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Acknowledgements
, 2004
"... I would like to thank my advisors Prof. Daniel Bienstock and Prof. Jay Sethuraman for their help and support in my studies and research. I am also very grateful to my coauthors and mentors Li ..."
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I would like to thank my advisors Prof. Daniel Bienstock and Prof. Jay Sethuraman for their help and support in my studies and research. I am also very grateful to my coauthors and mentors Li
Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice
, 2001
"... After several decades of sustained research and testing, linear programming has evolved into a remarkably reliable, accurate and useful tool for handling industrial optimization problems. Yet, large problems arising from several concrete applications routinely defeat the very best linear programming ..."
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Cited by 158 (4 self)
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After several decades of sustained research and testing, linear programming has evolved into a remarkably reliable, accurate and useful tool for handling industrial optimization problems. Yet, large problems arising from several concrete applications routinely defeat the very best linear programming codes, running on the fastest computing hardware. Moreover, this is a trend that may well continue and intensify, as problem sizes escalate and the need for fast algorithms becomes more stringent. Traditionally, the focus in optimization algorithms, and in particular, in algorithms for linear programming, has been to solve problems "to optimality." In concrete implementations, this has always meant the solution ofproblems to some finite accuracy (for example, eight digits). An alternative approach would be to explicitly, and rigorously, trade o# accuracy for speed. One motivating factor is that in many practical applications, quickly obtaining a partially accurate solution is much preferable to obtaining a very accurate solution very slowly. A secondary (and independent) consideration is that the input data in many practical applications has limited accuracy to begin with. During the last ten years, a new body ofresearch has emerged, which seeks to develop provably good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context ofthe modern theory ofalgorithms. The result ofthis work has been a family ofalgorithms with solid theoretical foundations and with growing experimental success. In this manuscript we will study these algorithms, starting with some ofthe very earliest examples, and through the latest theoretical and computational developments.
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 75 (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.
Computational Study of a Family of MixedInteger Quadratic Programming Problems
 Mathematical programming
, 1995
"... . We present computational experience with a branchandcut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables. Such problems arise in financial applications. The algorithm solves the largest reallife problems in a few minutes of run ..."
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Cited by 71 (6 self)
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. We present computational experience with a branchandcut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables. Such problems arise in financial applications. The algorithm solves the largest reallife problems in a few minutes of runtime. 1 Introduction. We are interested in optimization problems QMIP of the form: min x T Qx + c T x s.t. Ax b (1) jsupp(x)j K (2) 0 x j u j ; all j (3) where x is an nvector, Q is a symmetric positivesemidefinite matrix, supp(x) = fj : x j ? 0g and K is a positive integer. Problems of this type are of interest in portfolio optimization. Briefly, variables in the problem correspond to commodities to be bought, the objective is a measure of "risk", the constraints (1) prescribe levels of "performance", and constraint (2) specifies that not too many 1 different types of commodities can be chosen. All data is derived from statistical information. A good deal of previous work ha...
Developing a logistics service quality scale
, 1999
"... In the pursuit of competitive advantage, it is increasingly important to identify the demands and values of current and potential customers. ' Traditionally, logistics managers have done an excellent job of managing and moving inventorythe operational aspects of logistics. They often struggle ..."
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Cited by 20 (5 self)
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, however, have attempted to expand the theoretical domain of service quality to a businesstobusiness context, specifically in the arena of logistics service quality. In particular, Bienstock, Mentzer, and Bird developed a valid, reliable scale of what they termed physical distribution service quality
Minimum cost capacity installation for multicommodity network flows
 MATHEMATICAL PROGRAMMING
, 1998
"... Consider a directed graph G = (V; A), and a set of traffic demands to be shipped between pairs of nodes in V. Capacity has to be installed on the edges of this graph (in integer multiples of a base unit) so that traffic can be routed. In this paper we consider the problem of minimum cost installatio ..."
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Cited by 63 (12 self)
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Consider a directed graph G = (V; A), and a set of traffic demands to be shipped between pairs of nodes in V. Capacity has to be installed on the edges of this graph (in integer multiples of a base unit) so that traffic can be routed. In this paper we consider the problem of minimum cost installation of capacity on the arcs to ensure that the required demands can be shipped simultaneously between node pairs. We study two different approaches for solving problems of this type. The first one is based on the idea of metric inequalities (see Onaga and Kakusho[1971]), and uses a formulation with only jAj variables. The second uses an aggregated multicommodity flow formulation and has jV j \Delta jAj variables. We first describe two classes of strong valid inequalities and use them to obtain a complete polyhedral description of the associated polyhedron for the complete graph on 3 nodes. Next we explain our solution methods for both of the approaches in detail and present computational results. Our computational experience shows that the two formulations are comparable and yield effective algorithms for solving reallife problems.
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 39 (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.
Logistics Service Quality as a
"... SegmentCustomized Process Logistics excellence has become a powerful source of competitive differentiation within diverse marketing offerings of worldclass firms. Although researchers have suggested that logistics competencies complement marketing efforts, empirical evidence is lacking on what log ..."
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Cited by 1 (0 self)
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segment, which suggests that firms ought to customize their logistics services by customer segments. oth corporations and researchers are becoming increasingly aware of the strategic role of logistics services in a firm's overall success (Bienstock,
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 34 (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 complexity of covering vertices by faces in a planar graph
 SIAM J. COMPUT
, 1988
"... The pair (G, D) consisting of a planar graph G V, E) with n vertices together with a subset of d special vertices D V is called kplanar if there is an embedding of G in the plane so that at most k faces of G are required to cover all of the vertices in D. Checking 1planarity can be done in linear ..."
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Cited by 30 (0 self)
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The pair (G, D) consisting of a planar graph G V, E) with n vertices together with a subset of d special vertices D V is called kplanar if there is an embedding of G in the plane so that at most k faces of G are required to cover all of the vertices in D. Checking 1planarity can be done in lineartime since it reduces to a problem of checking planarity of a related graph. We present an algorithm which given a graph G and a value k either determines that G is not kplanar or generates an appropriate embedding and associated minimum cover in O(ckn) time, where c is a constant. Hence, the algorithm runs in linear time for any fixed k. The fact that the time required by the algorithm grows exponentially in k is to be expected since we also show that for arbitrary k, the associated decision problem is strongly NPcomplete, even when the planar graph has essentially a unique planar embedding, d 0(n), and all facial cycles have bounded length. These results provide a polynomialtime recognition algorithm for special cases of Steiner tree problems in graphs which are solvable in polynomial time.
Results 1  10
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