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We propose a game theoretic model for the spatial distribution of inspectors on a
transportation network.
The problem is to spread out the controls so as to enforce the payment of a transit
toll. We formulate a linear program to find
the control distribution which maximizes the expected toll revenue,
and a mixed integer program for the problem of minimizing
the number of evaders. Furthermore, we show that the problem of finding an optimal
mixed strategy for a coalition of $N$ inspectors can be solved
efficiently by a column generation procedure. Finally, we give experimental results
from an application to the truck toll on German motorways.
We propose a game theoretic model for the spatial distribution of inspectors on a transportation network. The problem is to spread out the controls so as to enforce the payment of a transit toll. We formulate a linear program to find the control distribution which maximizes the expected toll revenue, and a mixed integer program for the problem of minimizing the number of evaders. Furthermore, we show that the problem of finding an optimal mixed strategy for a coalition of $N$ inspectors can be solved efficiently by a column generation procedure. Finally, we give experimental results from an application to the truck toll on German motorways.
Today the railway timetabling process and the track allocation is one of the most challenging problems to solve by a railway company. Especially due to the deregulation of the transport market in the recent years several suppliers of railway traffic have entered the market in Europe. This leads to more potential conflicts between trains caused by an increasing demand of train paths. Planning and operating railway transportation systems is extremely hard due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. In order to make best use of the infrastructure and to ensure economic operation, efficient planning of the railway operation is indispensable. Mathematical optimization models and algorithms can help to automatize and tackle these challenges. Our contribution in this paper is to present a renewed planning process due to the liberalization in Europe and an associated concept for track allocation, that consists of three important parts, simulation, aggregation, and optimization. Furthermore, we present results of our general framework for real world data.
This paper proposes the first model for toll enforcement optimization on German motorways. The enforcement is done by mobile control teams and our goal is to produce a schedule achieving network-wide control, proportional to spatial and time-dependent traffic distributions. Our model consists of two parts. The first plans control tours using a vehicle routing approach with profits and some side constraints. The second plans feasible rosters for the control teams. Both problems can be modeled as Multi-Commodity Flow Problems. Adding additional coupling constraints produces a large-scale integrated integer programming formulation. We show that this model can be solved to optimality for real world instances associated with a control area in East Germany.
In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to feasible rosters for one month. We present computational results in a case-study on a German subnetwork which documents the practicability of our approach.
In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour
planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network
and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to
feasible rosters for one month. We present computational results in a
case-study on a German subnetwork which documents the practicability of our approach.
We present a game-theoretic approach to optimize the strategies of toll enforcement
on a motorway network. In contrast to previous approaches,
we consider a network with an arbitrary
topology, and we handle the fact that
users may choose their Origin-Destination path; in particular they may take a detour to
avoid sections with a high control rate. We show that a Nash equilibrium can be
computed with an LP (although the game is not zero-sum), and we give a MIP for the computation
of a Stackelberg equilibrium. Experimental results based on an application to the
enforcement of a truck toll on German motorways are presented.