Submit complete solutions to the following problems to your instructor: 1. Cross Median Method: Text Chapter 10 Exercise 6 2. Huff Method: Text Chapter 10 Exercise 9 3. Set Covering Method: Text Chapter 10 Exercise 12 Chapter 10 Exercise 6 10.6. You have been asked to help locate a catering service in the central business district of a city. The locations of potential customers on an xy coordinate grid areP1 = (4, 4), P2 = (12, 4), P3 = (2, 7), P4 = (11, 11), and P5 = (7, 14). The expected demand is weighted as w1 = 4, w2 = 3, w3 = 2, w4 = 4, and w5 = 1. Using the cross-median approach, recommend a location for the catering service that will minimize the total weighted distance traveled to serve the customers. Chapter 10 Exercise 9 10.9. A community is currently being served by a single self-serve gas station with six pumps. A competitor is opening a new facility with 12 pumps across town. Table 10.12 shows the travel times in minutes from the four different areas in the community to the sites and the number of customers in each area. a. Using the Huff retail location model and assuming that λ = 2, calculate the probability of a customer traveling from each area to each site. b. Estimate the proportion of the existing market lost to the new competitor. Table 10.2 Area1234 Old Station51915 New Competitor208126 Number of Customers1001508050 Chapter 10 Exercise 12 The Volunteer Fire Department serving the communities in Figure 10.8 has just purchased two used fire engines auctioned off by a nearby city. a. Select all possible pairs of communities in which the fire engines could be located to ensure that all communities can be reached within 30 minutes or less. b. What additional consideration could be used to make the final site selection from the community pairs found in part a? Figure 10.8 Service Area Network SEE ADDITIONAL ATTACHMENT FOR FIGURE 10.8 SERVICE AREA NETWORK The physical location can be an important decision for many types of services such as stores, restaurants and gas stations; a critical differentiator for defining success and failure. Such services require the physical presence and participation of customers in the service delivery process. The customers have to travel to these services to participate in the delivery of the service. Locations that are closer to the customers or are in places that are frequented by the customers tend to attract more customers. Services that involve no or minimal face-to-face contact can be located just about anywhere. Even services with high front office contact can have significant back office operations, which can be located at distant places. Sometimes, employees working for the back office can even work from home as they do not require significant face-to-face contact. Location for most businesses is a strategic decision and involves a long term commitment. Therefore, the location should be good and viable from a long term perspective and s ...

1. Submit complete solutions to the following problems to your
instructor:
1. Cross Median Method: Text Chapter 10 Exercise 6
2. Huff Method: Text Chapter 10 Exercise 9
3. Set Covering Method: Text Chapter 10 Exercise 12
Chapter 10 Exercise 6
10.6. You have been asked to help locate a catering service in
the central business district of a city. The locations of potential
customers on an xy coordinate grid areP1 = (4, 4), P2 = (12, 4),
P3 = (2, 7), P4 = (11, 11), and P5 = (7, 14). The expected
demand is weighted as w1 = 4, w2 = 3, w3 = 2, w4 = 4, and w5
= 1. Using the cross-median approach, recommend a location
for the catering service that will minimize the total weighted
distance traveled to serve the customers.
Chapter 10 Exercise 9
10.9. A community is currently being served by a single self-
serve gas station with six pumps. A competitor is opening a new
facility with 12 pumps across town. Table 10.12 shows the
travel times in minutes from the four different areas in the
community to the sites and the number of customers in each
area.
a. Using the Huff retail location model and assuming that λ = 2,
calculate the probability of a customer traveling from each area
to each site.
b. Estimate the proportion of the existing market lost to the new
competitor.

2. Table 10.2
Area1234
Old Station51915
New Competitor208126
Number of Customers1001508050
Chapter 10 Exercise 12
The Volunteer Fire Department serving the communities in
Figure 10.8 has just purchased two used fire engines auctioned
off by a nearby city.
a. Select all possible pairs of communities in which the fire
engines could be located to ensure that all communities can be
reached within 30 minutes or less.
b. What additional consideration could be used to make the final
site selection from the community pairs found in part a?
Figure 10.8 Service Area Network
SEE ADDITIONAL ATTACHMENT FOR FIGURE 10.8
SERVICE AREA NETWORK
The physical location can be an important decision for many
types of services such as

3. stores, restaurants and gas stations; a critical differentiator for
defining success and failure.
Such services require the physical presence and participation of
customers in the service
delivery process. The customers have to travel to these services
to participate in the delivery
of the service. Locations that are closer to the customers or are
in places that are frequented
by the customers tend to attract more customers.
Services that involve no or minimal face-to-face contact can be
located just about anywhere.
Even services with high front office contact can have significant
back office operations,
which can be located at distant places. Sometimes, employees
working for the back office
can even work from home as they do not require significant
face-to-face contact.
Location for most businesses is a strategic decision and
involves a long term commitment.
Therefore, the location should be good and viable from a long
term perspective and should
be able to withstand possible demographic and economic
changes in that location.
Fitzsimmons and Fitzsimmons (2011) have identified the
following strategic location
considerations:
Competitive clustering: Competitors, such as auto dealers,
locate themselves in the
same area, since the customers of automobiles tend to do
comparison shopping by
going to an area where multiple auto dealers are located.

4. Saturation marketing: Some firms, such as Dunkin Donuts,
create a concentrated
cluster of many outlets in high traffic areas such as downtowns.
This creates visibility
and awareness. The customer may not go to the first one they
see but may be
tempted to enter the next one.
Marketing intermediaries: A service organization, such as Visa
and Master card,
can reach millions more customers by using various banks and
credit unions as
intermediaries.
Substitute communication for travel: Banks, such as ING, can
reach customers
through internet and electronic transfers without the customers
having to travel to a
physical location.
Separation of front from back office: In many services, such as
dry cleaners, the
front and the back office operations need not be located in the
same place. While the
front office location provides convenience for the customers,
the centralized back
office location can provide economies of scale.
Impact of the internet on service location: The internet has
revolutionized many
services. Many service organizations, such as Expedia, operate
entirely through the
QSO 610 Module Seven 1

5. internet. Many brick and mortar organizations, such as AAA,
now offer services
through the internet.
Before a site can be selected, information and data are collected
on the important
characteristics of the available location alternatives in order to
determine the best location.
Geographical Information Systems (GIS) are very useful in
mapping information on different
geographical areas and sites. Site considerations, such as the
following, are commonly
considered depending on the type of service facility to be
located:
• Labor: Availability of labor with the right skills and the cost
of labor.
• Competition: Competitors located in the vicinity.
• Traffic: Areas frequented by customers are preferred.
• Taxes: Property and other taxes can add to the cost of
operating the site.
• Proximity to customers: Services, such as grocery stores, need
to be located close to
where the customers live.
• Parking: Availability of adequate parking on premises or
nearby.
• Access: Easy accessibility from highways and city roads, near
public transportation, and
without too much traffic congestion.

6. • Expansion: The site should allow room for expansion in the
future as the demand grows.
• Surroundings: Good and attractive surroundings tend to attract
customers to the service
outlet.
• Visibility: The site should be clearly visible to the nearby
traffic.
• Complementary Services: Locating restaurants near hotels and
motels would attract
travelers.
• Special considerations: Particular services may have special
and unique considerations,
such as rental car companies, need to be located at or near
airports.
It is always good to start from a model that is suited to a
particular location decision in order
to take the most important considerations into account and to
narrow down the choices.
Experience and judgment can be used last in making the final
decision.
Techniques that involve distances between two locations can
use either of the two measures
of distances:
Rectilinear distance: This is used when the movement is along
perpendicular directions,
i.e., when a city is divided into rectangular blocks. With as the
coordinates of
location i and as the coordinates of location
)y,x( ii

7. )y,x( jj j , the distance is computed as
follows, where the symbol | | denotes absolute value.
ijd
jijiij yyxxd −+−=
2 QSO 610 Module Seven
Euclidean distance: When the two locations are connected
approximately by a straight line
(as the crow flies), the distance is determined on the basis of
the Pythagoras theorem as
shown below:
22 )yy()xx(d jijiij −+−=
Example
If Erie is located at (50, 185) and State College is located at
(175, 100), what is the
rectilinear distance between them? What is the Euclidean
distance?

8. Solution
2108512510018517550 =+=−+−=ijdThe rectilinear distance
Euclidean distance
16151972572251562510018517550 22 .)()(dij ==+=−+−=
Regression Analysis
La Quinta Inn constructed a regression model based on the
location of existing hotels
(Kimes and Fitzsimmons, 1990). It used operating margin, by
adding depreciation and
interest expense to income and dividing by the total revenue, as
the dependent variable. It
used 35 factors relating to the sites as independent variables.
The regression yielded four
critical factors: price (room rate for the inn), income (average

9. family income), college (college
enrollment) and state (state population per inn). Once the
regression model was developed,
it was used to predict the operating margin at proposed new
sites in order to determine the
best site alternative that would maximize the operating margin.
Cross Median Approach
This approach is based on rectilinear distances. According to
this approach, the facility
should be located so that 50% of the concentration of total
weight should be on either side of
the location. The weight is determined by the number of
customers, demand, etc. Since the
weight may not be evenly divided on either side of the
theoretical median, the sites that are
closest on either side of the median along both x and y axes are
selected for inclusion in the
short list. Final selection is then made from this short list.
The following problem from Fitzsimmons and Fitzsimmons
(2011) will be used to illustrate
the Cross Median method.

10. QSO 610 Module Seven 3
Problem
A pizza delivery service has decided to open a branch near off-
campus student housing.
The project manager has identified five student apartment
complexes in the northwest area
of the city, the locations of which, on an xy coordinate grid in
miles, are C1 = (1, 2), C2 (2, 6),
C3 (3, 3), C4 = (4, 1), and C5 = (5, 4). The expected demand is
weighted as w1 = 5, w2 = 4,
w3 = 3, w4 = 1, and w5 = 5. Using the cross-median approach,
recommend a location for the
pizza branch that will minimize the total distance traveled.
Show the recommended location
on a graph.