Unformatted text preview: Chapter 10
Chapter
Service Facility Location Chapter 10 Homework Problems
10.1
a 10.3
a 10.5 a; also determine CG
a 10.11
a a (These are practice problems, not to be
(These
turned in)
turned Location Considerations
a How is the location decision different for
How
manufacturing vs. service environments?
manufacturing a For example, how would the criteria be
For
different for these two decisions?
different
• Location of an automobile assembly plant
• Location of a grocery store Types of Service Facilities
Facilities with direct (facetoface) contact
Facilities
with customers e.g., restaurant, retail store
with
a Facilities with either indirect contact or no
Facilities
contact with customers e.g., call center,
distribution center
distribution
a How is the location consideration different
How
for the two types?
for
a Strategic Location
Considerations
Competitive clustering (among competitors)
a Saturation marketing (same firm)
a Substitution of communication for travel
a Separation of front from back office
a • Front and back office need not be colocated
Front
e.g., dry cleaning, film processing
e.g.,
a Impact of the internet on service location
• Edistance (locating and navigating a web site) Location Factors
Location of customers, demographics
a Location of competitors
a Location of suppliers
a Costs
a Business climate
a Infrastructure
a Labor issues
a Location Factors
Community considerations
a Climate
a Environmental issues
a Regulations
a Potential for expansion
a Population trends
a Site Selection Factors
a
a
a
a
a
a
a
a Access
Visibility
Traffic
Parking
Expansion
Competition
Government
Labor Regression Analysis in Location
Decisions
a Model to predict profit for different locations
Model
based on significant factors
based
• La Quinta Inns example
• What factors would be important in the decision to
What
locate a hotel?
locate La Quinta Inns Example
a Factors include
Factors
• competitive factors (e.g., hotels in vicinity, room
competitive
rates)
rates)
• demand generators (e.g., employment, office space,
demand
tourists)
tourists)
• area demographics (e.g., income, population) a Use the model to predict the likelihood of success
Use
for a new inn at a proposed location
for Geographic Information Systems
(GIS)
Example is ArcView
a Can be used to translate data, such as
Can
demographic information, into a map
demographic
a Can help in determining site location
a Modeling Considerations
a Geographic representation
•
• Network
Plane
– Metropolitan metric
– Euclidian metric a Number of facilities
• Single
• Multiple a Optimization criteria
• Private sector
• Public sector Facility Location Techniques
a
a Factor rating
Single facility
•
•
•
• a Cross median (metropolitan metric)
Center of gravity
Euclidian metric
Gravity model (retail) Multiple facilities
• Location set covering
• Maximal covering Factor Rating Procedure
a
a
a Approach to evaluating location alternatives
Can include qualitative and quantitative inputs
Procedure • Determine relevant factors
• Assign a weight to each factor indicating its relative
Assign
importance
importance
• Score each location for each factor, using a common
Score
scale
scale
• Calculate a weighted score for each location
• Choose location with best (typically highest) weighted
Choose
score
score Factor Rating Example
Photoprocessing company wants to open a
Photoprocessing
new store. Information on two potential
locations is given. Which location would
you recommend? (Higher scores are better).
you Factor Rating Example
Scores
Factor Weight Location 1 Location 2 Traffic volume 0.4 70 80 Rental costs 0.2 90 60 Size 0.3 50 70 Accessibility 0.1 90 80 Factor Rating
a a Factor rating is a general technique, with
Factor
applications beyond facility location
applications
E.g., how would you use factor rating to choose
E.g.,
among different universities for an MBA?
among CrossMedian Technique
a
a
a
a To minimize weighted travel distances between
To
facility and demand locations
facility
Weights reflect demands
Travel distances are based on metropolitan
Travel
metric (rectangle)
metric
Distance between two points
Distance
•
• = sum of two edges of a rectangle
= difference between x coordinates
difference
+ difference between y coordinates CrossMedian Procedure
1. Calculate median
n wi
∑2
i =1
2.
3. Plot locations on a map
For x coordinate(s)
a
a
a Sum weights from left to right (west to east) till median is
Sum
reached or exceeded
reached
Sum weights from right to left (east to west) till median is
Sum
reached or exceeded
reached
Draw vertical line(s) for x coordinate(s) CrossMedian Procedure (contd.)
4. For y coordinate(s)
a Sum weights from bottom to top (south to north) till
Sum
median is reached or exceeded
median
a Sum weights from top to bottom (north to south) till
Sum
median is reached or exceeded
median
a Draw horizontal line(s) for y coordinate(s) 5. Location solution can be a point, a line, or an area CrossMedian Examples
a Problem 10.2 page 248
• Agency wants to open an office. There are 5
Agency
potential customers. Customer locations and
demand are given. Recommend a location for
the agency that will minimize total weighted
travel distance. Use metropolitan metric.
travel CrossMedian Examples (contd.)
a Problem 10.4 page 248
• Pizza delivery service wants to open a branch
Pizza
near student housing. Location of apartment
complexes and demand are given. Using
metropolitan metric, recommend a location for
the pizza branch that will minimize total
distance traveled.
distance Center of Gravity
• X coordinate
n ∑wx ii xcg = i =1
n ∑w i i =1 • Y coordinate
n ∑wy ii ycg = i =1
n ∑w
i =1 i Center of Gravity Examples
a Compute center of gravity for Problem
Compute 10.2
10.2
a Compute center of gravity for Problem
Compute 10.4
10.4 Euclidian Metric
a
a Distance “as the crow flies”
Along the hypotenuse of a triangle Euclidian Metric: Solution
Technique
Based on iterative procedure
a Start with an initial trial solution (either
Start
center of gravity or crossmedian solution
are good starting points)
are
a Update using formulas
a Stop when difference between successive
Stop
values of the coordinates is negligible (we
will only do one iteration to illustrate)
will
a Solution Technique (contd.)
a To calculate coordinates at any iteration
• Similar to center of gravity, except weights are
Similar
weights/distance
weights/distance
• Distance is euclidian distance between a point and the
Distance
current solution (based on hypotenuse of a right
triangle)
triangle)
1/2
dis = [(xi – xs)2 + (yi – ys)2] 1/2 Euclidian Metric Example
a a Using the data in Problem 10.2 and the CG
Using
as an initial solution, do one iteration of the
solution procedure
solution
Need procedure for Excel assignment
Need Gravity Model
Based on estimation of demand and market
Based
share
share
a Compute expected annual profit of each
Compute
potential site for various possible store sizes
(attractiveness of facility based on size and
travel time)
travel
a Choose the site that maximizes profit
a Skip details on page 241
a Multiple Facilities Location
Location set covering
Location
a Maximal covering
a Location Set Covering Problem
a Find the minimum number and location of
Find
facilities to serve all demand points within a
specified maximal service distance
specified a Maximal service distance
• Distance traveled by most distant customer to
Distance
reach a facility
reach Location set covering approach
For each community, identify the other sites
For
that can be reached from it within the travel
limit
limit
a For each community, identify the set of
For
sites that could serve (cover) the community
sites
a • Identify subsets
• Identify sites common to two or more subsets Location set covering examples
a Problem 10.12 page 250 a Problem 10.13a page 250 Maximal Covering Location Problem
a
a
a
a Variation of location set covering
Maximize the population covered within a desired
Maximize
service distance
service
Need information on population of each
Need
community
community
Greedy algorithm
• Add a location that covers the greatest amount of
Add
remaining uncovered population
remaining
• Repeat till everyone covered or limit on number of sites
Repeat
reached
reached ...
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 Spring '11
 KUMAR
 Center Of Mass, Distance, Metric space, Location Techniques

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