Optimizing Toll Enforcement in Transportation Networks: a Game-Theoretic Approach

Borndörfer, Ralf; Buwaya, Julia; Sagnol, Guillaume; Swarat, Elmar

doi:10.1016/j.endm.2013.05.100

Cited by 13 publications

(23 citation statements)

References 5 publications

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“…Usually, the quality of service measurement is estimated using surveys sent to costumers. A notable exception is the work of Borndörfer et al (2013), who write about a highway with tolls. In their case, the control decision is how often one should check whether drivers had paid the toll in a highway to minimize evasion.…”

Section: Mathematical Programmingmentioning

confidence: 95%

Design and Control of Public-Service Contracts and an Application to Public Transportation Systems

Lodi¹,

Malaguti

Stier-Moses

et al. 2016

Management Science

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U ntil the end of the 20th century it was common that cities organized, financed, and managed their own public transportation systems. More recently (in Italy mainly during the last decade), many countries liberalized the service provision of public transportation. Although offering local public transportation is a political and financial duty of governments, the service provision is outsourced to a private operator, while the government retains a control position, given to a regulatory agency. This is a common scheme not only in transportation. In close collaboration with the public transportation agency of the city of Bologna, Italy, we designed a methodology to optimize some aspects of the contractual relationship between that agency and the bus operator. We focus on the fines specified by the contract when the operator fails to comply with the service level it has agreed to provide, and on a procedure to measure that service level. Our approach has the advantage that it aligns the incentives of both parties to the benefit of bus riders. We model the agency-operator relationship as a multistage game and find its equilibrium to establish the best operating regime. The gametheoretical approach provides expressions for the fines that the operator should be charged if it does not satisfy the contracted services, and for the optimal agency's budget to devote to control activities. Second, to check the compliance of the operator with the schedule specified by the contract in a resource-efficient way, we compute how to position the agency's employees to verify if buses are running according to the specifications of the contract. This is achieved by counting bus services and by checking other quality indicators. We formulate this NP-hard problem as a mixed integer linear program and propose an algorithm to solve it that is effective in providing itineraries for the controllers working for the agency.

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Section: Mathematical Programmingmentioning

confidence: 95%

Design and Control of Public-Service Contracts and an Application to Public Transportation Systems

Lodi¹,

Malaguti

Stier-Moses

et al. 2016

Management Science

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“…As an alternative approach, we have proposed in a companion work a game theoretic approach that takes into account the behavior of drivers and fare evaders to distribute the controls in a more strategic way, see Borndörfer et al (2012aBorndörfer et al ( , 2013. The output there is not a roster or a tour plan but a probability distribution of the inspectors force over all arcs of the network.…”

Section: Problem Classificationmentioning

confidence: 98%

“…In addition, advanced problem specific algorithmic approaches like heuristics, multi-level algorithms or branch and price can be developed and investigated. A further aspect is the generation of rosters based on a mixed strategy of the inspectors which is the output of the game-theoretic approach from a companion paper (Borndörfer et al 2013). The mixed strategy corresponds to a probability distribution over the arcs of the toll network.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Optimal duty rostering for toll enforcement inspectors

et al. 2016

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We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, we developed a personalized crew rostering model, to schedule the crews of the tours. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The main focus of this paper extends our previous publications on how different requirements for the rostering can be modeled in detail. The second focus is on a bi-criteria analysis of the planning problem to find the balance between the control quality and the roster acceptance. Finally, computational results on real-world instances show the practicability of our method and how different input parameters influence the problem complexity.

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“…A SC game

G = (G, C, W, Q, α)

is formally defined by the following elements: A directed graph G = ( V , E ); A set of weighted commodities

C : = {(s_{k}, d_{k}, x_{k}), k \in K}

, representing origin‐destination pairs

(s_{k}, d_{k}) \in V^{2}

with x k > 0 users; A set of arc weights

W : = {(w_{e}, β_{e}, σ_{e}), e \in E}

, representing: A set

Q \subset {[0, 1]}^{| E |}

described by linear inequalities, representing possible distributions of the inspectors over the arcs of the graph. The quantity q e corresponds to the probability that some inspector is present on arc e ; A fraction α

\in

of penalties to be considered in the inspector's payoff. …”

Section: Spot‐checking Gamesmentioning

confidence: 99%

“…We start by showing that the model used in the conference paper at the origin of this article can be cast as a SC game. Here, the network users are assumed to travel over a network

G_{0} = (V_{0}, E_{0})

with arc costs w e and expected penalties σ e (conditionally to the presence of a controller on arc e ).…”

Section: Handling Practical Situations With Sc Gamesmentioning

confidence: 99%

Network spot‐checking games: Theory and application to toll enforcing in transportation networks

et al. 2015

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We introduce the class of spot-checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. In an SC game, the pure strategies of network users correspond to paths in a graph, and the pure strategies of the inspectors are subset of arcs to be controlled. Although SC games are not zero-sum, we show that a Nash equilibrium can be computed by linear programming. The computation of a strong Stackelberg equilibrium (SSE) is more relevant for this problem and we give a mixed integer programming (MIP) formulation for this problem. We show that the computation of such an equilibrium is NP-hard. More generally, we prove that it is NP-hard to compute a SSE in a polymatrix game, even if the game is pairwise zero-sum. Then, we give some bounds on the price of spite, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we report computational experiments on instances constructed from real data, for an application to the enforcement of a truck toll in Germany. These numerical results show the efficiency of the proposed methods, as well as the quality of the bounds derived in this article.

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Optimizing Toll Enforcement in Transportation Networks: a Game-Theoretic Approach

Cited by 13 publications

References 5 publications

Design and Control of Public-Service Contracts and an Application to Public Transportation Systems

Design and Control of Public-Service Contracts and an Application to Public Transportation Systems

Optimal duty rostering for toll enforcement inspectors

Network spot‐checking games: Theory and application to toll enforcing in transportation networks

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