This document discusses facility location decisions and methods for analyzing location strategies. It begins with an overview of what can be located, such as plants, warehouses, retail outlets, and key questions to consider around location. Common methods for solving single and multiple facility location problems are then presented, including the center-of-gravity (COG) method and optimization approaches. The document concludes with examples of applying COG and discussing other techniques like simulation and weighted checklists for analyzing retail location decisions.
Operation Research involves determining an optimum solution to a distribution problem. In order to suitably plan and assign vehicles to different routes, organizations can use the listing method described in the North-West corner rule. Research methods such as PERT and CPM are useful for timely completion of a project.
The above slides brought to you by Welingkar’s Distance Learning Division are on Operation Research Techniques in Transportation. Suitable operation research techniques are used to derive optimum solution to a distribution problem. North-West rule is explained in the presentation and PERT and CPM is used for timely completion of a project.
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How to determine demand Centers-of-Gravity in order to minimize transport costs when designing a supply chain network: visual explanation, algorithms, and free online tool
Tool can be found at http://www.stellingconsulting.nl/SC_centersofgravity.html
Route optimization algorithm are the mathematical formula that solve routing problems..
Some types of routing:
1) Vehicle Routing Problem (VRP)
2) Traveling Salesman Problem (TSP)
3) Ant Colony Optimization (ACO)
Vehicle routing and scheduling Models:
Travelling salesman problem
vehicle routing problem with time window
Pick up and delivery problem with time window
Operation Research involves determining an optimum solution to a distribution problem. In order to suitably plan and assign vehicles to different routes, organizations can use the listing method described in the North-West corner rule. Research methods such as PERT and CPM are useful for timely completion of a project.
The above slides brought to you by Welingkar’s Distance Learning Division are on Operation Research Techniques in Transportation. Suitable operation research techniques are used to derive optimum solution to a distribution problem. North-West rule is explained in the presentation and PERT and CPM is used for timely completion of a project.
For more such innovative content on management studies, join WeSchool PGDM-DLP Program: http://bit.ly/DistMang
Join us on Facebook: http://www.facebook.com/welearnindia
Follow us on Twitter: https://twitter.com/WeLearnIndia
Read our latest blog at: http://welearnindia.wordpress.com
Subscribe to our Slideshare Channel: http://www.slideshare.net/welingkarDLP
How to determine demand Centers-of-Gravity in order to minimize transport costs when designing a supply chain network: visual explanation, algorithms, and free online tool
Tool can be found at http://www.stellingconsulting.nl/SC_centersofgravity.html
Route optimization algorithm are the mathematical formula that solve routing problems..
Some types of routing:
1) Vehicle Routing Problem (VRP)
2) Traveling Salesman Problem (TSP)
3) Ant Colony Optimization (ACO)
Vehicle routing and scheduling Models:
Travelling salesman problem
vehicle routing problem with time window
Pick up and delivery problem with time window
Presentation by Maged Armanuse, Branch Chief, METS, California Department of Transportation (Caltrans), on recent revisions to the HWTT (AASHTO T324) test. Presentation delivered on Nov. 6, 2019 at the California Asphalt Pavement Association Fall Asphalt Pavement Conference in Sacramento, Calif.
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Two models are present, the first is point to point model and demonstrated the minimizing cost issue, while the other model is Multi-stops operating model, and it is addressing profit maximization.
International Journal of Computational Engineering Research(IJCER)ijceronline
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Multi depot Time-dependent Vehicle Routing Problem with Heterogeneous FleetArian Razmi Farooji
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and Multi Big Data in Transport Modeling,
Simulation and Optimization (CM3) in Jyväskylä, Finland.
What is Transportation model?
deals with a special class of linear programming problem in which the objective is to transport a homogenous commodity from various origins or factories to different destinations or markets at a total minimum cost.
Concept - addresses the concept of moving a thing from one place to another, without change
- used to analyze transportation systems and find the most efficient route
Presentation by Maged Armanuse, Branch Chief, METS, California Department of Transportation (Caltrans), on recent revisions to the HWTT (AASHTO T324) test. Presentation delivered on Nov. 6, 2019 at the California Asphalt Pavement Association Fall Asphalt Pavement Conference in Sacramento, Calif.
Presentation delivered by Frank Farshidi, Ph.D., P.E., City of San Jose, at the CalAPA Fall Asphalt Pavement Conference Oct. 24-25, 2018 in Sacramento, Calif.
Two models are present, the first is point to point model and demonstrated the minimizing cost issue, while the other model is Multi-stops operating model, and it is addressing profit maximization.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Multi depot Time-dependent Vehicle Routing Problem with Heterogeneous FleetArian Razmi Farooji
This presentation compares two multi-objective metaheuristic algorithms, namely Simulated Annealing and Non-dominated Sorting Genetic Algorithm (NSGA II) for solving Multi depot Time-dependent Vehicle Routing Problem with Heterogeneous Fleet and was presented at Computational Multi Physics, Multi Scales
and Multi Big Data in Transport Modeling,
Simulation and Optimization (CM3) in Jyväskylä, Finland.
What is Transportation model?
deals with a special class of linear programming problem in which the objective is to transport a homogenous commodity from various origins or factories to different destinations or markets at a total minimum cost.
Concept - addresses the concept of moving a thing from one place to another, without change
- used to analyze transportation systems and find the most efficient route
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
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Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
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When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
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My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
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4. 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
5. 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
6. 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.
7. 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)
8. 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
9. 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
10. 13-10CR (2004) Prentice Hall, Inc.
COG Method (Cont’d)
∑
∑
∑
∑ ==
i ii
i iii
i ii
i iii
RV
YRV
Y,
RV
XRV
X
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 located
Y,X
11. 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 cost
Point
i
Prod-
ucts Location
Annual
volume,
cwt.
Rate,
$/cwt/
mi. Xi Yi
1 S1 A Seattle 8,000 0.02 0.6 7.3
2 S2 B Atlanta 10,000 0.02 8.6 3.0
3 H1 A & B Los
Angeles
5,000 0.05 2.0 3.0
4 H2 A & B Dallas 3,000 0.05 5.5 2.4
5 H3 A & B Chicago 4,000 0.05 7.9 5.5
6 H4 A & B New York 6,000 0.05 10.6 5.2
13. 13-13CR (2004) Prentice Hall, Inc.
COG Method (Cont’d)
Solve the COG equations in table form
i Xi Yi Vi Ri ViRi ViRiXi ViRiYi
1 0.6 7.3 8,000 0.02 160 96 1,168
2 8.6 3.0 10,000 0.02 200 1,720 600
3 2.0 3.0 5,000 0.05 250 500 750
4 5.5 2.4 3,000 0.05 150 825 360
5 7.9 5.5 4,000 0.05 200 1,580 1,100
6 10.6 5.2 6,000 0.05 300 3,180 1,560
1,260 7,901 5,538
14. 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 convert
coordinates into miles.
∑ −+−= i iiii YYXXKRVTC 22
)()(
CR (2004) Prentice Hall, Inc.
16. 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
TCRiViYiXii
Calculate total cost at COG
22
1
4.40)(7.36.27)(0.6)(500)8,000(0.02TC −+−=
17. 13-17CR (2004) Prentice Hall, Inc.
Note The center-of-gravity method does not necessarily
give optimal answers, but will give good answers if there are
a large numbers of points in the problem (>30) and the
volume for any one point is not a high proportion of the total
volume. However, optimal locations can be found by the
exact center of gravity method.
∑
∑
∑
∑ ==
i iii
i iiiin
i iii
i iiiin
/dRV
/dYRV
Y,
/dRV
/dXRV
X
where
22
)Y(Y)X(Xd
n
i
n
ii
−+−=
and n is the iteration number.
COG Method (Cont’d)
18. 13-18CR (2004) Prentice Hall, Inc.
Solution procedure for exact COG
COG Method (Cont’d)
1) Solve for COG
2) Using find di
3) Re-solve for using exact formulation
4) 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,X
Y,X
Y,X
Y,X
19. 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 problem
that:
− Search for the best combination of facilities to minimize
costs
− Do so within a reasonable computational time
− Do not require enormous amounts of data for the analysis
Multiple Location Methods
20. 13-20
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
CR (2004) Prentice Hall, Inc.
21. 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
22. 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
23. 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
24. 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.
26. 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
27. 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)
Factor
Weight
(1 to 10)
a
Location Factors
(2)
Factor Score
(1 to 10)
b
(3)=(1)×(2)
Weighted
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
13-48
28. 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 PC
S T
S T
Cij ij i
j ij
a
j ij
a
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
29. 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 B
has 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 sales
potential of each shopping center?
Solution matrix
Custo-
mer i
Time from
Customer i
to Location j
Tij
2
S Tj ij/
2 P
S T
S T
ij
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