     Download Facility Layout -Quadratic Assignment On this page we use a different add-in to solve the layout problem. Some layout problems can be modeled as quadratic assignment problems. An example is shown in the figure below. Here we have 10 offices indicated as A though J and they are all the the same size (10x10). There are 10 possible locations for the departments, indexed 1 through 10, with the same dimensions as the offices. The figure shows the departments assigned in numerical order. The flow between each office is shown in the from-to matrix below. We only show flow in one direction, but since the distances between departments are symmetric, it is unnecessary to specify direction. We assume that the length of individual trips between the departments is measured by the rectilinear distance measure and that travel is between the centroids of the departments. The distance between the centroids of the 10 locations is computed in the matrix below. The problem is to assign locations to the offices to minimize the flow-distance measure. To evaluate the natural assignment shown in the example we multiply each number in the distance matrix by the corresponding number in the flow matrix and add the numbers. The result for the initial layout is 2100. The problem described is an example of a quadratic assignment problem (QAP). This problem is addressed by the Combinatorics add-in. The Optimize add-in is used for the analysis, so it also must be installed. For a discussion of the use of QAP for layout problems go to the QAP page of the Combinatorics add-in. The assignment determined by the add-in is shown below. The value of this solution is 950.  The assignment of departments to offices is shown in the figure. This assignment is not necessarily the optimum. It was found using a combinatorial search process. Ten random assignments were generated and the assignments were each improved by a 2-change method. The analysis required 9 seconds on the author's computer. The QAP approach is only valid when all departments have the same size.  Operations Management / Industrial Engineering
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by Paul A. Jensen
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