INFRASTRUCTURE MANAGERS AND FREIGHT SERVICE OPERATORS: Pricing strategy design for the rail freight service network|. DO
Sponsored by EPSRC and the Network Rail A RAIL FREIGHT INDUSTRY TOOL TO MAXIMISE PROFIT FOR INFRASTRUCTURE MANAGERS AND FREIGHT SERVICE OPERATORS: Pricing strategy design for the rail freight service
network
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DONGJUN LI (Second Year PhD Student)
NewRail | Newcastle University | UK.
Outline • • • • • • •
Background and motivation Research objectives and innovation Research methodology and research gap Mathematic models Solution procedure Numerical case Further plan
Chart for Current Pricing Process Department for Transport (DfT)
Office of Rail and Road (ORR)
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B
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Network Rail (IM)
Leader
Industry Companies and Organizations (including Freight Service Operators)
Follower
Passengers and freight customers
Gover nment
Safety Bodies
Expert Advisors
Chart for Pricing Process Applied Our Mechanism Department for Transport (DfT)
Office of Rail and Road (ORR)
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Infrastructure Manager （Network Rail ）
Player
Industry Companies and Organizations (including Freight Service Operators)
Player
Passengers and freight customers
Gover nment
Safety Bodies
Expert Advisors
Research objectives and Innovation produced at this stage • To identify weaknesses that exist in the rail freight pricing process • To get Freight Service Operators(FSO) actively involved in the pricing process as an equivalent player • To simplify the pricing process • To determine an optimal price in order for the rail freight system to achieve maximum profit • To develop a mechanism for Infrastructure Managers(IM) and Freight Service Operators(FSO) to collaborate (revenue share)
Research Methodology • • • •
Game theory Linear programming Stochastic programming Inverse Mixed Integer Linear Programming
Summarize for Literature Review on Methodology Methodology
Title of Paper Multicommodity, multimode freight transportation: A general modelling and algorithmic framework for the service network design problem. (Crainic & J.-M. Rousseau 1986) A model to design a national high-speed rail network for freight distribution (Pazour et al. 2010) Integrated operations planning and revenue management for rail freight transportation (Crevier et al. 2012) Service network design in freight transportation (Crainic 2000) Price Analysis of Railway Freight Transport under Marketing Mechanism (Shi et al. 2012) Optimizing the freight train connection service network of a large-scale rail system (Lin et al. 2012) Rail track charges in Great Britain—the issue of charging for capacity (Nash et al. 2004) Are rail charges connected to costs? (Calvo & De Oña 2012) Rail infrastructure, ITS and access charges (Franklin et al. 2013) Service network design for freight railway transportation: the Italian case (Lulli et al. 2011) Mathematical structure of a bilevel strategic pricing model (Marcotte et al. 2009) Current Research
Quantitative Game theory (unilateral or IM bilateral)
Qualitative
Deterministic or stochastic
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FSO
Network
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State of the art and the Research Gap • Deterministic model • Unilateral: either IM or FSO considered • Network
Infrastructure Manager model Max 𝑍 = ∑& ∑'(𝑝&' ⋅ 𝑓&' ) − ∑& ∑'(𝑎&' ⋅ 𝑓&' ) − ∑& ∑/ ∑' ∑0(𝑇&/0 1 𝑥&/'0 1 𝑉 1 𝑆) Constraints : Constraint1: ∑' 𝑓&' ≤ 𝑀&/ , 𝑓&' ∈ {0,1} Total amount of trains can’t exceed the maximum number of freight trains between a pair of O(⋅ )D(⋅ ) in rout n on day d ; Constraint 2 𝑥&/'0 ∈ {0,1}, 𝑥&/'0 is integer Constraint 3 𝑥&/'0 ≤ 𝑓&' The transportation task j can only be allocated to i when liner train i on day d in rout n has been purchased. Constraint 4 ∑' 𝑥&/'0 ≤ 1 No more than 1 train will be needed to serve job j which means job j can’t be transported separately. Constraint 5 ∑0 𝑥&/'0 ⋅ 𝑇&/0 ≤ 𝐶&/' This is the capacity constraint. The total amount of wagons required by all tasks allocated to train i can’t exceed the capacity of train i on day d in rout n. Constraint 6 𝑥&/'0 = 0 ∀ {i, j | O(j) ≠ O(i), D(j)≠ D(i)} //𝑥&/'0 = 0 Order j cannot be allocated to train i when j cannot be covered by train i geographically
Freight Service Operator Model ----two stage stochastic model The first stage: @
Max Z= − ∑& ∑'(𝑝&' ⋅ 𝑓&' ) + 𝑄 𝒙, 𝝃 A
∑𝒊 𝒇𝒏𝒊 ≤ 𝑴𝒏𝒅 Constraints 𝑓&' ∈ {0,1} Total amount of trains can’t exceed the maximum number of freight trains between a pair of O(⋅ )- D(⋅ ) in rout n on day d. The second stage: 𝑄 𝑥, 𝜉 = ∑& ∑/ ∑' ∑0 𝑥&/'0 1 𝑟 1 𝑇&/0
Model for the freight transportation system : Max Z=ML ∑& ∑/ ∑' ∑0(𝑥&/'0 1 𝑟 1 𝑇&/0 ) − ∑& ∑' 𝑎&' ⋅ 𝑓&' − ∑& ∑/ ∑' ∑0(𝑇&/0 1 𝑥&/'0 1 𝑉 1 𝑆)
constraints Constraint 1 𝑥&/'0 ∈ {0,1}, 𝑥&/'0 is integer Constraint 2 𝑥&/'0 ≤ 𝑓&' The transportation task j can only be allocated to i when liner train i in day d in rout n has been purchased. Constraint 3 ∑' 𝑥&/'0 ≤ 1 No more than 1 train will be needed to serve job j which means job j can’t be transported separately. Constraint 4 ∑0 𝑥&/'0 ⋅ 𝑇&/0 ≤ 𝐶&/' This is the capacity constraint. The total amount of rail cars required by all tasks allocated to train i can’t exceed the capacity of train i. Constraint 5 𝑥'0 = 0 ∀ {i, j | O(j) ≠ O(i), D(j)≠ D(i)} //𝑥'0 = 0 Order j cannot be allocated to train i when j cannot be covered by train i geographically Constraint 6 ∑' 𝑓&' ≤ 𝑀&/ , 𝑓&' ∈ {0,1} Total amount of trains can’t exceed the maximum number of freight trains between a pair of O(⋅ )- D(⋅ ) in rout n on day d ;
Solution procedure • Step 1: a virtual single company with full cooperation, solve the system model to get the optimal price, optimal network design (𝑥 N ) • Step 2: apply cutting plane algorithm to optimize the price (PK ← FSO model )
Implementation of the algorithm C++ Cplex
Numerical case Assumed Available Information: •
• • •
• • •
There are 3 available trains from Donnington to Burton and the customer demand in 3 days is: {8,6,6,7,6,7} {9,7,4,7,6,8} {7,1,2,4,5,5} The initial prices for 3 available trains are 120,130,130 pounds. The fixed operational cost between Donnington and Burton is 2 pounds. The profit for different order in different trains are {15,9,6,6,8,9}, {10,12,10,8,9,8}, {8,9,7,9,10,15}. The capacity for all the trains between Donnington and Burton is 30 railcars. The variable cost per railcar per mile is 0.01pound; The distance between Donnington and Burton is 100 mile.
Results Scenario
Price per line
IM profit
FSO profit
System profit
Purchasing plan
1
N/A
141
80.3
221.3
1,1,0
2
120,130,130
37
152.3
189.3
1,0,0
3
120,58,130
-25
214.3
189.3
0,1,0
4
58,58,130
7
214.3
221.3
1,1,0
Future plan • • • • • •
Profit allocation between IM and FSO More complex network More cost and profit elements More complex train operations More rigorous method to solve the gaming process Develop software tool for new models
Gantt chart of the project (Green -completed; Blue -planned) M1M3 1 Reading and Learning 1.1 Learning C++. Studying the classical book C++ Primer, which includes designing and testing with examples. 1.2 Learning Linear Programming. Studying the following books: Dantzig , G. B., Thapa, M. N., (2003). Linear Programming 1: Introduction。 Springer-Verlag Dantzig , G. B., Thapa, M. N., (2003). Linear programming 2: theory and extensions. Springer-Verlag 1.3 Learning the application of IBM ILOG CPlex. 1.4 Learning Game theory. For this I am currently studying the following book: Fudenbuerg , D., Tirole, J., Game theory. The MIT press. 1.5 Conducting literature review in revenue management, network design, game theory, and rail freight management. Draft for chapter 1,2,3 in flow chart 2 Mathematical Model Development 2.1 Understand infrastructure manager’s decision-making process in pricing rail freight service and data collection 2.2 Understand the rail freight service operator’s decision-making process in network design and facility location and data collection 2.3 Develop models 2.3.1 Develop IM’s models (draft for chapter 4) 2.3.2 Develop FSO’s models (draft for chapter 5) 2.3.3 Develop models when IM and FSO are deemed as a virtual company (draft for chapter 6) 2.3.4 Findings and Proof 2.4 Inverse linear programming (ILP) (draft for chapter 7) 2.4.1 Introduction of Inverse linear programming (ILP) 2.4.2 Application of ILP in simple operation mode 2.5 Numerical Case (draft for chapter 8) 2.6 Develop models for complex operation mode (draft for chapter 9) 2.6.1 Develop IM’s models 2.6.2 Develop FSO’s models 2.6.3 Develop models for integrated system
Year 1 M4M7M6 M9
M10M12
M1M3
Year 2 M4M7M6 M9
M10M12
M1M3
Year 3 M4M7M6 M9
M10M12
Year 4 M1M4M3 M6
M1M3 2.6.4 Application of ILP in complex operation mode 3 Mechanism Design and Papers (draft for chapter 10) 3.1 Numerical analysis based mechanism design 3.2 Continue dissemination in peer reviewed journals and conferences 3.3 Theoretical analysis of mechanism design 3.3.1 The existence of Nash-equilibrium 3.3.2 The global optimality 3.3.3 The optimal mechanism 3.4 Thesis: writing-up thesis, finalisation, and submission 4 Dissemination 4.1 Dissemination in peer reviewed journals and conferences 4.2 Viva preparation
M4M6
Year 1 M7M9
M10M12
M1M3
M4M6
Year 2 M7M9
M10M12
M1M3
M4M6
Year 3 M7M9
M10M12
M1M3
Year 4 M4M6
Thank you !
