# The Assignment Problem

With this formulation, it becomes easy to analyze any trial solution. We shall describe next how the Excel Solver can be used to quickly find the optimal solution. You have the choice of typing the range names or clicking on the cells in the spreadsheet.

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An assignment problem can be easily solved by applying Hungarian method which consists of two phases.The assignment problem is an archetypal combinatorial optimization problem.This paper presents a neural network based on a dynamic model for solving the assignment problem.To learn more or modify/prevent the use of cookies, see our Cookie Policy and Privacy Policy.The task assignment problem (TAP) of this section is the toy problem chosen by Tank and Hopfield (1987) in their Scientific American article to illustrate the workings of Hopfield networks on combinatorial cost-optimization problems.The main idea is to replace the assignment problem with a linear programming problem.On the basis of the Karush–Kuhn–Tucker optimality conditions, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the original problem.This kind of toy problem is very useful for comparing the performance of different algorithms and, here, the potentialities of inversion will be further tested in systems in which chromosomes composed of more than one multigene family are used.Indeed, the task assignment problem is solved very efficiently using only inversion as the source of genetic variation and two multigene families: one to encode the assistants (represented by 1-6) and another to encode the book collections (represented by A-F).Each assistant is familiar with the subject areas to varying degrees and shelves the collections accordingly. Each assistant (1-6) should be assigned to one collection of books (A-F) based on the rates at which books are shelved per minute (fitness cases).The input data or fitness cases in this task consist of the rates at which books are shelved per minute (Figure 6.6). Shaded squares show the best assignment with the largest sum of shelving rates, 44.

• ###### PDF An optimal new method to solve the Assignment problem

May 4, 2019. PDF Abstract The Assignment problem is introduced as the Maximum weighted Bipartite matching problem. Also, this problem nominates as a.…

• ###### The Hungarian Method for the Assignment Problem.

The formulation of the assignment problem as a linear program was well known, but a 10 by 10 assignment problem has 100 variables in its primal statement.…

• ###### For solving the assignment problem - IEEE Xplore

The Assignment Problem is very interesting to be researched because it is simple but wide in the applications. Hungarian Method, developed by Harold Kuhn i.…

• ###### Solving the Assignment Problem by Relaxation Operations.

This paper presents a new algorithm for solving the assignment problem. The algorithm is based on a scheme of relaxing the given problem into a series of.…

• ###### The task assignment problem - Gene Expression Programming

The task assignment problem TAP of this section is the toy problem chosen by Tank and Hopfield 1987 in their Scientific American article to illustrate the.…

• ###### The auction algorithm - Columbia University

Abstract. We propose a massively parallelizable algorithm for the classical assignment problem. The algorithm operates like an auction whereby unassigned.…