2. Chapter # 10 Quantitative Facilities Planning Models
Presented by:
Group 10
Inamullah IE-55
Arif Ali IE-56
Muhammad Badar 11-IE-65

3. Overview Facility Location Model:
Rectilinear Distance Facility Location:
Single Facility Rectilinear Minisum:
Euclidean Facility Location:
Single Facility Squared Euclidean Minisum:

4. Facility Location Model
The ”facility location Model”, also known as location analysis, is a branch of operations research and computational geometry concerned with the “optimal placement of facilities” to minimize transportation costs.
The techniques also apply to cluster analysis

5. Facility Location Problems can be classified:
Number of new facilities to be located
The solution space
The size of facilities
The criteria used to determine the location
The distance measured

6. Facility Location Model
Single-
Multi-
Minisum
Minimax
Rectilinear
Euclidean
Tchebyshev

7. Analytical Methods of Location Planning
The various analytical methods of location planning are affected by the way the “distances are measured”.
Distance measure:
A mathematical model used to evaluate flexible-flow layouts based on proximity factors.
There are two ways to measure the distance between two facilities.
Rectilinear Distance
Euclidean Distance

8. Rectilinear Distance Facility Location
When distance between two facilities is measured along path that is “orthogonal (90 degree)” to each other, then that distance is termed as rectilinear distance. Suppose two facilities are located at points represented by (X1,Y1) and at (X2,Y2) then the rectilinear distance between the facilities will be :
| X 1 - X 2 | + | Y 1 - Y 2 |

9. Applications of Rectilinear Distance
Rectilinear Distance facility location problem because it represents a situation commonly encountered in manufacturing and distribution settings.
It occurs in many cities, due to the layout streets.
An industrial example is a material transporter moving along Rectilinear aisles in a factory

10. Single Facility Rectilinear Minisum
The annual cost of travel B/W the new facility and existing facility is assumed to be proportional to the distance B/W the points X and Pi, with wi denoting the constant of proportionality.
The objective is to;

13. Solution:

16. Euclidean Distance Facility Location:
“Shortest distance between two points”
When distance is measured “along straight-line path” between the two facilities, then that distance is termed as “Euclidean distance”.
{( X 1 - X 2 )^2 + ( Y1 - Y2 )^2}1/2

17. Applications of Euclidean Distance Facility location:
There are situations in which Euclidean distance is an accurate representation of the location problem being studied
For examples:
Locating cell phone towers to provide coverage,
Determine where to locate sniper (shoot bullets in a straight line) Can be modeled accurately using “Euclidean Distances”.
In industrial setting “Conveyors” and “pneumatic tubes” often follow straight line paths (Euclidean distance).

18. Single Facility Squared Euclidean Minisum
Squared Euclidean Minisum often referred to as the “gravity problem”.
In this the “COST OF TRAVEL” between a single new facility and multiple existing facilities to be proportional to the square of the Euclidean distance between the facilities
The optimum solution for the gravity problem is “centroid location”

19. The gravity (Euclidean) problem can be formulated as:
Min. f(x , y) = Wi[ (x-a)2 +(y-b)2]
Taking partial derivate w.r.t X & Y, & setting them equal to zero
where,
X* = x, y = coordinates of the new facility
xi, yi = coordinates of existing facility
Wi = annual weight shipped from facility i
Y* =  
Xi *Wi  Wi 
Yi *Wi  Wi

21. Solution:
Using this formula

22. THANK YOU!!