The Assignment Problem

The Assignment Problem-84
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.

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