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  • 1.
    Blomvall, Jörgen
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Henningsson, Mathias
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    AN INTRODUCTORY PROJECT IN FINANCIAL ENGINEERING2008In: 4th International CDIO Conference,2008, 2008Conference paper (Other academic)
    Abstract [en]

      

  • 2.
    Henningsson, Mathias
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Ring network design in telecommunications: optimization based solution approaches2003Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    When designing a telecommunication network, one often wish to include some kind of survivability requirement, for example that the network should be two-connected. A two-connected network fulfills the requirement that there should be at least two paths with no links in common between all pairs of nodes. One form of design model is to prescribe that the network should be composed of connected rings of links. The network design problem is then to choose links from a given network, and compose them into a number of rings. A ring is reliable in the sense that there always exist two ways of sending traffic, clockwise or counter-clockwise, which means that a ring fulfills the two-connectivity requirement. There is often a number of requirements on a ring, such as a limited length and limited number of nodes connected to the ring. This means that a ring network will include a number of rings, and traffic between rings must be possible. The traffic between rings is usually made at certain nodes, called transit nodes. Therefore all rings should be connected to at least one of the transit nodes. We focus on the case where we have two transit nodes in the network.

    Each possible ring is associated with a certain fixed cost, and all links in a certain ring are given the same capacity. Reserve capacity is allocated according to certain principles. The number of possible rings in a network is an exponential function of the number of nodes in the network, so for larger networks is it impossible to a priori generate all possible rings.

    We describe the problem, and model it as a linear integer programming problem, where a set of rings are assumed to be known. The usage of rings, i.e., the allocation of demand to rings, is determined. In practice, too many rings can not be included in the model. Instead we must be able to generate useful rings. A Lagrangean relaxation of the model is formulated, and the dual solution is used in order to derive reduced costs which can be used to generate new better rings. The information generated describes only the physical structure of the ring, not the usage of it. The ring generation problem is a modified traveling salesman subtour problem, which is known to be difficult to solve. Therefore, we focus on heuristic solution methods for this problem.

    We also presents a column generation approach where the problem is modeled as a set covering problem. Here, a column describes both the topology of the ring and the exact usage of it. A similar ring generation problem appears as a subproblem, in order to generate new rings.

    All methods are computationally tested on both real life data and randomly generated data, similar to real life problems.

    List of papers
    1. A ring network design problem and heuristics for generating a set of feasible rings
    Open this publication in new window or tab >>A ring network design problem and heuristics for generating a set of feasible rings
    2003 (English)Report (Other academic)
    Abstract [en]

    We discuss the problem of designing a telecommunication network with the survivability requirement that the network should be composed of connected rings of links. The work design problem is then to choose links from a given network, and compose them into a number of rings. Furthermore, the rings should be connected at certain transit nodes. The traffic between rings may pass through other rings. Each ring is associated with a certain fixed cost depending on the length of the ring. We describe the problem, modeled as a linear integer programming problem. We find a feasible solution to the problem by first find good rings in the network using two heuristics, and then solve the optimization model using only these rings. Finally, we give some computational results for different networks.

    Place, publisher, year, edition, pages
    Linköping: Linköpings universitet, 2003. p. 33
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 16
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-22367 (URN)1575 (Local ID)1575 (Archive number)1575 (OAI)
    Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-08-29
    2. Lagrangean price directive ring generation for network design
    Open this publication in new window or tab >>Lagrangean price directive ring generation for network design
    2003 (English)Report (Other academic)
    Abstract [en]

    This paper addresses the problem of designing a telecommunication network with certain survivability requirements, namely that the network should be made up between connected rigs. This way single link failures do not kill the connection between any two nodes. One can make the network two-node-connected by including two specific nodes in all rings. This gives rise to a network design optimization problem with fixed costs on rings. In this paper we describe a solution approach for such problems, based on generation of rings. The approach is in principle a column generation technique, where the dual prices used for pricing out columns are obtained with the help of Lagrange duality, instead of the usual LP-duality. Computational tests are reported.

    Place, publisher, year, edition, pages
    Linköping: Linköpings universitet, 2003. p. 19
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 17
    Keywords
    network design, rings, column generation, Lagrange multipliers
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-22370 (URN)1578 (Local ID)1578 (Archive number)1578 (OAI)
    Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-08-29
    3. Calculating cost coefficients for generation of rings in network design
    Open this publication in new window or tab >>Calculating cost coefficients for generation of rings in network design
    2003 (English)Report (Other academic)
    Abstract [en]

    We discuss a telecommunication network problem where the aim is to design a network that should be composed of connected rings of links. Each possible ring is associated with a certain fixed cost. The traffic between rings may pass through other rings, where the switch between two rings must be done at certain transit nodes. Each ring must pass at least one transit node. We describe the problem, modeled as a linear integer programming problem. We focus on calculating cost coefficients for ring generation using Lagrangean relaxation.

    Place, publisher, year, edition, pages
    Linköping: Linköpings universitet, 2003. p. 27
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 18
    Keywords
    network design, rings, integer programming, column generation, lagrangean relaxation
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-22368 (URN)1576 (Local ID)1576 (Archive number)1576 (OAI)
    Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-08-29
    4. A ring generation problem based on the traveling salesman subtour problem
    Open this publication in new window or tab >>A ring generation problem based on the traveling salesman subtour problem
    2003 (English)Report (Other academic)
    Abstract [en]

    Survivability and high redundancy are two critical issues in field of telecommunications. If a telecommunication network is built up by rings, high redundancy can be established, since the traffic can be sent in either direction. Traffic is usually sent using one direction, and if a failure occurs, the opposite direction is used. There is often a number of requirements on a ring, such as a limit on the number of connected nodes. This means that the network will include a number of rings, and traffic between rings must be possible. Therefore, a network must include a number of transit nodes, where it is possible to send traffic between the rings. We focus on the case where network includes two transit nodes and each ring must include at least one transit node. Since the number of rings is enormous one needs to generate rings.

    This paper discusses how to generate new rings, given that each node has a reward for connecting the node to the ring. The problem that occurs is a modification of a traveling salesman subtour problem with a additional constraint on the number of nodes connected. A problem formulation is given and some solution approaches are suggested. Two different scenarios are discussed, one where the aim is to modify an already existing ring, and one where the aim is to build a complete new ring. Some computational results are given for a real data network.

    Place, publisher, year, edition, pages
    Linköping: Linköpings universitet, 2003. p. 27
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 19
    Keywords
    traveling salesman subtour problem, orienteering problem, prize collecting travelling salesman problem, ring generation
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-22369 (URN)1577 (Local ID)1577 (Archive number)1577 (OAI)
    Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-08-29
    5. A ring network design problem solved by a ring generation and allocation approach
    Open this publication in new window or tab >>A ring network design problem solved by a ring generation and allocation approach
    2003 (English)Report (Other academic)
    Abstract [en]

    The development of optical fibers in telecommunications has lead large changes in the field. When design a telecommunication network, capacity nowadays is cheap, and the minimal cost design tends to be a tree. Since such a design is very vulnerable for link or node failures, one often wish to include some kind of survivability requirement, for example that the network should be two-edge-connected or two-node-connected. Another form of design model is to prescribe that the network should be composed of connected rings of links. The network design problem is then to choose links from a give network, and compose them into a number of rings. Furthermore, the rings should be connected at certain transit nodes. Each possible ring is associated with a certain fixed cost, and all links in a certain ring are given the same capacity. Traffic between rings may pass through other rings, which is an important element of the problem. Finally, reserve capacity allocation according to certain principles is included. We describe the problem, modeled as a linear integer programming problem, and discuss different formulations and different solution methods. As the problem is quite difficult, we focus on heuristic solution methods, including elements of column generation and Lagrangean relaxation.

    Place, publisher, year, edition, pages
    Linköping: Linköpings universitet, 2003. p. 37
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 20
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-22366 (URN)1574 (Local ID)1574 (Archive number)1574 (OAI)
    Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-08-29
    6. A column generation approach for a ring network design problem
    Open this publication in new window or tab >>A column generation approach for a ring network design problem
    2003 (English)Report (Other academic)
    Abstract [en]

    When designing a telecommunication network, one often wish to include some kind of survivability requirement, for example that there should be at least two paths between every pair of nodes in the network. A design model who fulfills this requirement is a network build up with rings. The network design problem is to choose links from a given network, and compose them into a number of rings. The rings are connected to each other at certain transit nodes. The number of possible rings is enormous, and each possible ring is associated with a certain fixed cost. A ring has a fixed capacity, however, we model it as a linear cost depending on the traffic using the ring and the length of the ring. We describe the problem, and model it is a set covering model, where a column describes how a specific ring is used. Even with a small set of rings, number of possible columns in the model is large. Therefore, a column generation approach is used to solve the set covering model with a given set of rings. An important part of the problem is to generate new rings, were the dual solution from the set covering model gives rewards on the nodes, representing a nodes’ wish to be included in a new ring. The ring generation problem is a modification of a traveling salesman subtour problem. New rings are generated using a heuristic. We present some computational results for a real data network and a number of random generated networks.

    Publisher
    p. 26
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 21
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-87193 (URN)
    Available from: 2013-01-14 Created: 2013-01-14 Last updated: 2013-08-29
  • 3.
    Henningsson, Mathias
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    A ring generation problem based on the traveling salesman subtour problem2003Report (Other academic)
    Abstract [en]

    Survivability and high redundancy are two critical issues in field of telecommunications. If a telecommunication network is built up by rings, high redundancy can be established, since the traffic can be sent in either direction. Traffic is usually sent using one direction, and if a failure occurs, the opposite direction is used. There is often a number of requirements on a ring, such as a limit on the number of connected nodes. This means that the network will include a number of rings, and traffic between rings must be possible. Therefore, a network must include a number of transit nodes, where it is possible to send traffic between the rings. We focus on the case where network includes two transit nodes and each ring must include at least one transit node. Since the number of rings is enormous one needs to generate rings.

    This paper discusses how to generate new rings, given that each node has a reward for connecting the node to the ring. The problem that occurs is a modification of a traveling salesman subtour problem with a additional constraint on the number of nodes connected. A problem formulation is given and some solution approaches are suggested. Two different scenarios are discussed, one where the aim is to modify an already existing ring, and one where the aim is to build a complete new ring. Some computational results are given for a real data network.

  • 4.
    Henningsson, Mathias
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Calculating cost coefficients for generation of rings in network design2003Report (Other academic)
    Abstract [en]

    We discuss a telecommunication network problem where the aim is to design a network that should be composed of connected rings of links. Each possible ring is associated with a certain fixed cost. The traffic between rings may pass through other rings, where the switch between two rings must be done at certain transit nodes. Each ring must pass at least one transit node. We describe the problem, modeled as a linear integer programming problem. We focus on calculating cost coefficients for ring generation using Lagrangean relaxation.

  • 5.
    Henningsson, Mathias
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Lagrangean price directive ring generation for network design2003Report (Other academic)
    Abstract [en]

    This paper addresses the problem of designing a telecommunication network with certain survivability requirements, namely that the network should be made up between connected rigs. This way single link failures do not kill the connection between any two nodes. One can make the network two-node-connected by including two specific nodes in all rings. This gives rise to a network design optimization problem with fixed costs on rings. In this paper we describe a solution approach for such problems, based on generation of rings. The approach is in principle a column generation technique, where the dual prices used for pricing out columns are obtained with the help of Lagrange duality, instead of the usual LP-duality. Computational tests are reported.

  • 6.
    Henningsson, Mathias
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Rönnqvist, Mikael
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Värbrand, Peter
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    A column generation approach for a ring network design problem2003Report (Other academic)
    Abstract [en]

    When designing a telecommunication network, one often wish to include some kind of survivability requirement, for example that there should be at least two paths between every pair of nodes in the network. A design model who fulfills this requirement is a network build up with rings. The network design problem is to choose links from a given network, and compose them into a number of rings. The rings are connected to each other at certain transit nodes. The number of possible rings is enormous, and each possible ring is associated with a certain fixed cost. A ring has a fixed capacity, however, we model it as a linear cost depending on the traffic using the ring and the length of the ring. We describe the problem, and model it is a set covering model, where a column describes how a specific ring is used. Even with a small set of rings, number of possible columns in the model is large. Therefore, a column generation approach is used to solve the set covering model with a given set of rings. An important part of the problem is to generate new rings, were the dual solution from the set covering model gives rewards on the nodes, representing a nodes’ wish to be included in a new ring. The ring generation problem is a modification of a traveling salesman subtour problem. New rings are generated using a heuristic. We present some computational results for a real data network and a number of random generated networks.

  • 7.
    Henningsson, Mathias
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Rönnqvist, Mikael
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Värbrand, Peter
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    A ring network design problem and heuristics for generating a set of feasible rings2003Report (Other academic)
    Abstract [en]

    We discuss the problem of designing a telecommunication network with the survivability requirement that the network should be composed of connected rings of links. The work design problem is then to choose links from a given network, and compose them into a number of rings. Furthermore, the rings should be connected at certain transit nodes. The traffic between rings may pass through other rings. Each ring is associated with a certain fixed cost depending on the length of the ring. We describe the problem, modeled as a linear integer programming problem. We find a feasible solution to the problem by first find good rings in the network using two heuristics, and then solve the optimization model using only these rings. Finally, we give some computational results for different networks.

  • 8.
    Henningsson, Mathias
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Rönnqvist, Mikael
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Värbrand, Peter
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    A ring network design problem solved by a ring generation and allocation approach2003Report (Other academic)
    Abstract [en]

    The development of optical fibers in telecommunications has lead large changes in the field. When design a telecommunication network, capacity nowadays is cheap, and the minimal cost design tends to be a tree. Since such a design is very vulnerable for link or node failures, one often wish to include some kind of survivability requirement, for example that the network should be two-edge-connected or two-node-connected. Another form of design model is to prescribe that the network should be composed of connected rings of links. The network design problem is then to choose links from a give network, and compose them into a number of rings. Furthermore, the rings should be connected at certain transit nodes. Each possible ring is associated with a certain fixed cost, and all links in a certain ring are given the same capacity. Traffic between rings may pass through other rings, which is an important element of the problem. Finally, reserve capacity allocation according to certain principles is included. We describe the problem, modeled as a linear integer programming problem, and discuss different formulations and different solution methods. As the problem is quite difficult, we focus on heuristic solution methods, including elements of column generation and Lagrangean relaxation.

  • 9.
    Henningsson, Mathias
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Rönnqvist, Mikael
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Värbrand, Peter
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Ring network design by Lagrangean based column generation2002In: Telecommunications Systems, ISSN 1018-4864, E-ISSN 1572-9451, Vol. 21, no 2-4, p. 301-318Article in journal (Refereed)
    Abstract [en]

    We discuss the problem of designing a telecommunication network with the survivability requirement that the network should be composed of connected rings of links. The network design problem is then to choose links from a given network, and compose them into a number of rings. Furthermore, the rings should be connected at certain transit nodes. The traffic between rings may pass through other rings. Each ring is associated with a certain fixed cost depending on the length of the ring. We describe the problem, modeled as a linear integer programming problem, and a heuristic solution method, based on column generation and Lagrangean relaxation.

  • 10.
    Henningsson, Mathias
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Yuan, Di
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology, Communications and Transport Systems.
    Ring Network Design2006In: Handbook of Optimization in Telecommunications / [ed] Mauricio G.C. Resende, Panos M. Pardalos, New York: Springer Science + Business Media , 2006, p. 291-312Chapter in book (Other academic)
    Abstract [en]

    "I highly recommend The Handbook of Optimization in Telecommunications as an invaluable resource for anyone interested in understanding the impact of optimization on the most import problems facing the telecommunications industry today.

    The handbook is unprecedented in the breadth and depth of its coverage, illustrating that telecommunications offers a vast array of interesting and important optimization problems probably exceeding the traditional areas of transportation networks, engineering, economics and military operations.”

    —Clyde Monma, Retired Chief Scientist, Applied Research Area, Telcordia Technologies

    Telecommunications has had a major impact in all aspects of life in the last century. There is little doubt that the transformation from the industrial age to the information age has been fundamentally influenced by advances in telecommunications.

    Optimization problems are abundant in the telecommunications industry. The successful solution of these problems has played an important role in the development of telecommunications and its widespread use. Optimization problems arise in the design of telecommunication systems and in their operation.

    The Handbook of Optimization in Telecommunications brings together experts from around the world who use optimization to solve problems that arise in telecommunications. The editors made an effort to cover recent optimization developments that are frequently applied to telecommunications. The spectrum of topics covered includes planning and design of telecommunication networks, routing, network protection, grooming, restoration, wireless communications, network location and assignment problems, Internet protocol, World Wide Web, and stochastic issues in telecommunications. The editors’ objective is to provide a reference tool for the increasing number of scientists and engineers in telecommunications who depend upon optimization in some way.

    Each chapter in the handbook is of an expository nature, but of scholarly treatment, and includes a brief overview of the state-of-the-art thinking relative to the topic, as well as pointers to the key references in the field. Specialists as well as nonspecialists should find this handbook stimulating and helpful.

  • 11.
    Henningsson, Mathias
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Karlsson, Jenny
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Rönnqvist, Mikael
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Mixed Integer Programming models to support Tactical Forest Road Upgrade Planning2004Report (Other academic)
  • 12.
    Henningsson, Mathias
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Karlsson, Jenny
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Rönnqvist, Mikael
    Department of Finance and Management Science, Norwegian School of Economics and Business Administration, Bergen, Norway.
    Optimization models for forest road upgrade planning2007In: Journal of Mathematical Modelling and Algorithms, ISSN 1570-1166, E-ISSN 1572-9214, Vol. 6, no 1, p. 3-23Article in journal (Refereed)
    Abstract [en]

    Road blocking due to thawing or heavy rains annually contribute to a considerable loss in Swedish forestry. Companies are forced to build up large stocks of raw material (saw and pulp logs) in order to secure a continuous supply when access to the road network is uncertain. Storage outdoors leads to quality deterioration and monetary losses. Other related costs due to road blocking are road damage and longer haulage distances. One approach to reduce the losses due to road blocks is to upgrade the road network to a standard that guarantees accessibility. We consider the road upgrade problem from the perspective of Swedish forest companies with a planning horizon of about one decade. The objective is to minimize the combined upgrade and transportation costs. We present two mixed integer programming models, which are uncapacitated fixed charge network flow problems including multiple assortments, several time periods and a set of road classes. One model is based on arc flows and one on route flows. For a typical planning instance, the models become large and we propose how to improve solution performance through model strengthening. The models are tested in a case study for a major Swedish forest company.

  • 13.
    Lindholm, Anna
    et al.
    Lund University, Sweden.
    Johnsson, Charlotta
    Lund University, Sweden.
    Quttineh, Nils-Hassan
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Lidestam, Helene
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Henningsson, Mathias
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Wikner, Joakim
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Tang, Ou
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Nytzén, Nils-Petter
    Perstorp AB, Sweden.
    Forsman, Krister
    Perstorp AB, Sweden.
    Hierarchical Scheduling and Utility Disturbance Management in the Process Industry2013In: Proceedings for IFAC Conference on Manufacturing Modelling, Management and Control (MIM2013), 2013, Elsevier, 2013, p. 140-145Conference paper (Refereed)
    Abstract [en]

    The integration of scheduling and control in the process industry is a topic that has been frequently discussed during the recent years, but many challenges remain in order to achieve integrated solutions that can be implemented for large-scale industrial sites. In this paper we consider production control under disturbances in the supply of utilities at integrated sites together with the integration towards production scheduling. Utilities, such as steam and cooling water, are often shared between the production areas of a site, which enables formulation of an optimization problem for determining the optimal supply of utilities to each area at the occurrence of a disturbance. Optimization in two timescales is suggested to handle the scheduling and disturbance management problems in a hierarchical fashion. The suggested structure has been discussed with companies within the chemical process industry. A simple example is provided to show how the structure may be used

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