1. Facility Location I Chapter 10
Dr. Mohammed Othman

2. Facility Location
Factors that influence the facility location decision:
Transportation (availability, cost)
Labor (availability, cost, skills)
Materials (availability, cost, quality)
Equipment (availability, cost)
Land (availability, suitability, cost)
Market (size, potential needs)
Energy (availability, cost)
Water (availability, quality, cost)
Waste (disposal, treatment)
Financial institutions (availability, strength)
Government (stability, taxes, import and export restrictions)
Existing plants (proximity)
Competitors (size, strength and attitude in that region)
Geographical and weather conditions

3. Facility location problems
Can be classified based on the number of new facilities into:
Single –facility location problems
Multi-facility location problems
The solution space can be:
Continuous (choice of ANY site in the space)
Discrete (choice of specific locations)

4. Method of Factor Rating
Procedure:
Identification of the most important factors in evaluating alternative sites for the new facility.
Assignment of a weight for each factor
Evaluation of the alternative sites in terms of the selected factors (score between 0 and 100)
Calculation of weighted score for each location
The most weighted alternative is selected as the best alternative.

5. Example
Three alternative sites are being considered for a new facility. After evaluating the firm’s needs, the managers have narrowed the list of important selection criteria down into three major factors. Below are shown the weights which were assigned to the criteria and the evaluation of each site. Which site should be selected?

6. Example …continue
Calculate weighted scores: (site score)x(factor weight)
From these results, the largest total weight is for Site A. It appears to be the best location.

7. Example …continue What happens if we change the factor weights?
Let’s use the following factor weights: skilled labor ; raw materials ; and market
Then the following results are obtained:
In this case, Site C appears to be the best choice with largest weight score.
Factor rating method is very sensitive to the weights assigned to each factor.

8. Facility location problem Cost-Profit-Volume Analysis
Break-Even Analysis
If the fixed and variable costs for each site are known we can identify the location with the lowest cost.

9. Variable cost (per unit)
Example
A company is considering three alternative sites for its new production facility. The annual production volume is 250,000 units. Which site should be selected based on the cost information below?
Site
Fixed cost (per year)
Variable cost (per unit) A
10,000,000
250 B
25,000,000
150 C
60,000,000 50

10. Example …Continue
Total production cost = (fixed cost) + (variable unit cost) x (annual production volume)
Site A:
Prod. Cost = 10,000, x 250,000 = 72,000,000
Site B:
Prod. Cost = 25,000, x 250,000 = 62,000,000
Site C:
Prod. Cost = 60,000, x 250,000 = 72,000,000
At a production volume of 250,000 units, site B has the lowest cost
What about other production volumes?

11. Example … continue If production volume < 150,000 units
=>choose site A.
If 150,000 < production volume < 350,000 units
=> choose site B.
If production volume > 350,000 units
=>choose site C.
Annual production cost changes with different production volumes.

12. Continuous facility location problems
For the new facility we can choose ANY site in the space
For the existing related facilities (suppliers, customers, etc.) we know the coordinates (x,y) and the flows (cost) between them
The sole consideration is transportation cost
Facility location models have numerous applications
New airport, new hospital, new school
Addition of a new workstation
Warehouse location
Bathroom location in a facility etc.

13. Continuous facility location problems Distance measures

14. Rectilinear Facility Location Problems

15. Example
Determine the new location of a warehouse in Nablus area which provides materials to 5 different companies
Location of these companies (a, b) and the material movement between the new warehouse and the existing facilities (w) are provided:
Where should the new warehouse be located? a b W 1 5 2 6 8 4

16. Rectilinear Facility Location Problems
Various objectives can be used
Minisum location problem
Minimizing the sum of weighted distance between the new facility and the other existing facilities
Minimax location problem
Minimizing the maximum distance between the new facility and any existing facility

17. Single-facility minisum location problem

18. Single-facility minisum location problem
Procedure
1.Find x-coordinate:
Order the facilities based on the ascending order of their x-coordinates
Calculate partial sum of weights
Find the facility for which the partial sum first equals or exceeds one-half the total weight
The x-coordinate of the new facility will be the same as the x-coordinate of this facility
2.Find y-coordinate
Repeat the same for y-coordinate

19. Single-facility minisum location problem Alternate sites

20. Single-facility minisum location problem
• A new machine should be placed in the maintenance department. There are five machines that have material handling relationship with the new machine. Their current coordinates are M1=(1,1), M2=(5,2), M3=(2,8), M4=(4,4) and M5=(8,6). The cost per unit distance traveled between the machines is the same, but the number of trips per day between the new machine and each existing machine are 5,6,2,4 and 8.
Find a location for the new machine in the maintenance department.
Calculate total weighted distance for the new location.
If the machine cannot be placed in the optimal location, find the second best alternative sites out of (5,6), (4,2) and (8,4) .

21. Example … continue

27. Contour Lines
A contour line is a line of constant cost in the plane. Thus, locating the new facility at any point on a given contour line results in the same total cost.
Contour lines indicate at a glance the cost penalty associated with the choice of a non-optimum location.

28. Single-facility minisum location problem Iso-cost contour lines
Procedure:
1.Plot the locations of existing facilities
2.Draw vertical and horizontal lines through each existing facility
3.Sum the weights for all existing facilities having the same x-coordinate and enter the total at the bottom of the vertical lines. Do the same for y coordinates
4.Calculate “net pull” for each candidate x- coordinate. (pull to the right is positive and pull to the left is negative). Do the same for y coordinates
5.Determine the slope for each grid region enclosed by the candidate coordinates
The slope equals the negative of the ratio of the net horizontal pull and the net vertical pull
6.Construct an iso-cost contour line from any candidate coordinate point by following the appropriate slope in each grid.