DSpace at MIT
(35.359 recursos)
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A Dual Ascent Procedure for Large Scale Uncapacitated Network Design - Balakrishnan, Anantaram; Magnanti, Thomas L.; Wong, Richard T.
The fixed-charge network design problem arises in a variety of problem contexts including transportation, communication, and production scheduling.We develop a family of dual ascent algorithms for this problem. This approach generalizes known ascent procedures for solving shortest path, plant location,Steiner network and directed spanning tree problems. Our computational results for several classes of test problems with up to 500 integer and 1.98 million continuous variables and constraints shows that the dual ascent procedure and an associated drop-add heuristic generates solutions that, in almost all cases, are guaranteed to be within 1 to 3 percent of optimality. Moreover, the procedure requires...
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Pup Matching: Model Formulations and Solution Approaches - Bossert, John M.; Magnanti, Thomas L.
We model Pup Matching, the logistics problem of matching or pairing semitrailers known as pups to cabs that are able to tow one or two of the pups simultaneously, as an AfP-complete version of the Network Loading Problem (NLP). We examine a branch and bound solution approach tailored to the NLP formulation through the use of three families of cutting planes and four heuristic procedures. Theoretically, we specify facet defining conditions for a cut family that we refer to as odd flow inequalities and show that each heuristic yields a 2-approximation. Computationally, the cheapest of the four heuristic values achieved...
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Routing in Point-to-Point Delivery Systems - Leung, Janny M. Y.; Magnanti, Thomas L.; Singhal, Vijay
This paper was also printed as a Working Paper at the Yale School of Organization and Management, Series B, No. 103.
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Computation of Minimum Volume Covering Ellipsoids - Sun, Peng; Freund, Robert M.
We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points al,...,am C Rn . This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it has been the subject of much theoretical complexity analysis. Here we focus on computation. We present a combined interior-point and active-set method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m = 30, 000 and n = 30)...
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