View
230
Download
2
Category
Preview:
Citation preview
13-1
Facility Location Decisions
Chapter 13CR (2004) Prentice Hall, Inc.
13-2CR (2004) Prentice Hall, Inc.
Facility Location in Location Strategy
PL
AN
NIN
G
OR
GA
NIZ
ING
CO
NT
RO
LL
ING
Transport Strategy• Transport fundamentals• Transport decisions
Customer service goals
• The product• Logistics service• Ord . proc. & info. sys.
Inventory Strategy• Forecasting• Inventory decisions• Purchasing and supply
scheduling decisions• Storage fundamentals• Storage decisions
Location Strategy• Location decisions• The network planning process
PL
AN
NIN
G
OR
GA
NIZ
ING
CO
NT
RO
LL
ING
Transport Strategy• Transport fundamentals• Transport decisions
Customer service goals
• The product• Logistics service• Ord . proc. & info. sys.
Inventory Strategy• Forecasting• Inventory decisions• Purchasing and supply
scheduling decisions• Storage fundamentals• Storage decisions
Location Strategy•Location decisions• The network planning process
13-3CR (2004) Prentice Hall, Inc.
Location OverviewWhat's located? Sourcing points
Plants Vendors Ports
Intermediate points Warehouses Terminals Public facilities (fire, police, and ambulance
stations) Service centers
Sink points Retail outlets Customers/Users
13-4CR (2004) Prentice Hall, Inc.
Location Overview (Cont’d)
Key Questions
How many facilities should there be?
Where should they be located?
What size should they be?
Why Location is Important Gives structure to the network Significantly affects inventory and
transportation costs Impacts on the level of customer service to
be achieved
13-5CR (2004) Prentice Hall, Inc.
When to Analyze Location
Changing service requirements
Partnerships
Shifting locations (customer/supplier)
Changing corporate ownership
Cost pressure
Global markets
13-6CR (2004) Prentice Hall, Inc.
Nature of Location Analysis
Manufacturing (plants & warehouses)
Decisions are driven by economics. Relevant costs such as transportation, inventory carrying, labor, and taxes are traded off against each other to find good locations.
Retail
Decisions are driven by revenue. Traffic flow and resulting revenue are primary location factors, cost is considered after revenue.
Service
Decisions are driven by service factors. Response time, accessibility, and availability are key dimensions for locating in the service industry.
13-7CR (2004) Prentice Hall, Inc.
Methods of Solution
Single warehouse location
– Graphic
– Grid, or center-of-gravity, approach
Multiple warehouse location
– Simulation
– Optimization
– Heuristics
Location Overview (Cont’d)
13-8CR (2004) Prentice Hall, Inc.
-Finding solution can be challenging
-But with the advent of fast PCs, it is more widely used these days
-Model formulation
Optimization Method
13-9CR (2004) Prentice Hall, Inc.
Method appraisal A continuous location method Locates on the basis of transportation costs alone
The COG method involves Determining the volumes by source and destination
point Determining the transportation costs based on
$/unit/mi. Overlaying a grid to determine the coordinates of
source and/or destination points Finding the weighted center of gravity for the graph
COG Method
13-10CR (2004) Prentice Hall, Inc.
COG Method (Cont’d)
i ii
i iii
i ii
i iii
RV
YRVY,
RV
XRVX
where
Vi = volume flowing from (to) point I
Ri = transportation rate to ship Vi from (to) point i
Xi,Yi = coordinate points for point i
= coordinate points for facility to be locatedY,X
13-11CR (2004) Prentice Hall, Inc.
COG Method (Cont’d)Example Suppose a regional medical warehouse is to be established to serve several Veterans Administration hospitals throughout the country. The supplies originate at S1 and S2 and are destined for hospitals at H1 through H4. The relative locations are shown on the map grid. Other data are: Note rate is a
per mile costPointi
Prod-ucts Location
Annualvolume,
cwt.
Rate,$/cwt/
mi. Xi Yi1 S1 A Seattle 8,000 0.02 0.6 7.32 S2 B Atlanta 10,000 0.02 8.6 3.03 H1 A & B Los
Angeles5,000 0.05 2.0 3.0
4 H2 A & B Dallas 3,000 0.05 5.5 2.45 H3 A & B Chicago 4,000 0.05 7.9 5.56 H4 A & B New York 6,000 0.05 10.6 5.2
13-12CR (2004) Prentice Hall, Inc.
COG Method (Cont’d)Map scaling factor, K
13-13CR (2004) Prentice Hall, Inc.
COG Method (Cont’d)
Solve the COG equations in table form
i Xi Yi Vi Ri ViRi ViRiXi ViRiYi1 0.6 7.3 8,000 0.02 160 96 1,1682 8.6 3.0 10,000 0.02 200 1,720 6003 2.0 3.0 5,000 0.05 250 500 7504 5.5 2.4 3,000 0.05 150 825 3605 7.9 5.5 4,000 0.05 200 1,580 1,1006 10.6 5.2 6,000 0.05 300 3,180 1,560
1,260 7,901 5,538
13-14
COG Method (Cont’d)Now,
X = 7,901/1,260 = 6.27
Y = 5,538/1,260 = 4.40
This is approximately Columbia, MO.
The total cost for this location is found by:
where K is the map scaling factor to convertcoordinates into miles.
i iiii YYXXKRVTC 22 )()(
CR (2004) Prentice Hall, Inc.
13-15CR (2004) Prentice Hall, Inc.
COGCOG Method (Cont’d)
13-16CR (2004) Prentice Hall, Inc.
COG Method (Cont’d)
2,360,882Total
660,4920.056,0005.210.66
196,6440.054,0005.57.95
160,7330.053,0002.45.54
561,7060.055,0003.02.03
271,8250.0210,0003.08.62
509,4820.028,0007.30.61
TCRiViYiXiiCalculate total cost at COG
221
4.40)(7.36.27)(0.6)(500)8,000(0.02TC
13-17CR (2004) Prentice Hall, Inc.
Note The center-of-gravity method does not necessarilygive optimal answers, but will give good answers if there area large numbers of points in the problem (>30) and thevolume for any one point is not a high proportion of the totalvolume. However, optimal locations can be found by theexact center of gravity method.
i iii
i iiiin
i iii
i iiiin
/dRV
/dYRVY,
/dRV
/dXRVX
where
22 )Y(Y)X(Xdn
i
n
ii
and n is the iteration number.
COG Method (Cont’d)
13-18CR (2004) Prentice Hall, Inc.
Solution procedure for exact COG
COG Method (Cont’d)
1) Solve for COG2) Using find di
3) Re-solve for using exact formulation4) Use revised to find revised di
5) Repeat steps 3 through 5 until there is no change in
6) Calculate total costs using final coordinates
Y,XY,X
Y,X
Y,X
13-19CR (2004) Prentice Hall, Inc.
A more complex problem that most firms have. It involves trading off the following costs:
Transportation inbound to and outbound from the facilities Storage and handling costs Inventory carrying costs Production/purchase costs Facility fixed costs
Subject to: Customer service constraints Facility capacity restrictions
Mathematical methods are popular for this type of problemthat:
Search for the best combination of facilities to minimizecosts
Do so within a reasonable computational time Do not require enormous amounts of data for the analysis
Multiple Location Methods
13-20
Multiple COGFormulated as basic COG modelCan 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 procedureRank demand points from highest to lowest volumeUse the M largest as initial facility locations and assign
remaining demand centers to these locationsCompute the COG of the M locationsReassign all demand centers to the M COGs on the basis
of proximityRecompute the COGs and repeat the demand center
assignments, stopping this iterative process when there is no further change in the assignments or COGs
CR (2004) Prentice Hall, Inc.
13-21CR (2004) Prentice Hall, Inc.
Location of truck maintenance terminals
Location of public facilities such as offices, and police and fire stations
Location of medical facilities
Location of most any facility where transportation cost (rather than inventory carrying cost and
facility fixed cost) is the driving factor in location
As a suggestor of sites for further evaluation
Examples of Practical COG Model Use
13-22CR (2004) Prentice Hall, Inc.
A method used commercially- Has good problem scope- Can be implemented on a PC- Running times may be long and memory requirements substantial
- Handles fixed costs well- Nonlinear inventory costs are not well
handled
A linear programming-like solution procedure can be used (MIPROG in LOGWARE)
Mixed Integer Programming
13-23
Location by Simulation
CR (2004) Prentice Hall, Inc.
•Can include more variables than typical algorithmic methods
•Cost representations can be precise so problem can be more accurately described than with most
algorithmic methods
•Mathematical optimization usually is not guaranteed, although heuristics can be included to guide solution process toward satisfactory solutions
•Data requirements can be extensive
•Has limited use in practice
13-24
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.
CR (2004) Prentice Hall, Inc.
Commercial Models (Cont’d)
13-46
13-26CR (2004) Prentice Hall, Inc.
Retail Location
Methods
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
Weighted checklist - Good where many subjective factors are involved - Quantifies the comparison among alternate locations
CR (2004) Prentice Hall, Inc.
A Hypothetical Weighted Factor Checklist for a Retail Location Example
a Weights approaching 10 indicate great importance.b Scores approaching 10 refer to a favored location status.
(1)FactorWeight
(1 to 10)a Location Factors
(2)
Factor Score(1 to 10)b
(3)=(1)(2)
WeightedScore
8 Proximity to competing stores 5 405 Space rent/lease
considerations 3 15
8 Parking space 10 807 Proximity to complementary
stores 8 56
6 Modernity of store space 9 549 Customer accessibility 8 723 Local taxes 2 63 Community service 4 128 Proximity to major
transportation arteries 7 56 Total index 391
13-48
13-28CR (2004) Prentice Hall, Inc.
Retail Location (Cont’d) Huff's gravity model - A take-off on Newton's law of gravity. - "Mass" or retail "variety" attracts customers, and the distance from
customers repels them. - The basic model is:
E P C
S T
S TCij ij i
j ija
j ija
j
i= = /
/
where
Eij = expected demand from population center i that will be attracted to
retail location j Pij = probability of customers from point i traveling to retail location j
Ci = customer demand at point i
Sj = size of retail location j
Tij = travel time between customer location i and retail location j
n = number of competing locations j a = an empirically estimated parameter
CR (2004) Prentice Hall, Inc.
Retail Location (Cont’d)Example of Huff's method
Two shopping centers (RA and RB ) are to attract customers from C1, C2, and C3.Shopping center A has 500,000 square feet of selling area whereas center Bhas 1,000,000. The customer clusters have a buying potential of $10, $5, and$7 million respectively. The parameter a is estimated to be 2. What is the salespotential of each shopping center?
Solution matrix
Custo- mer i
Time from Customer i
to Location j Tij
2
S Tj ij/ 2
PS T
S Tij
j ij
j ijj
=
/
/
2
2
E P Cij ij i=
A B A B A B A B A B C1 30.0 56.6 900 3200 555 313 0.64 0.36 $6.4 $3.6 C2 44.7 30.0 2000 900 250 1111 0.18 0.82 0.9 4.1 C3 36.0 28.3 1300 800 385 1250 0.24 0.76 1.7 5.3
Total shopping center sales ($ million) $9.0 $13.0
13-50
13-30CR (2004) Prentice Hall, Inc.
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80Y
XTime (minutes)
Tim
e (m
inut
es)
C2
C1
C3
RB
RA
Retail Location (Cont’d)
13-31CR (2004) Prentice Hall, Inc.
Retail Location (Cont’d)
Location-Allocation Model
Mixed-Integer Programming Example – p.592
Recommended