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2.
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.
3.
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
4.
Need for Location DecisionsNeed for Location Decisions
• Marketing Strategy
• Cost of Doing Business
• Growth
• Depletion of Resources
5.
Making Location DecisionsMaking Location Decisions
• Decide on the criteria
• Identify the important factors
• Develop location alternatives
• Evaluate the alternatives
• Make selection
7.
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
8.
Factor RatingFactor Rating
General approach to evaluating locations that
includes quantitative and qualitative inputs.
9.
ExampleExample 11
A photoprocessing 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.
10.
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.
11.
Example 2Example 2
Solution:
Therefore, Location A is better.
12.
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.
13.
If the quantities to be shipped in everyIf 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
x
i∑
=
n
y
y
i∑
=
14.
When the number of units to be shippedWhen the number of units to be shipped
is not the same for all destinationsis not the same for all destinations
∑
∑
=
i
ii
Q
Qx
x
∑
∑
=
i
ii
Q
Qy
y
where
Qi = Quantity to be shipped to destination i
xi = x coordinate of destination i
yi = y coordinate of destination i
15.
ExampleExample 11
Destination x, y
D1 2, 2
D2 3, 5
D3 5, 4
D4 8, 5
18 16
5.4
4
18
===
∑
n
x
x
i
4
4
16
===
∑
n
y
y
i
Hence, the center of gravity is at (4.5,4).
16.
Example 2Example 2
Destination x, y Weekly Quantity
D1 2, 2 800
D2 3, 5 900
D3 5, 4 200
D4 8, 5 100
2000
3)to(round05.3
2000
6100
2000
)100(8)200(5)900(3)800(2
==
+++
==
∑
∑
i
ii
Q
Qx
x
70.3
2000
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).
17.
Example 3Example 3
Destination x,y
Coordinates
Weekly
Quantity
D1 3,5 20
D2 6,8 10
D3 2,7 15
D4 4,5 15
60
5.3
60
210
60
)15(4)15(2)10(6)20(3
=≡
+++
≡=
∑
∑
i
ii
Q
Qx
x
0.6
60
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
19.
Requirements for Transportation ModelRequirements for Transportation Model
• List of origins and each one’s capacity
• List of destinations and each one’s demand
• Unit cost of shipping
20.
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
21.
The Transportation ProblemThe Transportation Problem
D
(demand)
D
(demand)
D
(demand)
D
(demand)
S
(supply)
S
(supply)
S
(supply)
22.
• 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
23.
DESTINATION j
cc1111 cc1212 cc1j1j cc1n1n
cci1i1 cci2i2 ccijij ccinin
ccm1m1 ccm2m2 ccmnmn
S
O
U
R
C
E
i
1
2
i
m
1 2 j n
Demand b1 b2 bj bn
Supply
a1
a2
ai
am
24.
Transportation problem:Transportation problem:
represented as an LP modelrepresented as an LP model
njandmiforX
njbX
miaXtosubject
XcZMinimize
ij
j
m
i
ij
i
n
j
ij
ij
m
i
n
j
ij
,..1,...10
,.....,2,1
,....,2,1
:
1
1
1 1
==≥
=≥
=≤
=
∑
∑
∑∑
=
=
= =
25.
Summary of ProcedureSummary of Procedure
• Make certain that supply and demand are
equal
• Develop an initial solution using intuitive,
lowcost approach
• Check that completed cells = m+n1
• Evaluate each empty cell
• Repeat until all cells are zero or positive
26.
Determination of Starting Basic Feasible SolutionDetermination of Starting Basic Feasible Solution
•NORTHWEST Corner MethodNORTHWEST 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.
27.
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
28.
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
S
o
u
r
c
e
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
29.
TO
FROM
A B C SUPPLY
W 9 8 5
25
X 6 8 4
35
Y 7 6 9
40
DEMAND 30 25 45 100
100
ROW/COLUMN SECLOWEST COST ━ LOWEST COST = OPPORTCST
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
30.
VAM: VOGEL APPROXIMATION METHOD
TO
FROM
A B C SUPPLY
W 9 8 5
25
X 6 8 4
35
Y 7 6 9
40
DEMAND 30 25 45 100
100
ROW/COLUMN SECLOWEST COST ━ LOWEST COST = OPPORTCST
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
31.
VAM: VOGEL APPROXIMATION METHOD
TO
FROM
A B C SUPPLY
W 9 8 5
25
X 6 8 4
35
Y 7 6 9
40
DEMAND 30 25 45 100
100
ROW/COLUMN SECLOWEST COST ━ LOWEST COST = OPPORTCST
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
32.
TO
FROM
A B C SUPPLY
W WA 9 WB 8 WC 5
25
X XA 6 XB 8 XC 4
35
Y YA 7 YB 6 YC 9
40
DEMAND 30 25 45 100
100
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
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