**Consider the following simple ****example:**

**Example:**

Suppose that we want to arrange the six departments of a toy factory to minimize the interdepartmental material handling cost. Initially, let us make the assumption that all departments have the same amount of space say 40 feet by 40 feet and that the building is 80 feet wide and 120 feet long (and thus compatible with the department dimensions). The first thing we would want to know is the nature of the flow between departments and the way the material is transported. If the company has another factory that makes similar products information about flow patterns might be obtained from these records. On the other hand if this is a new product such information would have to come from routing sheets or from estimates by knowledgeable personnel such as process or industrial engineers. Of course these data regardless of their source have to be adjusted to reflect-the-nature of future orders over the projected life of the proposed layout. Let us assume that this -information is available. We find that material is-transported in a standard-size crate by forklift truck one crate to a truck (which constitutes one "load"). Now suppose that transportation costs are $1 to move' load be n adjacent.departments and extra Io reach department in bet ween. e assume there' two-way traffic' between departments.) The expected loads-between departments forth first year of operation are tabulated in Exhibit 8.2; the available plant space is depicted in Exhibit 8.3. Given this information. our first step is to illustrate the interdepartmental flow by a model. such as Exhibit 8.4. which is Exhibit 8.2 displayed in the building layout in Exhibit 8.3. this provides the basic layout pattern. which we are trying to improve.

The second step is to determine the annual cost of this layout by multiplying the material handling cost per load by the number of loads moved between each department. Exhibit 8.5 presents this information which is derived as follows: The annual material handling cost between Departments 1 and 2 is $175 ($1 x 175 moves), $460 between Departments I and 5 ($2 x 230 moves) and so forth. (The distances are taken from Exhibit 8.3 or 8.4, not Exhibit 8.2.)

The third step is a search for departmental changes that reduce costs. On the basis of the graph and the cost matrix, it appears desirable to place Departments 1 and 5 closer together to reduce their high move-distance costs. However this requires shifting another department thereby affecting other move distance costs and the total cost of the second solution. Exhibit 8.6 shows the revised layout resulting from relocating Department 5 and an adjacent department (Department 3 is arbitrarily elected for this purpose)The revised cost matrix for the exchange with the cost changes circled is given in Exhibit-8.7. Note.the to total cost is.now $345 less than in the initial solution While this trial and error approach resulted in a lower total cost in this case, even are small problem it is often difficult to identify the correct "obvious move" on the basis of casual inspection. The revised layout for the facility is shown in Exhibit

Thus far, we have shown only one exchange among a large number of potential exchanges in fact for a six department problem there are 61 (or 720) possible arrangements. Therefore the procedure we have employed would have only a remote possibility of achieving an optimal combination in a "reasonable" number of tries. Nor does our problem stop

here. Other factors must be taken into consideration. Suppose that we are able to arrive at a good trial-and-error solution solely on the basis of material handling cost. Continuing with our toy factory example, locating the sewing department

next to the painting department might not only be hazardous. but also may result in defective products with lint, thread, and cloth particles drifting onto the painted items before they can dry. Thus, issues like these also must be incorporated into the final choice of layout.