Location Planning and Analysis
DefinitionDefinition of Facility Planningof Facility Planning
Facility Planning determines how an activity’s tangible fixed assets
best support achieving the activity’s objectives.
Examples:
a. In manufacturing, the objective is to support production.
b. In an airport, the objective is to support the passenger airplane
interface.
c. In a hospital, the objective is to provide medical care to patients.
Hierarchy of Facility PlanningHierarchy of Facility Planning
Location: is the placement of a facility with respect to customers, suppliers, and other facilities with which it interfaces.
Structure: consists of the building and services (e.g., gas, water, power, heat, light, air, sewage).
Layout: consists of all equipment, machinery, and furnishings within the structure.
Handling System: consists of the mechanism by which all interactions required by the layout are satisfied (e.g., materials, personnel, information, and equipment handling systems).
Facility Planning
Structural Design
Facility Location
Facility Design
Layout Design
Handling System Design
Need for Location DecisionsNeed for Location Decisions
Marketing Strategy
Cost of Doing Business
Growth
Depletion of Resources
Making Location DecisionsMaking Location Decisions
Decide on the criteria Identify the important factors Develop location alternatives Evaluate the alternatives Make selection
Location Decision FactorsLocation Decision Factors
Regional Factors
Site-related Factors
Multiple Plant Strategies
Community Considerations
Evaluating LocationsEvaluating Locations
Transportation Model Decision based on movement costs of raw
materials or finished goods Factor Rating
Decision based on quantitative and qualitative inputs
Center of Gravity Method Decision based on minimum distribution costs
Factor RatingFactor Rating
General approach to evaluating locations that includes quantitative and qualitative inputs.
ExampleExample 1 1
A photo-processing company intends to open a new branch store. The following table contains information on two potential locations. Which is the better alternative?
Alternative 2 is better because it has the higher composite score.
Example 2Example 2
Using the following factor ratings, determine which location alternative should be chosen on the basis of maximum composite score, A, B, or C.
Example 2Example 2
Solution:
Therefore, Location A is better.
The Center of Gravity MethodThe Center of Gravity Method
The method use to determine the location of a facility that will minimize shipping costs or travel time to various destinations.
If the quantities to be shipped in every If the quantities to be shipped in every location are equallocation are equal
where:
n = Number of destinations.
xi = x coordinate of destination i.
yi = y coordinate of destination i.
n
x
xi
n
y
yi
When the number of units to be When the number of units to be shipped is not the same for all shipped is not the same for all
destinationsdestinations
i
ii
Q
Qx
x
i
ii
Q
Qy
y
whereQi = Quantity to be shipped to destination ixi = x coordinate of destination iyi = y coordinate of destination i
ExampleExample 1 1Destination x, y
D1 2, 2
D2 3, 5
D3 5, 4
D4 8, 5
18 16
5.44
18
n
x
xi
44
16
n
y
yi
Hence, the center of gravity is at (4.5,4).
Example 2Example 2Destination x, y Weekly Quantity
D1 2, 2 800
D2 3, 5 900
D3 5, 4 200
D4 8, 5 100
2000
3) to(round05.32000
6100
2000
)100(8)200(5)900(3)800(2
i
ii
Q
Qx
x
70.32000
7400
2000
)100(5)200(4)900(5)800(2
i
ii
Q
Qy
y
Hence, the center of gravity are approximately (3,3.7). This would place it south of destination D2, which has coordinates of (3,5).
Example 3Example 3
Destination x,yCoordinates
Weekly Quantity
D1 3,5 20
D2 6,8 10
D3 2,7 15
D4 4,5 15
60
5.360
210
60
)15(4)15(2)10(6)20(3
i
ii
Q
Qx
x
0.660
360
60
)15(5)15(7)10(8)20(5
i
ii
Q
Qy
y
Hence, the center of gravity has the coordinates x = 3.5 and y = 6.0
The Transportation Model
Requirements for Transportation Requirements for Transportation ModelModel
List of origins and each one’s capacity
List of destinations and each one’s demand
Unit cost of shipping
Transportation Model AssumptionsTransportation Model Assumptions
1. Items to be shipped are homogeneous
2. Shipping cost per unit is the same
3. Only one route between origin and destination
The Transportation ProblemThe Transportation Problem
D(demand)
D(demand)
D(demand)
D(demand)
S(supply)
S(supply)
S(supply)
m- number of sources n- number of destinations ai- supply at source I
bj – demand at destination j
cij – cost of transportation per unit from source i to destination j
Xij – number of units to be transported from the source i to destination j
DESTINATION j
cc1111 cc1212 cc1j1j cc1n1n
cci1i1 cci2i2 ccijij ccinin
ccm1m1 ccm2m2 ccmnmn
SOURCE i
12
i
m
1 2 j n
Demand b1 b2 bj bn
Supply a1
a2
ai
am
Transportation problem: Transportation problem: represented as an LP modelrepresented as an LP model
njandmiforX
njbX
miaXtosubject
XcZMinimize
ij
j
m
iij
i
n
jij
ij
m
i
n
jij
,..1,...10
,.....,2,1
,....,2,1
:
1
1
1 1
Summary of ProcedureSummary of Procedure
Make certain that supply and demand are equal
Develop an initial solution using intuitive, low-cost approach
Check that completed cells = m+n-1
Evaluate each empty cell
Repeat until all cells are zero or positive
Determination of Starting Basic Feasible Determination of Starting Basic Feasible SolutionSolution
•NORTH-WEST Corner MethodNORTH-WEST Corner Method - - is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North – West corner.
•LEAST COST Method - LEAST COST Method - This method takes consideration the lowest cost and therefore takes the less time to solve the problem.
•Vogel’s Approximation Method (VAM) - Vogel’s Approximation Method (VAM) - This method also takes costs into account in allocation.
VAM usually produces an optimal or near- optimal starting solution. One study found that VAM yields an optimum solution in 80 percent of the sample problems tested.
The Amulya Milk Company has three plants located throughout a state with production capacity 5000, 2000 and 3000 gallons. Each day the firm must furnish its four retail shops with at least 3000, 3000 , 2000, and 2000 gallons respectively.
Example 1Example 1
33 77 66 44 55
22 44 33 22 22
44 33 88 55 33
33 33 22 22
Destination 1 2 3 4 Supply Row Penalties
Source
1
2
3
Demand
Total shipping cost = 32
Column Penalties
1
0
1
1 1 3 2
2
0
1
-
1
1 4 - 1
3
0
3 0 0 2
TOFROM
A B C SUPPLY
W 9 8 525
X 6 8 435
Y 7 6 940
DEMAND 30 25 45 100100
ROW/COLUMN SEC-LOWEST COST ━ LOWEST COST = OPPORT-CST
ROW W 8 5 3 LARGEST
ROW X 6 4 2
ROW Y 7 6 1
COLUMN A 7 6 1
COLUMN B 8 6 2
COLUMN C 5 4 1
25
20
Example 2Example 2
VAM: VOGEL APPROXIMATION METHOD
TOFROM
A B C SUPPLY
W 9 8 525
X 6 8 435
Y 7 6 940
DEMAND 30 25 45 100100
ROW/COLUMN SEC-LOWEST COST ━ LOWEST COST = OPPORT-CST
ROW X 6 4 2
ROW Y 7 6 1
COLUMN A 7 6 1
COLUMN B 8 6 2
COLUMN C 9 4 5 LARGEST
25
20
20
15
VAM: VOGEL APPROXIMATION METHOD
TOFROM
A B C SUPPLY
W 9 8 525
X 6 8 435
Y 7 6 940
DEMAND 30 25 45 100100
ROW/COLUMN SEC-LOWEST COST ━ LOWEST COST = OPPORT-CST
ROW X 8 6 2 LARGEST
ROW Y 7 6 1
COLUMN A 7 6 1
COLUMN B 8 6 2 LARGEST
25
20
25
15
15
20
TOFROM
A B C SUPPLY
W WA 9 WB 8 WC 525
X XA 6 XB 8 XC 435
Y YA 7 YB 6 YC 940
DEMAND 30 25 45 100100
25
20
2515
15
Q X COST / UNIT = TC ($)
WC 25 5 125
XA 15 6 90
XC 20 4 80
YA 15 7 105
YB 25 6 150
TOTAL TRANSPORTATION COST 540
15
15
20