frequency systems. PathFinder model. Concept of strategy and the choice of lines by travelers. Connection with the principle of Wardrop equilibrium. Spiess and Florian's model. Congestion in public transportation systems. Queueing models at stops. Effective frequency. Use of the MSA method. Description of professional software packages incorporating PT models Solving an assignment problem in a non-congested network. Use of the method Spiess method. Perform an all-or-nothing assignment following full PathFinder model. Solving instances by hand of Spiess' assignment model of passenger to lines. Application of the MSA method for the case of congested networks. Extensions Learning time: 41h 40m Theory classes: 10h Practical classes: 5h Self study : 26h 40m Models of elastic demand and Beckman model. Transformation Gartner. Combined allocation-distribution models. Stochastic equilibrium concept. Models of stochastic assignment of private transport networks. STOCH algorithm. Fisk's model. Advanced models of assignment. Models with interactions and asymmetries between vehicles of different types and establishment as variational inequality formulation. Heuristic methods for solving interactions and asymmetries. Diagonalization method. Exercise in laboratory class and delivery of a report Solving by hand a small network combined model for assignment /modal choice. Run STOCH simplified algorithm. Meet and build traffic network models with interactions (asymmetric). Use the method of diagonalization in test cases. Qualification system 40% Laboratory exercises + 45% Final Exam + 15% Discusion of a Case Study 4 / 5

5 Regulations for carrying out activities A compendium of formulae in two sheets (maximum) and a pocket calculator. Bibliography Basic: Sheffi, Yosef. Urban transportation networks : equilibrium analysis with mathematical programming methods. Englewood Cliffs, NJ: Prentice Hall, ISBN Florian, Michael ; Hearn, Donald. "Network equilibrium models and algorithms". Handbooks in Operations Research and Management Science [on line]. Volume 8. Chapter 6, 1995, Pages [Consultation: 29/07/2014]. Available on: < Fourer, Robert ; Gay, D.M.; Kernighan, B.W. AMPL a modeling language for mathematical programming. 2nd ed. Pacific Grove, CA: Thomson/Brooks/Cole, ISBN Ortúzar S., Juan de Dios; Willumsen, Luis G. Modelling transport. 4th ed. Chichester: John Wiley & Sons, ISBN Complementary: Bertsekas, Dimitri P. Network optimization : continuous and discrete models. Belmont, MA: Athena Scientific, ISBN Ahuja Ravindra K. et al. Network flows : theory, algorithms, and applications. Englewood Cliffs: Prentice Hall, ISBN X. Others resources: Computer material Plataforma ATENEA Resource Sistema AMPL Estudiant Resource 5 / 5