Facility Location Decisions: Alexander Hamilton, 1791
Facility Location Decisions: Alexander Hamilton, 1791
Facility Location Decisions: Alexander Hamilton, 1791
Chapter 13
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13-1
Facility Location in Location
Strategy
Inventory Strategy
• Forecasting Transport Strategy
• Inventory decisions • Transport fundamentals
CONTROLLING
ORGANIZING
• Purchasing and supply • Transport decisions
PLANNING
scheduling decisions Customer
• Storage fundamentals service goals
• Storage decisions • The product
• Logistics service
• Ord . proc. & info. sys.
Location Strategy
Locationdecisions
••Location decisions
• The network planning process
X
VR X i i i i
,Y
i
VR Y i i i
VR i i i VR i i i
where
Vi = volume flowing from (to) point I
Ri = transportation rate to ship Vi from (to) point i
Xi,Yi = coordinate points for point i
X, Y
= coordinate points for facility to be located
X = 7,901/1,260 = 6.27
Y = 5,538/1,260 = 4.40
TC i Vi Ri K ( X i X ) 2 (Yi Y )2
X
n V R X /d
i i i i i n
,Y
V R Y /d
i i i i i
V R /d
i i i i V R /d
i i i i
where
n n
di (Xi X )2 (Yi Y )2
Total cost
Cost
Warehouse
fixed
Inventory carrying
and warehousing
Production/purchase
and order processing
Inbound and
outbound
transportation
0
0
Number of warehouses 13-20
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Multiple COG
Formulated as basic COG model
Can search for the best locations for a selected number of
sites.
Fixed costs and inventory consolidation effects are handled
outside of the model.
A multiple COG procedure
Rank demand points from highest to lowest volume
Use the M largest as initial facility locations and assign
remaining demand centers to these locations
Compute the COG of the M locations
Reassign all demand centers to the M COGs on the basis
of proximity
Recompute the COGs and repeat the demand center
assignments, stopping this iterative process when there is
no further change in the assignments or COGs 13-21
CR (2004) Prentice Hall, Inc.
Examples of Practical COG
Model Use
Location of truck maintenance terminals
t.
$0/cwt. 50,000 cwt.
/cw
(Cont’d)
$2
$5
Plant P1 Warehouse W1 $3
/cw
/cw
Production = $4/cwt. t.
t .
Capacity = .t
60,000 cwt. /cw
$1 Customer C2
Handling = $1/cwt.
t.
100,000 cwt.
/cw
$2
$4
$5
/cw
/cw
t. t
cw Warehouse W2
$2/
t.
Plant P2
Fixed = $100,000
A Multiple
Production = $4/cwt.
Capacity =
Unrestricted
Capacity = 110,000 cwt.
Fixed = $500,000
Customer C3
50,000 cwt.
Product
Capacity =
Unrestricted
Network
Product 2
Handling = $2/cwt.
$3
/cw
t
Customer C1 Design
t.
$0/cwt.
Problem
20,000 cwt.
cw
$3/
$5
Plant P1 Warehouse W1 $2
/cw
cw/
Production = $3/cwt. t.
t .
Capacity = t.
50,000 cwt. /cw
$2 Customer C2
Handling = $1/cwt.
t.
30,000 cwt.
/cw
$3
$4
$4
/cw
/cw
t. t
cw
$2 / Warehouse W2
t.
Plant P2
Production = $2/cwt.
Capacity = Customer C3
Unrestricted 60,000 cwt.
13-25
Mixed Integer programming
13-26
13-27
Guided Linear Programming
Searches for the best locations.
A typical problem is shown in the next figure and can be configured as
a transportation problem of linear programming in terms of its variable
costs.
c wt.
$2/
$3
$5
Plant P1 Warehouse W1 /c
/cw
wt
Production = $4/cwt. .
t.
.
Capacity =
/c wt
60,000 cwt. $1 Customer C2
t.
100,000 cwt.
cw
$4/
$5/
$2
/c
cwt
t. Warehouse W2 wt
/ c w
.
$2
Handling = $1/cwt.
Capacity =
Plant P2
Unrestricted
Production = $4/cwt. Customer C3
Fixed = $400,000
Capacity = 50,000 cwt.
Unrestricted Inventory carrying cost =
100(Throughput)0.7
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13-29
Guided Linear Programming (Cont’d)
Example
Use data from the network figure.
Allocate the fixed costs. Assume initially that each warehouse handles the
entire volume. Hence,
Warehouse 1
100,000/200,000 = $0.50/cwt.
Warehouse 2
400,000/200,000 = $2.00/cwt.
Allocate inventory carrying costs. Assume that throughput for each product is
equally divided between warehouses.
Total customer demand
Each warehouse
0.7
100{[200,000/2) ]/(200,000/2)} = $3.2
No. of whses
Build the cost matrix for the transportation problem of LP. Note its special
structure.
CR (2004) Prentice Hall, Inc. 13-38
Matrix of Cell Costs and Solution Values for the First
Iteration in the Example Problem
Warehouses Customers
Plant &
warehouse
W1 W2 C1 C2 C3 capacities
a b
4 9 99 99 99
P1 60,000 60,000
Plants
8 6 99 99 99 c
P2 140,000 999,999
d
0 99 9.7 8.7 10.7
W1 60,000 60,000
Warehouses b e
99 0 8.2 7.2 8.2 c
W2 50,000 40,000 50,000 999,999
Warehouse
capacity &
customer
c
demand 60,000 999,999 50,000 100,000 50,000
a
Production plus inbound transport rates, that is, 4 + 0 = 4.
b
Used to represent an infinitely high cost.
c
Used to represent unlimited capacity.
d
Inventory carrying, warehousing, outbound transportation, and fixed rates, that is,
3.2 + 2 + 4 + 0.5 = 9.7.
e
3.2 + 1 + 2 + 2.0 = 8.2. 13-39
Guided Linear Programming (Cont’d)
Solve as an LP problem, transportation type. Note the results in the
solution matrix.
Recompute the per-unit fixed and inventory costs from the first solution
results as follows.
C1 C2 C3
a
W1 11.36 10.36 12.36
b
W2 8.72 7.72 8.72
a
2 + 4 + 1.67 + 3.69 = 11.36
b
1 + 2 + 3.57 + 2.86 = 9.43
CR (2004) Prentice Hall, Inc. 13-40
Guided Linear Programming (Cont’d)
The revised solution shows that all volume should be produced at plant 2
and all customers served from warehouse 2.
Once the throughputs are known, they are used to compute the cost
summaries shown in the solution table. Actual costs are used, not the
cell costs of the LP problem. The solution is:
Warehouse 1 Warehouse 2
Cost type 0 cwt. 200,000 cwt.
Production $0 200,0004 = $800,000
Inbound transportation 0 200,0002 = 400,000
Outbound transportation 50,0002 = 100,000
100,0001 = 100,000
0 50,0002 = 100,000
Fixed 0 400,000
0.7
Inventory carrying 0 100(200,000) = 513,714
Handling 0 200,0001 = 200,000
Subtotal $0 $2,613,714
Total $2,613,714
The iterative process is repeated until there are no changes. The answer
is to have only warehouse 2 open. 13-33
Location by Simulation
•Can include more variables than typical algorithmic
methods
Shycon/Maffei Simulation
Read in
all customer
order data
and locations
Volume
Preprocessing
shipment
program
orders
Orders filled
through ware-
housing system
Read in Read in
Test warehouse
freight rates,
warehousing costs, program location
taxes, etc. configuration
to be evaluated
Cost of warehouse
location configuration
Is another Yes
run desired?
No
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13-35
Stop
Commercial Models for Location
Features
•Includes most relevant location costs
•Constrains to specified capacity and customer
service levels
•Replicates the cost of specified designs
•Handles multiple locations over multiple echelons
•Handles multiple product categories
•Searches for the best network design
CR (2004) Prentice Hall, Inc. 13-36
Commercial Models (Cont’d)
Plants/ Level 2 Level 1 Customers/
vendors/ warehouses warehouses demand
ports/ or stocking or stocking centers/
sources points points sinks
Supply
Demand
Inventory &
warehousing Inventory &
costs warehousing
Production/
costs
purchase costs Transportation costs
CR (2004) Prentice Hall, Inc. 13-45
Commercial Models (Cont’d)
Retail Location
Contrasts with plant and warehouse location.
- Revenue rather than cost driven
- Factors other than costs such as parking, nearness to competitive
outlets, and nearness to customers are dominant
Methods
Weighted checklist
- Good where many subjective factors are involved
- Quantifies the comparison among alternate locations
CR (2004) Prentice Hall, Inc. 13-39
A Hypothetical Weighted Factor Checklist for a
Retail Location Example
(1) (2) (3)=(1)(2)
Factor
Weight Factor Score Weighted
a b
(1 to 10) Location Factors (1 to 10) Score
8 Proximity to competing stores 5 40
5 Space rent/lease
considerations 3 15
8 Parking space 10 80
7 Proximity to complementary
stores 8 56
6 Modernity of store space 9 54
9 Customer accessibility 8 72
3 Local taxes 2 6
3 Community service 4 12
8 Proximity to major
transportation arteries 7 56
Total index 391
a
Weights approaching 10 indicate great importance.
b
Scores approaching 10 refer to a favored location status.
CR (2004) Prentice Hall, Inc. 13-48