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We study an extension of the shortest path network interdiction problem and present a novel real-world application in this area. We consider the problem of determining optimal locations for toll control stations on the arcs of a transportation network. We handle the fact that drivers can avoid control stations on parallel secondary roads. The problem is formulated as a mixed integer program and solved using Benders decomposition. We present experimental results for the application of our models to German motorways.
Duty rostering problems occur in different application contexts and come in different flavors. They give rise to very large scale integer programs which ypically have lots of solutions and extremely fractional LP relaxations. In such a situation, heuristics can be a viable algorithmic choice. We propose an mprovement method of the Lin-Kernighan type for the solution of duty rostering problems. We illustrate its versatility and solution quality on three different applications in public transit, vehicle routing, and airline rostering with a focus on the management of preferences, fairness, and fatigue, respectively.
Duty rostering problems occur in different application contexts and come in different flavors. They give rise to very large scale integer programs which ypically have lots of solutions and extremely fractional LP relaxations. In such a situation, heuristics
can be a viable algorithmic choice. We propose an mprovement method of the Lin-Kernighan type for the solution of duty rostering problems. We illustrate its versatility and solution quality on three different applications in public transit, vehicle routing, and
airline rostering with a focus on the management of preferences, fairness, and fatigue, respectively.
The Graduate-Level Research in Industrial Projects (G-RIPS) Program provides an
opportunity for high-achieving graduate-level students to work in teams on a
real-world research project proposed by a sponsor from industry or the public
sector. Each G-RIPS team consists of four international students (two from
the US and two from European universities), an academic mentor, and an industrial sponsor.
This is the report of the Rail-Lab project on the definition and integration of
robustness aspects into optimizing rolling stock schedules. In general, there is
a trade-off for complex systems between robustness and efficiency. The ambitious
goal was to explore this trade-off by implementing numerical simulations and
developing analytic models.
In rolling stock planning a very large set of industrial railway requirements,
such as vehicle composition, maintenance constraints, infrastructure capacity,
and regularity aspects, have to be considered in an integrated model. General
hypergraphs provide the modeling power to tackle those requirements.
Furthermore, integer programming approaches are able to produce high quality
solutions for the deterministic problem.
When stochastic time delays are considered, the mathematical programming problem
is much more complex and presents additional challenges. Thus, we started with a
basic variant of the deterministic case, i.e., we are only considering
hypergraphs representing vehicle composition and regularity.
We transfered solution approaches for robust optimization
from the airline industry to the setting of railways and attained a
reasonable measure of robustness. Finally, we present and discuss different
methods to optimize this robustness measure.
Integrated treatment of hitherto individual steps in the planning process of public transit companies discloses opportunities to reduce costs and to improve the quality of service. The arising integrated planning problems are complex and their solution requires the development of novel mathematical methods. This article proposes a mathematical optimization approach to integrate duty scheduling and rostering in public transit, which allows to significantly increase driver satisfaction at almost zero cost. This is important in order to to increase the attractiveness of the driver profession. The integration is based on coupling the subproblems by duty templates, which, compared to a coupling by duties, drastically reduces the problem complexity.
We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the feasibility condition for arc capacities in ordinary multi-commodity flows.
The concept allows to solve large-scale real-world line planning problems in public transport including a novel passenger routing model that favors direct connections over connections with transfers.
We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.
Network spot-checking games: Theory and application to toll enforcing in transportation networks
(2015)
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.