Facility Layout
- Craft Method


On this and the next page we investigate procedures for searching for an optimum solution. The methods described are the ones implemented in the Layout add-in. Although some manual user intervention is allowed by the add-in we concentrate on the automated procedures.


Initial Solution


Any automated procedure must start with an initial solution, and for some methods the final results are greatly influenced by this solution. The add-in allows the user to manually define the solution, however, we concentrate here on the aisle layout described below. The plant for the layout is assumed to be on a single level with a given plant length and width. The area prescribed for the plant must be at least as great as the sum of the areas of the departments. For the example, the plant width is 15 and the plant length is 11. The area is slightly larger than the total of the department areas.

Given a set of departments and their associated areas, the layout is determined by an aisle width and a permutation or sequence of the first n integers. In the case below, the aisle width is 5 cells and the sequence is {1, 2, … , 10}. We construct the initial layout using an approach similar to the ALDEP construction method.

The layout is determined by placing the first department in the sequence in the upper left corner using as many cells as necessary to place the entire area. The cells are used from left to right until the aisle boundary is reached. When the department is complete, the second department is placed starting with the next vacant cell. The process continues down the first (leftmost) aisle until the complete length of the plant is used, and the placement continues up the second aisle. The placement continues in this serpentine fashion, sequentially placing departments first down and then up the aisles, until all departments are placed. Because all areas for the example are a multiple a 5, the choice of an aisle width of 5 results in rectangular departments except D4 which spans two aisles.

A width of 4 as illustrated below results in a less attractive layout. Notice that when the aisle width is not a integer divisor of the plant width, the last aisle covers the remainder.

An alternative allowed by the add-in is to expand the department areas to occupy only full aisle widths. For the example with an aisle width of 4, the plant width must be increased to 16 cells to accommodate the larger department areas. Only when departments span more than one aisle will they have non-rectangular shapes.

Whatever the initial layout, it is evaluated using the metric selected. In the example, we are using the rectilinear distance between department centroids as the measure to be minimized. The value of the layout is shown in the upper left of the figure.

Given the plant dimensions and aisle width, every permutation of the n integers provides a unique layout. This feature is used by the Sequential layout method described on the next page.


Craft Method

A well known automated procedure for searching for the optimum is called the CRAFT method. The method tries to improve an initial layout by switching the locations of department. Candidates for switching are pairs of departments that have the same area or pairs of departments that are adjacent in the layout. Switching departments that are not adjacent and that have different areas would obviously result in non-contiguous departments. The diagrams and computations illustrated below were provided by the Layout add-in. We begin with the aisle layout determined by the sequence {1, 2, … , 10} and an aisle width of 5.

To illustrate department switches, consider the feasible switches that involve department 6 in the layout above. Departments 2 and 8 have the same area, so the pairs (2, 6) and (6, 8) are feasible. Departments that are adjacent to 6 are departments 3, 5, 7, 9 and 10, so the pairs involving these departments and department 6 are also feasible.

To evaluate the effect of switching the two departments, the CRAFT method assumes that the centroids of the two departments are switched and computes the resultant cost savings. Switching the centroids of the two departments is equivalent to switching the interdepartmental distances involving the two departments. The entire layout need not be evaluated, but only the terms involving the two departments as shown below for the general switch of departments k and l.

For a given layout we evaluate the effects of all feasible departmental switches and choose the one with the most negative value of . If there are no negative values, the process terminates. When the two departments are the same size, this evaluation is accurate. When the departments have different sizes, the centroids of the departments do not exactly switch locations. In this case the evaluation may be not be accurate and a switch that looks promising may actually increase the cost of the layout. The CRAFT method implemented by the add-in terminates if this occurs.

For the example, the best feasible pair is 9 and 10. Since the two departments are different sizes, there are many alternatives for arranging the cells of the smaller sized department 9 into the larger area formerly holding department 10. The Layout add-in has an algorithm for choosing the arrangement that results in the layout below. Although one might question the logic of this arrangement, it is difficult to program an algorithm that always makes the assignment that would appear most reasonable to the human designer. The objective value for the changed layout is shown above the upper-left corner in the figure below. The layout has an improved objective compared to the initial solution.

The next iteration switches departments 2 and 3.

The next iteration switches departments 2 and 5.

The program next estimates that if the centroids of departments 7 and 8 are switched, the cost of the layout will be reduced. When the switch is actually made, the cost increases. This occurs because the centroids used by the evaluation are quite different than the centroids after the departments are switched. The CRAFT method must terminate at this point because no improving switches are available.

The results of the CRAFT method depend on the initial solution and the sequence of switches performed. The add-in generates random initial solutions, so better solutions may be found by repeating the process for different random initial solutions. The results are often not very satisfactory for problems with departments of different sizes. As in the example, the final layout has departments far from the desired rectangular shape. It is even possible that departments may be split into sets of non-adjacent cells.

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

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