Facility Layout
- Evaluation


The layout problem is to arrange the physical spaces required for several departments in a given space provided for the departments. In practice the facility layout problem is often solved by intuition, using the artistic and spatial skills of the human designer; however, when there are quantitative considerations associated with the layout problem, the human is at a disadvantage as compared to the computer. In this section we concentrate on computerized procedures for solving the layout problem. In this section we explain the problem by specifying the data and describing the decisions.

Here we are considering the problem of arranging several departments on a plant with a single level and fixed rectangular dimensions.

Certain data is necessary to describe the layout problem.

  • Number of departments, n,
  • Physical area of each department, for i = 1…n
  • Physical dimensions of the plant in which the departments are to be placed: Length, L, and Width, W.
  • Product flow between every pair of departments:
  • Material handling cost between every pair of departments measured in dollars per unit-length measure:

We illustrate the data requirement with an example used for the Layout add-in.

The example has 10 departments with various area dimensions shown above. Area is specified in both a spatial measure (square meters) and cells. For purposes of the add-in the cell represents an indivisible area represented by a single Excel worksheet cell. A scale factor is used to translate between the spatial measure and the cell, for the example it is one square meter to one cell. The F/V parameter indicates whether the department is fixed or variable in location. For the example all are variable.

The flow between departments is given in the Flow Matrix. This chart is also called the From-To matrix.

The material handling cost is 1 for all interdepartmental flows for this example.





Our models involve the distance from one department to another. The distance depends on the layout. To illustrate consider a layout of the example departments shown below. Since only the areas of the departments are specified there are a great many possible layouts. We generally assume that departments should not be split up into non-contiguous areas and that they should be roughly rectangular shapes.

To construct the initial layout, the plant width is divided into three equal width columns of 5 cells each. Starting in the upper left corner the departments are placed in the plant in numerical order passing down the first column. There is not sufficient length to place the entire area of D4 in the first column, so the remainder of D4 is placed in the second column. The process continues going up in the second column until D8. D9 and D10 are placed in the third column. Since the total area of the departments is less than the area of the plant, some cells remain unused at the bottom of the third column.

To develop a criterion for comparing layouts, distances are measured between department centroids. We use the upper left corner of the plant as the origin and compute the centroid (x, y) as the distance below, y, and to the right, x,of the origin. The centroids for the original layout are in the two right-hand columns below.

There are different metrics one can use to evaluate the distance between departments, including the Euclidean distance and rectilinear distance measures. It is common in layout analyses to use the rectilinear measure based on the assumption that travel between departments will follow aisles that are parallel to the borders of the facility.

The distances between the departments for the initial layout are given by the matrix above.


Criterion for Evaluation


We compute the cost for the flow from i to j as the product of the material handling cost, the flow, and the distance between the departments. The cost of the layout is the sum of the flow costs.

The cost for the initial layout is 4049.

The quantities and are given as data, but the quantity depends on the layout. This makes optimization difficult.


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Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved

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