2,262 research outputs found

    On location-allocation problems for dimensional facilities

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    This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the existence of optimal solutions under mild, natural assumptions. To achieve these results we borrow tools from optimal transport mass theory that allow us to give explicit solution structure of the considered lower level problem. We also provide a discretization approach that can approximate, up to any degree of accuracy, the optimal solution of the original problem. This discrete approximation can be optimally solved via a mixedinteger linear program. To address very large instance sizes we also provide a GRASP heuristic that performs rather well according to our experimental results. The paper also reports some experiments run on test data.Ministerio de Economía y Competitividad (MINECO). Españ

    The Network Improvement Problem for Equilibrium Routing

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    In routing games, agents pick their routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average delay have received substantial attention, including network tolls, Stackelberg routing, and edge removal. A related approach with arguably greater practical relevance is that of making investments in improvements to the edges of the network, so that, for a given investment budget, the average delay at equilibrium in the improved network is minimized. This problem has received considerable attention in the literature on transportation research and a number of different algorithms have been studied. To our knowledge, none of this work gives guarantees on the output quality of any polynomial-time algorithm. We study a model for this problem introduced in transportation research literature, and present both hardness results and algorithms that obtain nearly optimal performance guarantees. - We first show that a simple algorithm obtains good approximation guarantees for the problem. Despite its simplicity, we show that for affine delays the approximation ratio of 4/3 obtained by the algorithm cannot be improved. - To obtain better results, we then consider restricted topologies. For graphs consisting of parallel paths with affine delay functions we give an optimal algorithm. However, for graphs that consist of a series of parallel links, we show the problem is weakly NP-hard. - Finally, we consider the problem in series-parallel graphs, and give an FPTAS for this case. Our work thus formalizes the intuition held by transportation researchers that the network improvement problem is hard, and presents topology-dependent algorithms that have provably tight approximation guarantees.Comment: 27 pages (including abstract), 3 figure

    Bilevel models on the competitive facility location problem

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    Facility location and allocation problems have been a major area of research for decades, which has led to a vast and still growing literature. Although there are many variants of these problems, there exist two common features: finding the best locations for one or more facilities and allocating demand points to these facilities. A considerable number of studies assume a monopolistic viewpoint and formulate a mathematical model to optimize an objective function of a single decision maker. In contrast, competitive facility location (CFL) problem is based on the premise that there exist competition in the market among different firms. When one of the competing firms acts as the leader and the other firm, called the follower, reacts to the decision of the leader, a sequential-entry CFL problem is obtained, which gives rise to a Stackelberg type of game between two players. A successful and widely applied framework to formulate this type of CFL problems is bilevel programming (BP). In this chapter, the literature on BP models for CFL problems is reviewed, existing works are categorized with respect to defined criteria, and information is provided for each work.WOS:000418225000002Scopus - Affiliation ID: 60105072Book Citation Index- Science - Book Citation Index- Social Sciences and HumanitiesArticle; Book ChapterOcak2017YÖK - 2016-1

    Policy-making tool for optimization of transit priority lanes in urban network

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    Transit improvement is an effective way to relieve traffic congestion and decrease greenhouse gas emissions. Improvement can be in the form of new facilities or giving on-road priority to transit. Although construction of off-road mass transit is not always viable, giving priority to transit can be a low-cost alternative. A framework is introduced for optimization of bus priority at the network level. The framework identifies links on which a bus lane should be located. Allocation of a lane to transit vehicles would increase the utility of transit, although this can be a disadvantage to auto traffic. The approach balances the impact on all stakeholders. Automobile advocates would like to increase traffic road space, and the total travel time of users and total emissions of the network could be reduced by a stronger priority scheme. A bilevel optimization is applied that encompasses an objective function at the upper level and a mode choice, a traffic assignment, and a transit assignment model at the lower level. The proposed optimization helps transport authorities to quantify the outcomes of various strategies of transit priority. A detailed sensitivity analysis is carried out on the relative weight of each factor in the objective function. The proposed framework can also be applied in the context of high-occupancy-vehicle lanes and heavy-vehicle priority lanes

    Line planning with user-optimal route choice

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    We consider the problem of designing lines in a public transport system, where we include user-optimal route choice. The model we develop ensures that there is enough capacity present for every passenger to travel on a shortest route. We present two different integer programming formulations for this problem, and discuss exact solution approaches. To solve large-scale line planning instances, we also implemented a genetic solution algorithms. We test our algorithms in computational experiments using randomly generated instances along realistic data, as well as a realistic instance modeling the German long-distance network. We examine the advantages and disadvantages of using such user-optimal solutions, and show that our algorithms sufficiently scale with instance size to be used for practical purposes
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