The Assignment Problem

For this simple six-by-six problem there are already 6!

= 720 possible assignments of assistants to book collections.

For example, if we assign Person 1 to Task 1, cell C10 equals 1. What is the overall measure of performance for these decisions? Explanation: The SUM functions calculate the number of tasks assigned to a person and the number of persons assigned to a task.

The overall measure of performance is the total cost of the assignment, so the objective is to minimize this quantity. To make the model easier to understand, name the following ranges. Total Cost equals the sumproduct of Cost and Assignment. The result should be consistent with the picture below.

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For further information, including about cookie settings, please read our Cookie Policy .By continuing to use this site, you consent to the use of cookies.We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services.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).The best solution has the highest sum of rates for the chosen assistants.For the particular set of fitness cases shown in Figure 6.6, f = 44.The goal is to minimize the total cost for accomplishing all tasks or, stated differently, to maximize the overall output of all the workers as a whole.Suppose we had to shelve n book collections in a library using n shelving assistants.

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