Browsing by Author "Obreque, Carlos"

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    A branch and cut algorithm for the hierarchical network design problem
    (ELSEVIER SCIENCE BV, 2010) Obreque, Carlos; Donoso, Macarena; Gutierrez, Gabriel; Marianov, Vladimir
    The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added. branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes. (C) 2008 Elsevier B.V. All rights reserved.
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    An optimal procedure for solving the hierarchical network design problem
    (TAYLOR & FRANCIS INC, 2007) Obreque, Carlos; Marianov, Vladimir
    The hierarchical network design problem consists of finding a minimum cost bilevel network that connects all the nodes in a set, created by a loopless main path and a forest. The main path is formed by primary (higher cost) arcs, providing a path between an origin node and a destination node. The forest, built using secondary (lower cost) arcs, connects all the nodes not on the main path, to the path itself. We state and prove some properties of the problem, which allow finding good upper bounds to the solution in polynomial time when the primary costs are proportional to secondary costs. We also propose an O(n(4)) procedure to improve on these bounds. In turn, these bounds are used to significantly reduce the number of nodes and arcs of the problem. Once the problem is reduced, large instances can be solved to optimality. At this stage, we use one of two linear integer optimization formulations. The first and preferred one is based on multicommodity flows, which avoids the formation of subtours. The second formulation avoids subtours by iteratively adding ad hoc constraints. We show some examples and provide computational experiments performed on networks with sizes up to 600 nodes and 14 000 arcs.
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    Lagrangean relaxation heuristics for the p-cable-trench problem
    (PERGAMON-ELSEVIER SCIENCE LTD, 2012) Marianov, Vladimir; Gutierrez Jarpa, Gabriel; Obreque, Carlos; Cornejo, Oscar
    We address the p-cable-trench problem. In this problem, p facilities are located, a trench network is dug and cables are laid in the trenches, so that every customer - or demand - in the region is connected to a facility through a cable. The digging cost of the trenches, as well as the sum of the cable lengths between the customers and their assigned facilities, are minimized. We formulate an integer programming model of the problem using multicommodity flows that allows finding the solution for instances of up to 200 nodes. We also propose two Lagrangean Relaxation-based heuristics to solve larger instances of the problem. Computational experience is provided for instances of up to 300 nodes. (C) 2011 Elsevier Ltd. All rights reserved.
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    Minimum cost path location for maximum traffic capture
    (PERGAMON-ELSEVIER SCIENCE LTD, 2010) Gutierrez Jarpa, Gabriel; Donoso, Macarena; Obreque, Carlos; Marianov, Vladimir
    A free path (with no preset extreme nodes) is located on a network, in such a way as to minimize the cost and maximize the traffic captured by the path. Traffic between a pair of nodes is captured if both nodes are visited by the path. Applications are the design of the route and locations of mailboxes for a local package delivery company, or the design of bus or subway lines, in which the shape of the route and the number of stops is determined by the solution of the optimization problem. The problem also applies to the design of an optical fiber network interconnecting WiFi antennas in a university campus. We propose two models and an exact solution method. Computational experience is presented for up to 300 nodes and 1772 arcs, as well as a practical case for the city of Concepcion, Chile. (C) 2009 Elsevier Ltd. All rights reserved.
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    Optimal design of hierarchical networks with free main path extremes
    (ELSEVIER SCIENCE BV, 2008) Obreque, Carlos; Marianov, Vladimir; Rios, Miguel
    We propose an optimal, two-stage procedure for the optimal design of minimum cost hierarchical spanning networks, consisting of a main path and secondary trees. The optimal location of the origin and destination nodes of the path is also found. We test our procedure and compare it with a known method. (C) 2007 Elsevier B.V. All rights reserved.
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    Scheduling operating rooms with consideration of all resources, post anesthesia beds and emergency surgeries
    (2016) Latorre Núñez, Guillermo; Lüer Villagra, Armin Mauricio; Marianov Kluge, Vladimir; Obreque, Carlos; Ramis, Francisco; Neriz, Liliana