We will discuss three techniques to help a location decision--the location rating factor, the center-of-gravity technique, and the load-distance technique. The location factor rating mathematically evaluates location factors, such as those identified in the previous section. The center-of-gravity and load-distance techniques are quantitative models that centrally locate a proposed facility among existing facilities.

The decision where to locate is based on many different types of information and inputs. There is no single model or technique that will select the "best" site from a group. However, techniques are available that help to organize site information and that can be used as a starting point for comparing different locations.

In the **location factor rating** system, factors that are important in the location decision are identified. Each factor is weighted from 0 to 1.00 to prioritize the factor and reflect its importance. A subjective score is assigned (usually between 0 and 100) to each factor based on its attractiveness compared with other locations, and the weighted scores are summed. Decisions typically will not be made based solely on these ratings, but they provide a good way to organize and rank factors.

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The Dynaco Manufacturing Company is going to build a new plant to manufacture ring bearings (used in automobiles and trucks). The site selection team is evaluating three sites, and they have scored the important factors for each as follows. They want to use these ratings to compare the locations.
The weighted scores for each site are computed by multiplying the factor weights by the score for that factor. For example, the weighted score for "labor pool and climate" for site 1 is The weighted scores for each factor for each site and the total scores are summarized as follows: Site 3 has the highest factor rating compared with the other locations; however, this evaluation would have to be used with other information, particularly a cost analysis, before making a decision. |

In general, transportation costs are a function of distance, weight, and time. The **center-of-gravity,** or *weight center,* technique is a quantitative method for locating a facility such as a warehouse at the center of movement in a geographic area based on weight and distance. This method identifies a set of coordinates designating a central location on a map relative to all other locations.

The starting point for this method is a grid map set up on a Cartesian plane, as shown in Figure 9.4. There are three locations, 1, 2, and 3, each at a set of coordinates (*x _{i},*

The coordinates for the location of the new facility are computed using the following formulas:

- where
*x, y*= coordinates of the new facility at center of gravity*x*= coordinates of existing facility_{i}, y_{i}*i**W*= annual weight shipped from facility_{i}*i*

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The Burger Doodle restaurant chain purchases ingredients from four different food suppliers. The company wants to construct a new central distribution center to process and package the ingredients before shipping them to their various restaurants. The suppliers transport ingredient items in 40-foot truck trailers, each with a capacity of 38,000 pounds. The locations of the four suppliers, A, B, C, and D, and the annual number of trailer loads that will be transported to the distribution center are shown in the following figure: Using the center-of-gravity method, determine a possible location for the distribution center.
Thus, the suggested coordinates for the new distribution center location are |

A variation of the center-of-gravity method for determining the coordinates of a facility location is the **load-distance technique.** In this method, a single set of location coordinates is not identified. Instead, various locations are evaluated using a load-distance value that is a measure of weight and distance. For a single potential location, a load-distance value is computed as follows:

- where
- LD = the load-distance value
*l*= the load expressed as a weight, number of trips, or units being shipped from the proposed site to location_{i}*i**d*= the distance between the proposed site and location_{i}*i*

The distance *d _{i}* in this formula can be the travel distance, if that value is known, or can be determined from a map. It can also be computed using the following formula for the straight-line distance between two points, which is also the hypotenuse of a right triangle:

- where
- (
*x, y*) = coordinates of proposed site - (
*x*) = coordinates of existing facility_{i}, y_{i}

The load-distance technique is applied by computing a load-distance value for each potential facility location. The implication is that the location with the lowest value would result in the minimum transportation cost and thus would be preferable.

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Burger Doodle wants to evaluate three different sites it has identified for its new distribution center relative to the four suppliers identified in Example 9.2. The coordinates of the three sites under consideration are as follows:
First, the distances between the proposed sites (1, 2, and 3) and each existing facility (A, B, C, and D), are computed using the straight-line formula for Next, the formula for load distance is computed for each proposed site: Since site 3 has the lowest load-distance value, it would be assumed that this location would also minimize transportation costs. Notice that site 3 is very close to the location determined using the center-of-gravity method in Example 9.2. |

Location factor ratings can be done with Microsoft Excel. Exhibit 9.1 shows the Excel spreadsheet for Example 9.1. Notice that the active cell is E12 with the formula (shown on the formula bar at the top of the spreadsheet) for computing the weighted score for site 1.

POM for Windows also has a module for computing location factor ratings as well as the center-of-gravity technique. The solution screen for the application of the center-of-gravity technique in Example 9.2 is shown in Exhibit 9.2.

Excel OM also has modules for location factor ratings and the center-of-gravity technique. Exhibit 9.3 and Exhibit 9.4 show the solution screens for Examples 9.1 and 9.2, respectively.

**9-17.** The following businesses are considering locating in your community:

- A pizza delivery service
- A sporting good store
- A small brewery
- A plant making aluminum cans

**9-18.** Assume that you are going to open a fast-food restaurant in your community. Select three sites. Perform a location factor analysis for each and select the best site.

**9-19.** Suppose your college or university were planning to develop a new student center and athletic complex with a bookstore, theaters, meeting areas, pool, gymnasium, and weight and exercise rooms. Identify three potential sites on your campus for this facility and rank them according to location factors you can identify.