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  • 1.
    Daneva (Mitradjieva), Maria
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Lindberg, Per Olov
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    The Stiff is Moving - Conjugate Direction Frank -Wolfe Methods with Applications to Traffic Assignment2013In: Transportation Science, ISSN 0041-1655, E-ISSN 1526-5447, Vol. 47, no 2, p. 280-293Article in journal (Refereed)
    Abstract [en]

    We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, conjugate direction Frank-Wolfe (CFW), bi-conjugate Frank-Wolfe (BFW), and "partanized" Frank-Wolfe methods to some classical Traffic Assignment Problems show that CFW and BFW compare favorably to the other methods. This spurred a more detailed study, comparing our methods to an origin-based algorithm. This study indicates that our methods are competitive for accuracy requirements ensuring link flow stability. We also show that CFW is globally convergent. We further point at independent studies by other researchers that show that our methods compare favorably with recent bush-based and gradient projection algorithms on computers with several cores

  • 2.
    Engevall, Stefan
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Göthe-Lundgren, Maud
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Värbrand, Peter
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
    The heterogeneous vehicle-routing game2004In: Transportation Science, ISSN 0041-1655, E-ISSN 1526-5447, Vol. 38, no 1, p. 71-85Article in journal (Refereed)
    Abstract [en]

    In this paper, we study a cost-allocation problem that arises in a distribution-planning situation at the Logistics Department at Norsk Hydro Olje AB, Stockholm, Sweden. We consider the routes from one depot during one day. The total distribution cost for these routes is to be divided among the customers that are visited. This cost-allocation problem is formulated as a vehicle-routing game (VRG), allowing the use of vehicles with different capacities. Cost-allocation methods based on different concepts from cooperative game theory, such as the core and the nucleolus, are discussed. A procedure that can be used to investigate whether the core is empty or not is presented, as well as a procedure to compute the nucleolus. Computational results for the Norsk Hydro case are presented and discussed.

  • 3.
    Holmberg, Kaj
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    The (Over)zealous Snow Remover Problem2019In: Transportation Science, ISSN 0041-1655, E-ISSN 1526-5447, Vol. 53, no 3, p. 867-881Article in journal (Refereed)
    Abstract [en]

    Planning snow removal is a difficult, infrequently occurring optimization problem, concerning complicated routing of vehicles. Clearing a street includes several different activities, and the tours must be allowed to contain subtours. The streets are classified into different types, each type requiring different activities. We address the problem facing a single vehicle, including details such as precedence requirements and turning penalties. We describe a solution approach based on a reformulation to an asymmetric traveling salesman problem in an extended graph, plus a heuristic for finding feasible solutions and a reordering procedure. The method has been implemented and tested on real life examples, and the solution times are short enough to allow online usage. We compare the solutions to lower bounds obtained by solving a mixed integer programming model. We study two different principles for the number of sweeps on a normal street, encountered in discussions with snow removal contractors. A principle using a first sweep in the middle of the street around the block, in order to quickly allow usage of the streets, is found to yield interesting theoretical and practical difficulties.

  • 4.
    Joborn, M.
    et al.
    Carmen Consulting, Maria Bangata 6, Stockholm SE-118 63, Sweden.
    Crainic, T.G.
    Intelligent Transp. Systems Lab., Ctr. de recherche sur les transports, Université de Montréal, Montréal, Que. H3C 3J7, Canada, Dept. de management et technologie, Ecoles des Sciences de la Gestion, Univ. du Quebec à Montreal, Montréal, Que. H3C 4R2, Canada.
    Gendreau, M.
    Ctr. de recherche sur les transports, Dept. d'info./rech. operationnelle, Université de Montréal, Montréal, Que. H3C 3J7, Canada.
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Lundgren, Jan
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
    Economies of scale in empty freight car distribution in scheduled railways2004In: Transportation Science, ISSN 0041-1655, E-ISSN 1526-5447, Vol. 38, no 2, p. 121-134Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider empty freight car distribution in a scheduled railway system. We analyze the cost structure for the repositioning of empty cars, and conclude that the distribution cost shows an economy-of-scale behavior. In addition to the cost proportional to the number of cars sent from origin to destination, there is a cost related to car-handling operations at yards, which depends on the number of car groups that are handled. Thus, if we can find a transportation pattern in which fewer but larger groups of cars are built, the total distribution cost can be decreased. The objective of the paper is to propose an optimization model that explicitly takes this economy-of-scale effect into account. We use a time-dependent network to describe the possible car movements in time and space, and show how this network can be transformed into a network with fixed costs on links representing movements of cars with identical origin and destination terminals. The resulting optimization model is a capacitated network design model, where each capacity constraint limits the flow on several arcs. We describe a tabu heuristic for solving the model, and present computational results. © 2004 INFORMS.

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