@MISC{Pardalos_nonlinearassignment, author = {Panos M. Pardalos and Leonidas S. Pitsoulis}, title = {Nonlinear Assignment Problems in Manufacturing}, year = {} }

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Abstract

Introduction Nonlinear Assignment Problems (NAP's) are NP-hard combinatorial optimization problems that are natural extensions of the classical Linear Assignment Problem (LAP). NAPs have numerous applications in different fields, ranging from the assignment of facilities to locations in location theory, to the tracking of elementary particles in high energy physics. We begin this section with the most basic of all assignment problems, the linear assignment problem. Consider that we are given n facilities and locations, and a matrix IR n\Thetan 3 C := (c ij ) where c ij represents the cost of placing facility i to location j. The objective is to find an optimal assignment of facilities to locations such that the total placement cost is minimized. Using the decision variables x ij 2 f0; 1