Lecture 2

Analytical Methods of Location Planning

The various analytical methods of location planning are affected by the way the distances are measured and the objective function is used.

Distance measure

The distance measure involved in a facility location problem is an important element in formulating an analytical model. There are two ways to measure the distance between two facilities.

1. Rectilinear Distance
2. Euclidean Distance

Rectilinear distance

When distance between two facilities is measured along path that is orthogonal to each other, then that distance is termed as rectilinear distance. Suppose two facilities are located at points represented by ( X 1 , Y 1 ) and at ( X 2 , Y 2 ) (figure 1), then the rectilinear distance between the facilities will be :

| X 1 - X 2 | + | Y 1 - Y 2 |

Figure 1: Rectilinear Distance

Euclidean distance

When distance is measured along straight-line path between the two facilities, then that distance is termed as Euclidean distance. Suppose two facilities are located at points represented by ( X 1 , Y 1 ) and at ( X 2 , Y 2 ) (figure 2), then the Euclidean distance between the facilities will be

{ ( X 1 - X 2 ) 2 + ( Y 1 - Y 2 ) 2 } 1 / 2

Figure 2: Euclidean Distance

The whole family of distance measure ( D K ) for the distance between two points ( X 1 , Y 1 ) and ( X 2 , Y 2 ) is defined by the following formula:

D K = { ( | X 1 - X 2 | ) K + ( |Y 1 - Y 2 |) K } 1 / K

when K =1 the above equation takes the form as:

D 1 = { ( | X 1 - X 2 | ) + ( |Y 1 - Y 2 | ) }

This equation gives the measure of rectilinear distance.

when K =2 the above equation takes the form as:

D 2 = { ( | X 1 - X 2 | ) 2 + ( |Y 1 - Y 2 |) 2 } 1 / 2

This gives the measure of Euclidean distance.

Techniques of conducting a facility location study

The following techniques may be used for deciding the best location of a facility.

• Factor rating method
• Transportation method

Factor rating method

The factor rating method is explained below by an example of deciding the best site out of the three proposed sites.

• To evaluate these alternative sites we identify five factors such as raw material, market, land cost, community attitude, and transportation facility.
• Provide the weights to each factor. Suppose we allocate 10 points to market and raw material, 8 points to land cost, 7 points to community attitude, and 6 points to transportation facilities.
• Rate each alternative for each factor on a scale of 10. Suppose, for factor raw material the A alternative gets 9 points, B alternative gets 10 points and C alternative gets 8 points.
• Tabulate all the above information as given in Table 1.
• Repeat the same procedure (step 3 and 4) for other factors.
• Multiply the weights of each factor with the rating of each alternative and record on the lower half of the rectangle under each alternative.
• Add the score of each alternative and record in front of Total.
• The best alternative is that alternative which has the maximum score. If two or more alternatives have the maximum score, then those alternatives should be selected and a separate evaluation should be made for those alternatives only.

Table 1: Factor Rating Chart

 Factors Weights Location A Location B Location C Raw material 10 9 90 10 100 8 80 Market 10 8 80 8 80 9 90 Land cost 8 7 56 8 64 8 64 Community attitude 7 10 70 9 63 10 70 Transportation facilities 6 8 48 7 42 10 60 Total 347 349 364*

* Best Alternative is Location C

Transportation method:

The transportation problem is concerned with the distribution of goods or services from various sources to various destinations. The transportation problem can be formulated as a linear programming problem. The total transportation cost at various locations can be calculated and the location with the least total transportation cost can be chosen (Turner, W.C, et al., Introduction to Industrial and System Engineering, Second Edition, Prentice –Hall, Inc. New Jersey 1987).

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