@inproceedings{BorndoerferOmontSagnoletal.2012, author = {Bornd{\"o}rfer, Ralf and Omont, Bertrand and Sagnol, Guillaume and Swarat, Elmar}, title = {A Stackelberg game to optimize the distribution of controls in transportation networks}, volume = {105}, booktitle = {Proceedings of the 3rd International Conference on Game Theory for Networks (GAMENETS 2012)}, doi = {http://dx.doi.org/10.1007/978-3-642-35582-0_17}, pages = {224 -- 235}, year = {2012}, abstract = {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.}, language = {en} } @misc{BorndoerferOmontSagnoletal.2012, author = {Bornd{\"o}rfer, Ralf and Omont, Bertrand and Sagnol, Guillaume and Swarat, Elmar}, title = {A Stackelberg game to optimize the distribution of controls in transportation networks}, issn = {1438-0064}, doi = {10.1007/978-3-642-35582-0_17}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14995}, year = {2012}, abstract = {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.}, language = {en} } @misc{BorndoerferSagnolSchwartz2015, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Schwartz, Stephan}, title = {An Extended Network Interdiction Problem for Optimal Toll Control}, issn = {1438-0064}, doi = {10.1016/j.endm.2016.03.040}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-55405}, year = {2015}, abstract = {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.}, language = {en} } @article{BorndoerferBuwayaSagnoletal.2015, author = {Bornd{\"o}rfer, Ralf and Buwaya, Julia and Sagnol, Guillaume and Swarat, Elmar}, title = {Network spot-checking games: Theory and application to toll enforcing in transportation networks}, volume = {65}, journal = {Networks}, publisher = {Wiley Periodicals, Inc.}, doi = {10.1002/net.21596}, pages = {312 -- 328}, year = {2015}, abstract = {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.}, language = {en} } @inproceedings{SagnolBorndoerferSchlechteetal.2014, author = {Sagnol, Guillaume and Bornd{\"o}rfer, Ralf and Schlechte, Thomas and Swarat, Elmar}, title = {The Price of Spite in Spot-checking games}, volume = {8768}, booktitle = {7th International Symposium on Algorithmic Game Theory (SAGT'2014)}, editor = {Lavi, Ron}, publisher = {Springer}, isbn = {978-3-662-44802-1}, doi = {10.1007/978-3-662-44803-8}, pages = {293}, year = {2014}, abstract = {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. 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 is more relevant for this problem, but we show that this is NP-hard. However, we give some bounds on the \emph{price of spite}, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we demonstrate the quality of these bounds for a real-world application, namely the enforcement of a truck toll on German motorways.}, language = {en} } @misc{BorndoerferSagnolSchlechteetal.2013, author = {Bornd{\"o}rfer, Ralf and Sagnol, Guillaume and Schlechte, Thomas and Swarat, Elmar}, title = {Optimal Toll Enforcement - an Integration of Vehicle Routing and Duty Rostering}, issn = {1438-0064}, doi = {10.1007/s10479-016-2152-1}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-45107}, year = {2013}, abstract = {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, the crews of the tours have to be scheduled. Thus, we developed a personalized crew rostering model. 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 paper focuses first on different requirements for the rostering and how they can be modeled in detail. The second focus is on a bicriterion analysis of the planning problem to find the balance between the control quality and the roster acceptance. On the one hand the tour planning is a profit maximization problem and on the other hand the rostering should be made in a employee friendly way. Finally, computational results on real-world instances show the practicability of our method.}, language = {en} } @misc{SagnolHarman2014, author = {Sagnol, Guillaume and Harman, Radoslav}, title = {Optimal Designs for Steady-state Kalman filters}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-52808}, year = {2014}, abstract = {We consider a stationary discrete-time linear process that can be observed by a finite number of sensors. The experimental design for the observations consists of an allocation of available resources to these sensors. We formalize the problem of selecting a design that maximizes the information matrix of the steady-state of the Kalman filter, with respect to a standard optimality criterion, such as \$D-\$ or \$A-\$optimality. This problem generalizes the optimal experimental design problem for a linear regression model with a finite design space and uncorrelated errors. Finally, we show that under natural assumptions, a steady-state optimal design can be computed by semidefinite programming.}, language = {en} } @article{SagnolSchmidtgenanntWaldschmidt2021, author = {Sagnol, Guillaume and Schmidt genannt Waldschmidt, Daniel}, title = {Restricted Adaptivity in Stochastic Scheduling}, volume = {204}, journal = {29th Annual European Symposium on Algorithms (ESA 2021)}, doi = {10.4230/LIPIcs.ESA.2021.79}, pages = {79:1 -- 79:14}, year = {2021}, abstract = {We consider the stochastic scheduling problem of minimizing the expected makespan on m parallel identical machines. While the (adaptive) list scheduling policy achieves an approximation ratio of 2, any (non-adaptive) fixed assignment policy has performance guarantee Ω(logm/loglogm). Although the performance of the latter class of policies are worse, there are applications in which non-adaptive policies are desired. In this work, we introduce the two classes of δ-delay and τ-shift policies whose degree of adaptivity can be controlled by a parameter. We present a policy - belonging to both classes - which is an O(loglogm)-approximation for reasonably bounded parameters. In other words, an exponential improvement on the performance of any fixed assignment policy can be achieved when allowing a small degree of adaptivity. Moreover, we provide a matching lower bound for any δ-delay and τ-shift policy when both parameters, respectively, are in the order of the expected makespan of an optimal non-anticipatory policy.}, language = {en} } @article{PronzatoSagnol2021, author = {Pronzato, Luc and Sagnol, Guillaume}, title = {Removing inessential points in c- and A-optimal design}, volume = {213}, journal = {Journal of Statistical Planning and Inference}, doi = {10.1016/j.jspi.2020.11.011}, pages = {233 -- 252}, year = {2021}, abstract = {A design point is inessential when it does not contribute to an optimal design, and can therefore be safely discarded from the design space. We derive three inequalities for the detection of such inessential points in c-optimal design: the first two are direct consequences of the equivalence theorem for c-optimality; the third one is derived from a second-order cone programming formulation of c-optimal design. Elimination rules for A-optimal design are obtained as a byproduct. When implemented within an optimization algorithm, each inequality gives a screening test that may provide a substantial acceleration by reducing the size of the problem online. Several examples are presented with a multiplicative algorithm to illustrate the effectiveness of the approach.}, language = {en} }