Matthew V. Galati

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Decomposition algorithms such as Lagrangian relaxation and Dantzig-Wolfe decomposition are well-known methods that can be used to generate bounds for mixed-integer linear programming problems. Traditionally, these methods have been viewed as distinct from polyhedral methods, in which bounds are obtained by dynamically generating valid inequalities to(More)
Both cutting plane methods and traditional decomposition methods are procedures that compute a bound on the optimal value of an integer linear program (ILP) by constructing an approximation to the convex hull of feasible solutions. This approximation is obtained by intersecting the polyhedron associated with the continuous relaxation, which has an explicit(More)
We report on the use of a revised business game as a supplemental teaching aid in a production and inventory control course in Industrial and Manufacturing Systems Engineering at Lehigh University. The revisions were born out of student evaluations of an original game developed at Stanford and implemented at Georgia Tech and Lehigh. The basic premise of the(More)
Decomposition algorithms such as Lagrangian relaxation and Dantzig-Wolfe decomposition are well-known methods that can be used to develop bounds for integer programming problems. We draw connections between these classical approaches and techniques based on generating strong valid inequalities. We also discuss several methods for incorporating dynamic cut(More)
Agronomic research employs genomics to develop breeding strategies that improve the disease resistance, health, and yield of agricultural crops. Plant genome complexity necessitates understanding how DNA markers across the genome are related by building genetic maps that group and order markers based on their inheritance. This biological challenge is an(More)
Decomposition algorithms such as Lagrangian relaxation and Dantzig-Wolfe decomposition are well-known methods that can be used to compute bounds for integer programming problems. We discuss a framework for integrating dynamic cut generation with traditional decomposition methods in order to obtain improved bounds and present a new paradigm for separation(More)
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