Journal Article10.1287/MNSC.9.4.586
The Quadratic Assignment Problem
964
TL;DR: In this article, the equivalence of the Koopmans-beckmann problem to a linear assignment problem with certain additional constraints is demonstrated, and a method for calculating a lower bound on the cost function is presented, and this forms the basis for an algorithm to determine optimal solutions.
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Abstract: This paper presents a formulation of the quadratic assignment problem, of which the Koopmans-Beckmann formulation is a special case. Various applications for the formulation are discussed. The equivalence of the problem to a linear assignment problem with certain additional constraints is demonstrated. A method for calculating a lower bound on the cost function is presented, and this forms the basis for an algorithm to determine optimal solutions. Further generalizations to cubic, quartic, N-adic problems are considered.
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Citations
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References
An Automatic Method for Solving Discrete Programming Problems
Ailsa H. Land,Alison G. Doig +1 more
TL;DR: In the late 1950s there was a group of teachers and research assistants at the London School of Economics interested in linear programming and its extensions, in particular Helen Makower, George Morton, Ailsa Land and Alison Doig.
•Posted Content
Assignment Problems and the Location of Economic Activities
2.1K
Optimal and Suboptimal Algorithms for the Quadratic Assignment Problem
TL;DR: A recent article by Steinberg as discussed by the authors describes a suboptimal procedure for solving the backboard wiring problem, which is a generalization of the quadratic assignment problem in the more general form in which it was discussed by Koopmans and Beckmann [2].
480
Solving the transportation problem
L. R. Ford,D. R. Fulkerson +1 more
TL;DR: In this article, a simplified description of a new computing procedure for the Hitchcock-Koopmans transportation problem is given, together with a step-by-step solution of an illustrative example.
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