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Before graduation   PhD Research    Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                   Life after graduation
                       Innovative Transport Pricing

                                           Erik-Sander Smits



                                          November 22, 2012
Before graduation   PhD Research   Innovative Transport Pricing      Transport Model   Stakeholders Model   Wrap-up




                                     Before graduation

       Utrecht University
            • BSc. Computing Science
            • BSc. + MSc. Mathematics


       Graduation internship @ Omnitrans International
       O-D matrix estimation

                           A Priori O-D matrix
                                                                  ⇒ New O-D Matrix
                                 Traffic counts

                                  Matrix estimation
                             O-D matrix       Route proportions
                                         Assignment
Before graduation       PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                         Before graduation


       After internship @ Omnitrans
            • Writing Thesis
            • Searching for a job: What do I want?
                    •   Consultancy (Engineering)?
                    •   Consultancy (Strategy)?
                    •   Private Equity?
                    •   Trader (Finance)?
                    •   Science?
Before graduation       PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                         Before graduation


       After internship @ Omnitrans
            • Writing Thesis
            • Searching for a job: What do I want?
                    •   Consultancy (Engineering)?
                    •   Consultancy (Strategy)?
                    •   Private Equity?
                    •   Trader (Finance)?
                    •   Science?
            • What do I find important?
                    • → Challenge! I want to apply my analytical skills.
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                   PhD Research @ T & P
                                              Your own project



                               4-year long challenge!



          Gather knowledge ... execute the research ... publish your results




                    The finale is the thesis defense.
Before graduation   PhD Research     Innovative Transport Pricing     Transport Model   Stakeholders Model   Wrap-up




                                   PhD Research @ TU Delft


Courses
                                                              Teaching
    • Soft skills (e.g. Scientific Writing)
    • Hard skills (e.g. Discrete Choice                             • Give lectures
       Analysis)                                                    • Supervise MSc students


Conferences                                                   Exchange
    • Transportation Research Board                                 • One to three months
    • TRAIL Congress                                                • All around the world
    • ...
Before graduation   PhD Research     Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                   PhD Research @ TU Delft
Before graduation    PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                              Innovative Transport Pricing
                                                  Introduction




            • Transport Pricing:
                    • How do users pay for mobility?
                    • Traditionally: Car purchase tax, Road tax, Public transport ticket
Before graduation    PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                              Innovative Transport Pricing
                                                  Introduction




            • Transport Pricing:
                    • How do users pay for mobility?
                    • Traditionally: Car purchase tax, Road tax, Public transport ticket
            • Initiatives for different measures are proposed since 1977 in
               The Netherlands
                    • Toll roads
                    • Peak hour sticker
                    • Kilometre charge
Before graduation    PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                              Innovative Transport Pricing
                                                  Introduction




            • Transport Pricing:
                    • How do users pay for mobility?
                    • Traditionally: Car purchase tax, Road tax, Public transport ticket
            • Initiatives for different measures are proposed since 1977 in
               The Netherlands
                    • Toll roads
                    • Peak hour sticker
                    • Kilometre charge

            • All proposals failed to be implemented.
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                             Innovative Transport Pricing
                                              Research Project




            • Deliverable: Decision support system for the design and
               evaluation of innovative pricing schemes.
            • Underlying goal: Sustainable mobility and accessibility in the
               Randstad area.
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                             Innovative Transport Pricing
                                              Research Project




            • Deliverable: Decision support system for the design and
               evaluation of innovative pricing schemes.
            • Underlying goal: Sustainable mobility and accessibility in the
               Randstad area.

            • Model studies on transport pricing are numerous, but lack a
               complete solution.
            • Task: Combine state-of-the-art models and fill in the gaps.
Before graduation                   PhD Research                                       Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                                                                   Innovative Transport Pricing
                                                                                                Schematic overview
  Mo lders




                                                                       Groningen

                                                       Friesland
      del
     eho




                                                                       Drenthe
                                        Noord-
                                        Holland

                                                      Flevo-
                                                    land
                                                                   Overijssel


                                          Utrecht         Gelderland
                              Zuid-
                              Holland
Stak




                                        Noord-Brabant
                    Zeeland


                                                        Limburg
Before graduation                   PhD Research                                       Innovative Transport Pricing    Transport Model    Stakeholders Model   Wrap-up




                                                                                   Innovative Transport Pricing
                                                                                                Schematic overview




                                                                                                                      Insurance fee
                                                                                                                                          Toll
  Mo lders




                                                                                                             Parking fee    Pricing               Fuel price
                                                                                                                            Scheme
                                                                       Groningen

                                                       Friesland
      del




                                                                                                                                               Ticket price
     eho




                                                                       Drenthe
                                        Noord-
                                        Holland

                                                      Flevo-
                                                    land




                                                                                                                                    Kilometre charge
                                                                   Overijssel


                                          Utrecht         Gelderland
                              Zuid-
                              Holland
Stak




                                        Noord-Brabant
                    Zeeland


                                                        Limburg
Before graduation                   PhD Research                                       Innovative Transport Pricing    Transport Model    Stakeholders Model   Wrap-up




                                                                                   Innovative Transport Pricing
                                                                                                Schematic overview




                                                                                                                      Insurance fee
                                                                                                                                          Toll
  Mo lders




                                                                                                             Parking fee    Pricing               Fuel price
                                                                                                                            Scheme
                                                                       Groningen

                                                       Friesland
      del




                                                                                                                                               Ticket price
     eho




                                                                       Drenthe
                                        Noord-
                                        Holland

                                                      Flevo-
                                                    land




                                                                                                                                    Kilometre charge
                                                                   Overijssel


                                          Utrecht         Gelderland
                              Zuid-
                              Holland
Stak




                                        Noord-Brabant
                    Zeeland


                                                        Limburg




                                                                                                                                                       Tra ic Mo
                                                                                                                                                       Tra
                                                                                                                                          +




                                                                                                                                                          nsp
                                                                                                                                                           ff
                                                                                                                                                              ort el
                                                                                                                                                                 &
                                                                                                                                                                 d
Before graduation                   PhD Research                                       Innovative Transport Pricing    Transport Model    Stakeholders Model   Wrap-up




                                                                                   Innovative Transport Pricing
                                                                                                Schematic overview




                                                                                                                      Insurance fee
                                                                                                                                          Toll
  Mo lders




                                                                                                             Parking fee    Pricing               Fuel price
                                                                                                                            Scheme
                                                                       Groningen

                                                       Friesland
      del




                                                                                                                                                Ticket price
     eho




                                                                       Drenthe
                                        Noord-
                                        Holland

                                                      Flevo-
                                                    land




                                                                                                                                    Kilometre charge
                                                                   Overijssel


                                          Utrecht         Gelderland
                              Zuid-
                              Holland
Stak




                                        Noord-Brabant
                    Zeeland


                                                        Limburg




                                                                                                                                                       Tra ic Mo
                                                                                                                                                       Tra
                                                                                                                                          +
                                                               Safety




                                                                                                                                                          nsp
                                                                                                                                                           ff
              dB
                              Accessibility                                          Effects




                                                                                                                                                              ort el
         PM10                                                                                   Congestion
                                                                                      CO2




                                                                                                                                                                 &
                                                                                                                                                                 d
                              User Equity                                                   NOX
Before graduation    PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                        Transport Model
                                                  Introduction




            • Input
                    • Pricing Scheme
                    • Multimodal Network
                    • Potential OD demand
Before graduation    PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                        Transport Model
                                                  Introduction




            • Input
                    • Pricing Scheme
                    • Multimodal Network
                    • Potential OD demand
            • Output
                    • Travel Times
                    • Emissions
                    • Other quantified effects

       Results are obtained by calculating the user equilibrium.
Before graduation     PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model     Wrap-up




                                         Transport Model
                                             Schematic Overview


                                                                                      Assignment model
                                                     Dynamic
  Choice set generator                              multimodal
                                                     route set
                                                                                             Route choice

Demand model

                                                                                          Flow propagation
                                                                                               model
        Trip choice
                                                                                             Dynamic
                                                     Potential
                                                                                             Multimodal
                                                     demand
                                                                                             Multiple user
                                                                                             classes
       Destination
                                                                                             Spillback
         choice
                                                                                             Shockwaves
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                       Transport Model
                                           Choice set generator
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                       Transport Model
                                           Choice set generator
Before graduation       PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                           Transport Model
                                           Multimodal choice model




            • Simultaneous mode, route and departure time choice.
            • Discrete choice model for a multimodal route set.
            • Model takes into account
                    • Travel times in several modes
                    • Waiting and transfer time
                    • Fuel costs, parking costs, public transport price and road
                        pricing costs
                    •   Compensation of costs
                    •   Different income groups
                    •   Penalties for early/late departure/arrival
                    •   Stay home alternative
Before graduation   PhD Research      Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                          Transport Model
                                   Dynamic Network Loading with the LTM



       Fundamentals of the Link Transmission Model (LTM)
            • Consistent with first order kinematic wave theory (shockwaves
               & spillback).
            • Based on cumulative flows.
            • Time discretized.
            • No space discretization (other than the network
               representation).
            • Triangular fundamental diagram.
Before graduation   PhD Research      Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                          Transport Model
                                   Dynamic Network Loading with the LTM



       Fundamentals of the Link Transmission Model (LTM)
            • Consistent with first order kinematic wave theory (shockwaves
               & spillback).
            • Based on cumulative flows.
            • Time discretized.
            • No space discretization (other than the network
               representation).
            • Triangular fundamental diagram.
       The LTM can only be applied on road networks and should be
       combined with a public transport network loading model.
Before graduation    PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                    Stakeholders Model
                                                  Introduction




            • Input
                    • Stakeholders’ preferences on effects
                    • Stakeholders’ hierarchy and interaction
                    • Stakeholders’ executive control
Before graduation    PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                    Stakeholders Model
                                                  Introduction




            • Input
                    • Stakeholders’ preferences on effects
                    • Stakeholders’ hierarchy and interaction
                    • Stakeholders’ executive control
            • Output
                    • Unique pricing scheme

       Results are obtained by iterating over the underlying transport
       model.
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                   Stakeholders Model
                                       Mathematical formulation




            • Price vector p = (p1 , . . . , pn )
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                   Stakeholders Model
                                       Mathematical formulation




            • Price vector p = (p1 , . . . , pn )
            • Effects vector e = (e1 , . . . , em )
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                   Stakeholders Model
                                       Mathematical formulation




            • Price vector p = (p1 , . . . , pn )
            • Effects vector e = (e1 , . . . , em )
            • DTA(p) : Rn → Rm is the operator mapping the prices to effects
               under user equilibrium in the transport model.
Before graduation   PhD Research   Innovative Transport Pricing    Transport Model   Stakeholders Model   Wrap-up




                                   Stakeholders Model
                                       Mathematical formulation




            • Price vector p = (p1 , . . . , pn )
            • Effects vector e = (e1 , . . . , em )
            • DTA(p) : Rn → Rm is the operator mapping the prices to effects
               under user equilibrium in the transport model.
       The classical approach is:

                                               min         f (e)
                                                  p

                                      such that            e = DTA(p)

       where f : Rm → R is the preference of the stakeholder.
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model     Wrap-up




                                   Stakeholders Model
                                          Multiple stakeholders




            • S is the set of stakeholders.
            • Every stakeholder s ∈ S has objective function:

                                                   fs (e) : Rm → R                                       (1)
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model     Wrap-up




                                   Stakeholders Model
                                          Multiple stakeholders




            • S is the set of stakeholders.
            • Every stakeholder s ∈ S has objective function:

                                                   fs (e) : Rm → R                                       (1)



            • Every stakeholder minimizes its objective by setting p.
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model     Wrap-up




                                   Stakeholders Model
                                          Multiple stakeholders




            • S is the set of stakeholders.
            • Every stakeholder s ∈ S has objective function:

                                                   fs (e) : Rm → R                                       (1)



            • Every stakeholder minimizes its objective by setting p.
            • Because of the multiple objective functions a formulation as a
               simple mathematical problem is not feasible.
Before graduation    PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                    Stakeholders Model
                                       Game Theoretical Approach




            • Game theoretical solution algorithms are used.
            • The stakeholders can either cooperate or act selfishly.
                    • Under cooperation coalitions between stakeholders can be
                      formed and monetary transactions are allowed.
                    • Without cooperation each stakeholder will make independent
                      decisions based on self-interest.
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                                Example

                                                                  City A




                                       City B




                                                                  City C
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




                                                Wrap-up

       After graduation:
            • Find out what you find important in your career!
            • Doing PhD research is challenging and offers a lot more than
               just desktop work
       Innovative Transport Pricing
            • A comprehensive model framework is required to evaluate and
               design pricing measures
            • Cooperation between stakeholders can improve the transport
               system
            • The method provides insight for stakeholders in the benefit of
               forming a coalition (and can be used as decision support
               system)
Before graduation   PhD Research   Innovative Transport Pricing   Transport Model   Stakeholders Model   Wrap-up




       Questions?
       e.smits@tudelft.nl
       Room: 4.14

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Smits_InnovativeTransportPricing

  • 1. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Life after graduation Innovative Transport Pricing Erik-Sander Smits November 22, 2012
  • 2. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Before graduation Utrecht University • BSc. Computing Science • BSc. + MSc. Mathematics Graduation internship @ Omnitrans International O-D matrix estimation A Priori O-D matrix ⇒ New O-D Matrix Traffic counts Matrix estimation O-D matrix Route proportions Assignment
  • 3. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Before graduation After internship @ Omnitrans • Writing Thesis • Searching for a job: What do I want? • Consultancy (Engineering)? • Consultancy (Strategy)? • Private Equity? • Trader (Finance)? • Science?
  • 4. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Before graduation After internship @ Omnitrans • Writing Thesis • Searching for a job: What do I want? • Consultancy (Engineering)? • Consultancy (Strategy)? • Private Equity? • Trader (Finance)? • Science? • What do I find important? • → Challenge! I want to apply my analytical skills.
  • 5. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up PhD Research @ T & P Your own project 4-year long challenge! Gather knowledge ... execute the research ... publish your results The finale is the thesis defense.
  • 6. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up PhD Research @ TU Delft Courses Teaching • Soft skills (e.g. Scientific Writing) • Hard skills (e.g. Discrete Choice • Give lectures Analysis) • Supervise MSc students Conferences Exchange • Transportation Research Board • One to three months • TRAIL Congress • All around the world • ...
  • 7. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up PhD Research @ TU Delft
  • 8. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Innovative Transport Pricing Introduction • Transport Pricing: • How do users pay for mobility? • Traditionally: Car purchase tax, Road tax, Public transport ticket
  • 9. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Innovative Transport Pricing Introduction • Transport Pricing: • How do users pay for mobility? • Traditionally: Car purchase tax, Road tax, Public transport ticket • Initiatives for different measures are proposed since 1977 in The Netherlands • Toll roads • Peak hour sticker • Kilometre charge
  • 10. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Innovative Transport Pricing Introduction • Transport Pricing: • How do users pay for mobility? • Traditionally: Car purchase tax, Road tax, Public transport ticket • Initiatives for different measures are proposed since 1977 in The Netherlands • Toll roads • Peak hour sticker • Kilometre charge • All proposals failed to be implemented.
  • 11. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Innovative Transport Pricing Research Project • Deliverable: Decision support system for the design and evaluation of innovative pricing schemes. • Underlying goal: Sustainable mobility and accessibility in the Randstad area.
  • 12. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Innovative Transport Pricing Research Project • Deliverable: Decision support system for the design and evaluation of innovative pricing schemes. • Underlying goal: Sustainable mobility and accessibility in the Randstad area. • Model studies on transport pricing are numerous, but lack a complete solution. • Task: Combine state-of-the-art models and fill in the gaps.
  • 13. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Innovative Transport Pricing Schematic overview Mo lders Groningen Friesland del eho Drenthe Noord- Holland Flevo- land Overijssel Utrecht Gelderland Zuid- Holland Stak Noord-Brabant Zeeland Limburg
  • 14. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Innovative Transport Pricing Schematic overview Insurance fee Toll Mo lders Parking fee Pricing Fuel price Scheme Groningen Friesland del Ticket price eho Drenthe Noord- Holland Flevo- land Kilometre charge Overijssel Utrecht Gelderland Zuid- Holland Stak Noord-Brabant Zeeland Limburg
  • 15. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Innovative Transport Pricing Schematic overview Insurance fee Toll Mo lders Parking fee Pricing Fuel price Scheme Groningen Friesland del Ticket price eho Drenthe Noord- Holland Flevo- land Kilometre charge Overijssel Utrecht Gelderland Zuid- Holland Stak Noord-Brabant Zeeland Limburg Tra ic Mo Tra + nsp ff ort el & d
  • 16. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Innovative Transport Pricing Schematic overview Insurance fee Toll Mo lders Parking fee Pricing Fuel price Scheme Groningen Friesland del Ticket price eho Drenthe Noord- Holland Flevo- land Kilometre charge Overijssel Utrecht Gelderland Zuid- Holland Stak Noord-Brabant Zeeland Limburg Tra ic Mo Tra + Safety nsp ff dB Accessibility Effects ort el PM10 Congestion CO2 & d User Equity NOX
  • 17. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Transport Model Introduction • Input • Pricing Scheme • Multimodal Network • Potential OD demand
  • 18. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Transport Model Introduction • Input • Pricing Scheme • Multimodal Network • Potential OD demand • Output • Travel Times • Emissions • Other quantified effects Results are obtained by calculating the user equilibrium.
  • 19. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Transport Model Schematic Overview Assignment model Dynamic Choice set generator multimodal route set Route choice Demand model Flow propagation model Trip choice Dynamic Potential Multimodal demand Multiple user classes Destination Spillback choice Shockwaves
  • 20. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Transport Model Choice set generator
  • 21. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Transport Model Choice set generator
  • 22. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Transport Model Multimodal choice model • Simultaneous mode, route and departure time choice. • Discrete choice model for a multimodal route set. • Model takes into account • Travel times in several modes • Waiting and transfer time • Fuel costs, parking costs, public transport price and road pricing costs • Compensation of costs • Different income groups • Penalties for early/late departure/arrival • Stay home alternative
  • 23. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Transport Model Dynamic Network Loading with the LTM Fundamentals of the Link Transmission Model (LTM) • Consistent with first order kinematic wave theory (shockwaves & spillback). • Based on cumulative flows. • Time discretized. • No space discretization (other than the network representation). • Triangular fundamental diagram.
  • 24. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Transport Model Dynamic Network Loading with the LTM Fundamentals of the Link Transmission Model (LTM) • Consistent with first order kinematic wave theory (shockwaves & spillback). • Based on cumulative flows. • Time discretized. • No space discretization (other than the network representation). • Triangular fundamental diagram. The LTM can only be applied on road networks and should be combined with a public transport network loading model.
  • 25. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Introduction • Input • Stakeholders’ preferences on effects • Stakeholders’ hierarchy and interaction • Stakeholders’ executive control
  • 26. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Introduction • Input • Stakeholders’ preferences on effects • Stakeholders’ hierarchy and interaction • Stakeholders’ executive control • Output • Unique pricing scheme Results are obtained by iterating over the underlying transport model.
  • 27. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Mathematical formulation • Price vector p = (p1 , . . . , pn )
  • 28. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Mathematical formulation • Price vector p = (p1 , . . . , pn ) • Effects vector e = (e1 , . . . , em )
  • 29. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Mathematical formulation • Price vector p = (p1 , . . . , pn ) • Effects vector e = (e1 , . . . , em ) • DTA(p) : Rn → Rm is the operator mapping the prices to effects under user equilibrium in the transport model.
  • 30. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Mathematical formulation • Price vector p = (p1 , . . . , pn ) • Effects vector e = (e1 , . . . , em ) • DTA(p) : Rn → Rm is the operator mapping the prices to effects under user equilibrium in the transport model. The classical approach is: min f (e) p such that e = DTA(p) where f : Rm → R is the preference of the stakeholder.
  • 31. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Multiple stakeholders • S is the set of stakeholders. • Every stakeholder s ∈ S has objective function: fs (e) : Rm → R (1)
  • 32. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Multiple stakeholders • S is the set of stakeholders. • Every stakeholder s ∈ S has objective function: fs (e) : Rm → R (1) • Every stakeholder minimizes its objective by setting p.
  • 33. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Multiple stakeholders • S is the set of stakeholders. • Every stakeholder s ∈ S has objective function: fs (e) : Rm → R (1) • Every stakeholder minimizes its objective by setting p. • Because of the multiple objective functions a formulation as a simple mathematical problem is not feasible.
  • 34. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Stakeholders Model Game Theoretical Approach • Game theoretical solution algorithms are used. • The stakeholders can either cooperate or act selfishly. • Under cooperation coalitions between stakeholders can be formed and monetary transactions are allowed. • Without cooperation each stakeholder will make independent decisions based on self-interest.
  • 35. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Example City A City B City C
  • 36. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Wrap-up After graduation: • Find out what you find important in your career! • Doing PhD research is challenging and offers a lot more than just desktop work Innovative Transport Pricing • A comprehensive model framework is required to evaluate and design pricing measures • Cooperation between stakeholders can improve the transport system • The method provides insight for stakeholders in the benefit of forming a coalition (and can be used as decision support system)
  • 37. Before graduation PhD Research Innovative Transport Pricing Transport Model Stakeholders Model Wrap-up Questions? e.smits@tudelft.nl Room: 4.14