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33
Capacitated Network Design  Polyhedral Structure and Computation
 INFORMS JOURNAL ON COMPUTING
, 1994
"... We study a version of the capacity expansion problem (CEP) that arises in telecommunication network design. Given a capacitated network and a traffic demand matrix, the objective in the CEP is to add capacity to the edges, in batches of various modularities, and route traffic, so that the overall co ..."
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Cited by 59 (8 self)
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We study a version of the capacity expansion problem (CEP) that arises in telecommunication network design. Given a capacitated network and a traffic demand matrix, the objective in the CEP is to add capacity to the edges, in batches of various modularities, and route traffic, so that the overall cost is minimized. We study the polyhedral structure of a mixedinteger formulation of the problem and develop a cuttingplane algorithm using facet defining inequalities. The algorithm produces an extended formulation providing both a very good lower bound and a starting point for branch and bound. The overall algorithm appears effective when applied to problem instances using reallife data.
On Capacitated Network Design CutSet Polyhedra
 Mathematical Programming
, 2000
"... This paper provides an analysis of capacitated network design cutset polyhedra. We give a complete linear description of the cutset polyhedron of the single commodity  single facility capacitated network design problem. Then we extend the analysis to single commodity  multifacility and multi ..."
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Cited by 36 (7 self)
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This paper provides an analysis of capacitated network design cutset polyhedra. We give a complete linear description of the cutset polyhedron of the single commodity  single facility capacitated network design problem. Then we extend the analysis to single commodity  multifacility and multicommodity  multifacility capacitated network design problems. The valid inequalities described here have coefficients for both inflow and outflow arcs of a cutset and are applicable to network design problems with an arbitrary number of facility types and arbitrary capacities. We report a computational study to test the effectiveness of the new inequalities. 1 Introduction Given a network and a set of demands on the vertices of the network, the capacitated network design problem is to install integer multiples of capacities on the arcs of the network and route the flow so that the total capacity installation and flow routing costs are minimized. For instance, installing or leasing fiber...
A BranchandCut Algorithm for Capacitated Network Design Problems
 MATHEMATICAL PROGRAMMING
, 1998
"... We present a branchandcut algorithm to solve capacitated network design problems. Given a capacitated network and pointtopoint traffic demands, the objective is to install more capacity on the edges of the network and route traffic simultaneously, so that the overall cost is minimized. We study ..."
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Cited by 32 (2 self)
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We present a branchandcut algorithm to solve capacitated network design problems. Given a capacitated network and pointtopoint traffic demands, the objective is to install more capacity on the edges of the network and route traffic simultaneously, so that the overall cost is minimized. We study a mixedinteger programming formulation of the problem and identify some new facet defining inequalities. These inequalities, together with other known combinatorial and mixedinteger rounding inequalities, are used as cutting planes. To choose the branching variable, we use a new rule called "knapsack branching". We also report on our computational experience using reallife data.
Strong Inequalities for Capacitated Survivable Network Design Problems
 MATHEMATICAL PROGRAMMING
, 1999
"... We present several classes of facetdefining inequalities to strengthen polyhedra arising as subsystems of network design problems with survivability constraints. These problems typically involve assigning capacities to a network with multicommodity demands, such that after a vertex or edgedeletio ..."
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Cited by 31 (5 self)
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We present several classes of facetdefining inequalities to strengthen polyhedra arising as subsystems of network design problems with survivability constraints. These problems typically involve assigning capacities to a network with multicommodity demands, such that after a vertex or edgedeletion at least some prescribed fraction of each demand can be routed.
On the facets of the mixed–integer knapsack polyhedron
 MATH. PROGRAM., SER. B 98: 145–175 (2003)
, 2003
"... We study the mixed–integer knapsack polyhedron, that is, the convex hull of the mixed–integer set defined by an arbitrary linear inequality and the bounds on the variables. We describe facet–defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities cont ..."
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Cited by 28 (12 self)
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We study the mixed–integer knapsack polyhedron, that is, the convex hull of the mixed–integer set defined by an arbitrary linear inequality and the bounds on the variables. We describe facet–defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities containing a single integer variable. These inequalities strengthen and/or generalize known inequalities for several special cases. We report computational results on using the inequalities as cutting planes for mixed–integer programming.
Robust Capacity Planning in Semiconductor Manufacturing
 Report RC22196, IBM, T.J. Watson Research
, 2001
"... We present a scenario approach to capacity planning in semiconductor manufacturing under demand uncertainty. We formulate an integer programming model in which we minimize the expected value of the unmet demand, subject to capacity and budget constraints, to arrive at a tool set that does well acros ..."
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Cited by 10 (0 self)
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We present a scenario approach to capacity planning in semiconductor manufacturing under demand uncertainty. We formulate an integer programming model in which we minimize the expected value of the unmet demand, subject to capacity and budget constraints, to arrive at a tool set that does well across all of the scenarios. This is a dicult twostage stochastic integer program that is tackled with a heuristic approach. Analysis of the results in some reallife situations are presented. 1
Experiments With a Network Design Algorithm Using EpsilonApproximate Linear Programs
, 1998
"... We describe an upperbound algorithm for multicommodity network design problems that relies on new results for approximately solving certain linear programs, and on the greedy heuristic for setcovering problems. 1 Introduction. Network design problems are mixedinteger programs that have the fo ..."
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Cited by 8 (3 self)
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We describe an upperbound algorithm for multicommodity network design problems that relies on new results for approximately solving certain linear programs, and on the greedy heuristic for setcovering problems. 1 Introduction. Network design problems are mixedinteger programs that have the following broad structure. Given a graph, and a set of "demands"  positive amounts to be routed between pairs of vertices  capacity must be added to the edges and/or vertices of the graph, in discrete amounts, and at minimum cost, so that a feasible routing is possible. Problem of this form are increasingly important in telecommunications applications, because of the great expense inherent in maintaining and upgrading metropolitan networks. A wide variety of special cases have been studied. For example, one may be constrained to using a fixed family of paths to carry out the routing, or to using a single path for each demand, or to using integral flows. The precise manner in which capacit...
01 Reformulations of the Multicommodity Capacitated Network Design Problem
, 2007
"... We study 01 reformulations of the multicommodity capacitated network design problem, which is usually modeled with general integer variables to represent, design decisions on the number of facilities to install on each arc of the network. The reformulations are based on the multiple choice model, a ..."
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Cited by 8 (2 self)
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We study 01 reformulations of the multicommodity capacitated network design problem, which is usually modeled with general integer variables to represent, design decisions on the number of facilities to install on each arc of the network. The reformulations are based on the multiple choice model, a generic approach to represent piecewise linear costs using 01 variables. This model is improved by the addition of extended linking inequalities, derived from variable disaggregation techniques. We show that these extended linking inequalities for the 01 model are equivalent to the residual capacity inequalities, a class of valid inequalities derived for the model with general integer variables. In this paper, we compare two cuttingplane algorithms to compute the same lower bound on the optimal value of the problem: one based on the generation of residual capacity inequalities within the model with general integer variables, and another based on the addition of extended linking inequalities to the 01 reformulation. To further improve the computational results of the latter approach, we develop a columnandrow generation approach; the resulting algorithm is shown to be competitive with the approach relying on residual capacity inequalities.
Cover and Pack Inequalities for (Mixed) Integer Programming
"... We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 01 knapsack set, the mixed 01 knapsack set, the integer knapsack set, and the mixed integer knapsack set. Our aim is to give a common presentation of the inequalities based ..."
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Cited by 6 (4 self)
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We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 01 knapsack set, the mixed 01 knapsack set, the integer knapsack set, and the mixed integer knapsack set. Our aim is to give a common presentation of the inequalities based on covers and packs and highlight the connections among them. The focus of the paper is on recent research on the use of superadditive functions for the analysis of knapsack polyhedra. We also