# The Assignment Problem

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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.

Formulate the Model | Trial and Error | Solve the Model Use the solver in Excel to find the assignment of persons to tasks that minimizes the total cost.

The model we are going to solve looks as follows in Excel. For this problem, we need Excel to find out which person to assign to which task (Yes=1, No=0).

In the first phase, row reductions and column reductions are carried out.

In the second phase, the solution is optimized on iterative basis.

Such a chromosome is shown below: It contains two different MGFs, the first encoding the assistants and the second the book collections.

And its expression gives: where the assignments are represented by the arrows.

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.

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