Chapter 10 Long-Term Planning (Facilities, Location, and Layout)
Review Questions
1.
With four work centers and four locations there are how many possible layouts?
Answer: Four factorial (4! = 4*3*2*1 =24). The first assignment of a work center to a location
can be done in four different ways, the second can be done in three ways, etc. This number
grows quickly as more work centers/locations are added. Just one more variant and the number
of permutations increases five times. Also, if layout includes variations in equipment
placement at each specific location, the number of permutations can become very large (e.g.,
12 factorial = 479,001,400).
2.
Finding the best locations for police and fire stations is a pressing urban problem. Discuss the
nature of this problem and what variables are likely to be important. How does this compare
to the facility layout problem?
Answer: Speed of response is one critical factor. Extent and competence of response is a
second critical factor. The third element involves what happens if another emergency occurs
in a different place. What resources are still uncommitted that can be directed to the new
emergency? Locations should be chosen that are located closest to those areas that are most
likely to be in need of assistance. The probability of more than one emergency arising in a
given time period will determine the inventory of spare resources that should be available in
the second instance of an emergency. Extra resources for additional requests for help must
always be factored into the system.
There are many similarities to the facility layout problem. Speed of response is equivalent to
distance traveled by parts and components. In both cases, the best solution is the one that
minimizes distance traveled for the system as a whole. The questions of which jobs should be
done first, second, etc. are somewhat like the prioritization of emergency calls. The main
factors that are different reflect the humanitarian issues (i.e., triage concepts) as compared to
maximizing efficiency to control costs. Police and fire department managers never forget that
they are always constrained by a budget. One of the most important observations that can be
made at this time is the similarity of police and fire department operational questions with the
humanitarian aid problems faced by P/OM. See Chapter 11 where these aspects of P/OM are
discussed.
This is a very demanding question with a variety of implications so we have taken the liberty
of providing a more lengthy discussion than is normal for a review question. We have already
noted that the location problem is conjoint with a capacity problem. That is, should there be a
few large stations or many small ones? This particular location problem is further complicated
because of the public nature of the services. Individuals as citizens and voters (not consumers)
are affected. Police and fire services are monopolistic. They do not face competitive pressures
in the ordinary sense. Bad decisions are reflected (not in reduced demand and profit) but in
high crime rates, substantial fire damage, and dissatisfied voters.
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The location decision may rely on density and center-of-gravity models to place stations
where the greatest demands are expected to be. The decision may also rely on the
transportation model in two ways: one to hold down costs of providing service; the other to
optimize the speed of response to calls for service. Peak demand in one area may be met by
dispatching personnel and equipment from others—this is the concept underlying a “twoalarm” fire. In this case, the distances from one station to another become part of the problem.
It is possible that the load-distance model could be used; this model crosses the boundary
between location decisions and layout decisions.
3.
Why do services usually profit by being close to the customer?
Answer: Key to good service is recognition of the personal contact required. Customers feel
more secure when they know how to get in touch with a service provider. For example, if car
servicing requires many miles of travel and much time, the sense of rapport with the service
provider is strained. In fact, the word rapport which means a close and harmonious
relationship where people understand each other’s feelings sums up the need for both physical
and psychological nearness by service providers.
4.
Is it true that plant selection should, at least in part, be based on estimates of labor costs for
different areas of the country? Explain.
Answer: Labor costs can differ markedly by region in any country. If labor is a significant
part of the total cost of goods or services sold, then it behooves management to factor
location with respect to labor costs into planning. Services are generally labor-intensive.
Consequently, locating services close to the customer make good sense. Off-shoring is
another form of labor cost differentials. Robotics is a growing part of the cost of goods and
services. Robot-servicing skills become more important than manual labor costs where robots
can be utilized. There is equivalent thinking for services. For example, voice recognition
capabilities are replacing operators in call centers. In a different sense, students learn a lot
from discussing why there are different labor costs in different regions. This discussion often
starts with questions about whether low labor costs always occur in areas where low cost of
living exists. Dense urban centers such as New York, Boston, and San Francisco are often
associated with high costs.
5.
Gasoline station location often is based on traffic density studies. What would be the criteria
for a good location in terms of traffic density and patterns?
Answer: A good location for a gasoline station should have high enough traffic density to be
profitable but not so high that drivers are uncomfortable trying to get out of lane. A high
traffic count that is the result of a few very busy (rush) hours only on weekdays might not be
desirable. Density studies might also consider the mix of sedans versus trucks. Specific to
location is what kind of layout can the station design? This includes the station’s ingress and
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egress flexibility. The traffic stream often makes it difficult for drivers to move across lanes
and to re-enter traffic. Very often the traffic pattern will only allow one road direction to
have station access (i.e., crossing the center line is prohibited or not feasible). Other station
layout issues that should be considered include: the waiting line leading to gas pumps has to
be reasonable; can other services be offered including food, drink, bathrooms, tire repair, air,
etc. Another issue is the location of stations drivers encounter before reaching the station.
Are other alternatives available past the location under consideration?
6.
With the scoring model, what happens when a weight of zero is chosen for one of the factors?
Answer: If the scoring model uses a weighted sum such as in Table 10.2 where Brazil has
the highest score, then a zero weight indicates no importance. In that table, labor unions have
a weight of 0.02. It labor unions had a zero weight that would mean this category does not
affect the final weighted-sum. As an exercise, add 0.02 to the weight of political climate and
subtract 0.02 from the weight of labor unions. The result is: (5.43, 5.61, 4.74, 6.62). All four
countries improve and Brazil retains first place.
If a scoring model with weighted powers is used (i.e., product of the powers), then weights
become exponents. Any expression raised to the zero power yields a result of one. Since this
scoring model is multiplicative, multiplying by one has no effect on the final result. Thus, a
weight of zero is equivalent to leaving the factor out of the calculations. This is the same kind
of effect experienced with the weighted sum model in the paragraph above.
7.
One of the best known, most used, and most abused scoring models is the credit scoring
model. The credit score is used by lenders to impute the likelihood that a customer will
default. Discuss the strengths and weaknesses of credit scoring as it is presently used.
Answer: There are three well-known credit scoring agencies and their credit ratings for any
one individual do not agree with each other many times. The problems of associating data
(such as how fast bills are paid, how many credit cards are used, whether credit is sought for
car, house, and shopping bills) with credit riskiness are numerous. They are weighted
differently by each agency. The weaknesses of credit scoring include determining the right
factors to use, the best weights for each factor and the lack of good data quality. When those
problems are properly addressed, the potential strength of credit scoring emerges.
8 Company X has been renting a facility in the Columbus, OH area. This is a great general
location because a 600 mile circle drawn around the city contains a large percentage of X’s
customers. The building in which X rents has been sold and the new owners intend to
refurbish it and raise the rents significantly. The president of X has hired you as a consultant to
help in relocation. She points out that zoning is of great importance. Prepare a list of questions
that you must ask so that you can approach this problem in a systematic way.
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Answer: The president knows the location that he or she wants for Company X. The first
question to ask is do you want to continue to rent or would there be advantages in buying or
building? Assume that the answer will depend on the rental details and what buildings or lots
are available. What is the ideal building and how much would it cost to build this ideal?
Where could it be located given the zoning rules? Start with the ideal and then look at the list
of availabilities both buying a building and renting. How close can Company X get to the
ideal and what are the various costs of actual options?
9. Some of the following industries tend to form high-density clusters in specific geographic
areas. Identify those industries that have strong clusters and try to find the rational explanation
for these specific clusters. In the same sense, identify those industries that do not have strong
clusters and try to find the rational explanation for the lack of clustering.
a.
Financial services
b.
U.S. automobiles
c.
Stockyards
d.
Steel
e.
Textiles-bathing suits
f.
Semiconductors
g.
Aerospace
h.
Garlic processing
i.
Motion pictures
j.
Publishing
k.
Tobacco products
l.
Petroleum
m. Credit card processing
n.
Non-U.S. automobiles
o.
Theme parks and resorts
p.
Advertising agencies
q.
Soy products
r.
Pharmaceuticals
Answers:
a. Financial services cluster “where the money is”—banks, stock exchanges, investment houses,
etc. in rank order: 1. London, 2. New York, 3. Hong Kong, 4. Singapore, 5. Tokyo, 6. Zurich,
7. Boston, 8. Geneva, 9. Frankfurt, 10. Seoul
b. Automobile manufacturing used to cluster near raw materials (steel, rubber) and transport
hubs (rail and ship); nowadays they cluster to take advantage of beneficial state tax policies and
non-union labor relations. That accounts for the switch away from Detroit which was once the
traditional center of auto activity. Recently, with the influx of foreign automakers into the United
States, manufacturing has dispersed into many Southeastern states in the U.S.A. (See n. below.)
c. Stockyards cluster near transport hubs (rail and truck), and where meat-processing facilities
have been built. Kansas City and Chicago satisfy these conditions.
d. Steel and Pittsburgh used to be practically synonymous in the U.S.A. That is no longer true.
Some of the places where steel is still made in the U.S.A. include the Great Lakes, Southeastern
states (e.g., Montgomery, Alabama) and Northeastern states (e.g., Pittsburgh). The biggest steel
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producers are China, Japan, Korea, India, Brazil, and Mexico. Clusters still make sense for minimills. Steel requires iron ore and coal. Both materials are expensive to transport; rail and ship are
the preferred shipping methods. Steel manufacture must be near both simultaneously, and still
have good outbound transport for finished products. The product is globally produced and the
clusters are no longer homogeneous.
e. Textiles at one time clustered in the northeast, where the labor and the demand were
concentrated; textiles moved to the southeast as the cotton gin revolutionized cotton production;
textiles have moved again, now to low-wage countries. This suggests that textiles are sensitive to
several factors, and will move rather quickly to new cluster sites. For example, many bathing
suits today are manufactured in China. The low labor costs are certainly a major consideration.
f. Semiconductors are concentrated in Silicon Valley, California, Austin, Texas, Maynard,
Massachusetts, among other sites. The concentration follows the demand for the most critical
component—a well-educated and well-trained labor force. It is not coincidental that these
clusters are near concentrations of universities. Globally Japan and Taiwan and various countries
in Europe are involved with various aspects of the semiconductor industry.
g. Aerospace in its broadest sense is found somewhere in every major country. In India
Bangalore is a big center. France and Germany participate broadly through Airbus/EADS. Brazil
has Embraer, Canada has Bombardier. In the U.S.A. aerospace is found in such cities as Seattle
(Boeing); NASA and its connections tie in with locations in Texas and Florida. Space X is a new
player located in California. Proximity to labor force is a primary concern, but the numerous
clusters have strong political elements as well as operational ones.
h. Garlic processing is done close to where garlic is grown. Gilroy, California is known as the
“garlic capital of the U.S.,” so it’s not surprising that garlic processing is done in this area.
Processing garlic in another region would require transporting the raw garlic hundreds of miles
to a processing facility, which is costly and could promote spoilage. Gilroy deserves all the credit
although some would say the smell around the town is not worth it. Recent trends show major
increases in garlic imported from China. Even in Gilroy, much garlic processing is of imported
product.
i. Motion pictures gravitated to Hollywood almost a century ago. The growth of the studio
system created a magnetism that attracted other parts of the industry. Movies are now made in
many other places. For example, Bollywood is a well-established film center in Mumbai. The
movie industry likes itself so much that it tends to cluster in places where stars and wannabes can
see other frequently.
j. Publishing now can be located wherever a decent computer system exists. Self-publishing is a
reality. However, the publishing industry is similar to the movie industry. In other words, it likes
itself so much that it clusters in places like New York, London, and San Francisco. That way, the
infrastructure of the publishing bureaucracy likes to hob knob with itself. Can you imagine Boca
Raton in Florida being a publishing center? It actually is the site of CRC Publications.
k. Cigarettes locate where the tobacco is, and that is North Carolina. The historical hub of this
activity is Raleigh-Durham and Winston-Salem. Cigar manufacturers do the same thing: tobacco
used for cigars is grown in the Dominican Republic, and that is where many of the cigars (sold in
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the U.S.) are made. During the early 1900s, cigar production in the U.S. was concentrated in
Tampa, Florida. Ask students why they think so many cigars were produced in Tampa, even
though it is hundreds of miles from the closest tobacco farms. The answer is that after World
War II, Tampa was the main supplier of cigars in the U.S.A. Google Newman cigars.
1. Petroleum refining in the U.S.A. tends to locate at the confluence of oil reserves, rail hubs, and
seaports. East Texas, Louisiana, New Jersey, and California are good examples. OPEC countries
control and account for the cluster of suppliers which include Russia. This supply chain system
has changed dramatically. Brilliant entrepreneurs, with almost no one noticing, developed a new
approach. Probably, they would have been stopped if any traditional politician in any country in
the world had noticed what was happening. Fracking had been discovered. Many would have
liked to have stopped it. Their objections came too late. North Dakota is not the only place where
natural gas is recoverable using the new procedures of fracking which will change everything
about who supplies what, how and when in the new era of natural gas. Eventually, fracking will
not be limited to the U.S.A. Many countries in the world will make petroleum available at much
lower prices than previously existed. The clusters can be identified pretty quickly when you
google fracking.
m. At one time, credit card processing was concentrated in states that had liberal banking laws
(such as South Dakota, Delaware, and Florida). Change has occurred in many ways and locations
are not clustered because the service only requires computers and telecommunications which can
be situated anywhere. Processing can take place in any country and is often outsourced. In the
U.S.A., centers can be found in Omaha, Cincinnati, and Fort Lauderdale. The service is offered
by some well-known companies such as PayPal. For a broad picture of selling points from
vendors it helps to study this link: http://credit-card-processing-review.toptenreviews.com/
n. There are two interpretations for non-U.S. automobile industries. One is factories located
outside the U.S.A. that are exporting product to the U.S.A. Assembly plants in Europe and Asia
are the major exporters. Many of these companies are partially or fully owned by Ford, Chrysler,
General Motors, Honda, Hyundai, Nissan and Toyota. That leads to the second variation of nonU.S.A. automobile industries. These are the companies which have assembly plants in the U.S.A.
They may also have engine plants and other component plants in North America. For the most
part, these companies have gone to Southeastern U.S. states like Tennessee, Kentucky, and
Alabama. BMW, Volkswagen and Mercedes-Benz are three examples of German companies
with plants in the Southeastern states. The economics of these states is favorable for running auto
assembly. Many of these same companies have plants in Mexico and Canada.
A variety of reasons explain the choice including the fact that Southeastern state governments
were anxious to subsidize the auto industry. Many SE states had lost their textile industry to Asia
and were economically underperforming the U.S.A. averages. Tennessee became a leading role
model by providing tax benefits for the transplants and educational subsidies for the training of
workers. The now defunct Saturn brand was located in Spring Hill, TN. It is the only Detroit
entry in that area and is still being used for other GM purposes. It had been rated as one of the
most efficient auto plants in North America. (See Wikipedia: re Spring Hill Manufacturing). The
history of what happened to Saturn deserves a book in its own right.
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o. Theme parks cluster where large numbers of people can travel inexpensively for a vacation in
a comfortable climate for the year round. It helps to be near good beaches, wonderful hotels, and
a hospitality environment which means that employees are aware of the need to make travelers
feel welcome. A cluster example is around Kissimmee, south of Orlando where Walt Disney
World, Universal Studios, and Sea World form the nucleus of a much larger cluster of theme
parks. It is useful to ask students to name other such clusters in the U.S.A. and to discuss theme
parks abroad. Resort hotels have clustered at very attractive sites, relatively short distances from
large cities—the Poconos and White Mountains are examples. Ski resorts, on the other hand,
must cluster where the snow is—Colorado, Utah, Idaho, for example.
p. Once upon a time, advertising agencies clustered in the leading cities of the world. New York
was the ad capital for the U.S.A.; London for the U.K.; Paris for France; and Tokyo for Japan.
After waves of mergers and increasing focus on regional markets, ad agencies became as
decentralized as quick service restaurants. The entire advertising business has changed in ways
that were unexpected just 10 years ago. Google has major impact for online advertising. Internet
advertising is deeply involved with the future of social media such as Facebook and Tweeter.
q. Soy growers are where the soy bean farms are which in the U.S.A. is throughout the heartland
and further. Here is a list of some states with soybean councils to provide money for marketing
benefits of the product: Arkansas, Delaware, Illinois, Indiana, Kentucky, Maryland, Michigan,
Minnesota, Nebraska, North Dakota, Ohio, South Dakota, Virginia and Wisconsin. Soy products
are made in many different locations and there is no clustering among soy retailers. The farmers
have a common interest which does create clusters of advocacy in Washington, D.C. and state
capitals. The soy system deserves constant monitoring. Meanwhile, the basic soy market has
shifted from the U.S.A. to Chinese imports by companies such as Dean Foods (Silk brand
products), Bunge, Cargill, and Arthur Daniels Midland.
r. Location clusters of pharmaceutical firms is historically on the East Coast in New Jersey and
New York. Three giants, Pfizer, Johnson & Johnson, and Merck, are examples. In Chicago there
is Abbott Laboratories and in Indianapolis, Eli Lilly. At least initially, a major reason for clusters
was that these companies, and other chemical process companies in their neighborhoods, trained
their work forces, creating an increasing pool of talent available in that area. These companies, in
effect, were schools that hired, trained, and traded workers amongst themselves. Over time, work
force mobility led to dispersal of locations on a national scale. For example, new California firms
such as Amgen and Genentech became true research leaders. These days there are many startups
in biopharmaceuticals. Firms are testing new theories such as the use of vaccines against cancer
and DNA-related hypotheses that did not exist a few decades ago. International pharmaceutical
firms are globally dispersed but there are clusters in various countries where chemical industries
were precursors (e.g., the UK, France, Germany, Switzerland and Sweden). Among international
firms we can list AstraZeneca, Novartis, Bayer, Roche, GlaxoSmithKline, and Sanofi.
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PROBLEMS
1.
The cost of improving plant layout is $100,000 to be depreciated over a 5-year period. The
estimated annual improvements in profit are $6,000 from better quality, $4,000 from higher
productivity, and $11,000 from health benefits. Is the layout improvement recommended?
Solution:
Straight-line depreciation of $100,000 over five years yields a cost of $20,000 a year. The
resulting yearly improvements in profit (benefits) are $6,000 (better quality) + $4,000 (higher
productivity) + $11,000 (health benefits) = $21,000. Since the benefits exceed the costs, the
layout might be recommended. Managers must consider intangibles such as disruption during
this project and the possibility of something going wrong. In particular, the health benefits
estimate should be scrutinized since it is an intangible claim which might be much larger in a
systems sense or a false claim.
2.
The cost of improving office layout is $27,000 to be treated as a one-time expense. The office
manager does not have any way of estimating improved profits resulting from quality
changes but says that the new layout will save time and miles of walking for the 40 office
employees. She estimates that the new layout will cut the amount of walking for the average
employee by 100 miles per year. How much will the layout improvement be worth?
Solution:
Since 40 employees  100 miles = 4,000 total miles of walking per year are eliminated, the cost
is $27,000/4,000 or $6.75 per mile, which seems like a good investment in terms of the cost of
time saved which is calculated below. Four thousand (4,000) miles of non-productive employee
walking time are eliminated per year by means of this one-time $27,000 investment. Using an
average walking speed of 3 miles per hour, this represents 1,333.33 hours saved. If the average
pay per hour is $15.00, the saving is $20,000 per year and $27,000 is paid off in 1.35 years. A
few questions to answer first, however, include: Will the change continue to provide benefits
over the years or are new alterations going to be required as time passes; are there any health
benefits from walking 100 miles per year; do employees meet more often this way and exchange
ideas?
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3.
A feasible solution for a 3-plant, 3-market problem is given below.
Markets
Supply/Day
Plants
MA MB MD
P1
40
P2
20
40
P3
Demand/Day 40
60
60
30
70
60
60
90
The costs of shipping per unit are given in the following table.
Markets
Plants MA
MB
MD
P1
$ 23 $ 32 $ 25
P2
$ 16 $ 25 $ 19
P3
$30
$ 38 $ 42
What is the total cost associated with this assignment?
Solution: The Total cost associated with this solution is:
(40  23) + (20  32) + (40  25) + (30 x 19) + (60 x 42) = 920 + 640 + 1000 + 570 + 2,520 = $5,650.
There are many solutions to this problem. Some of them may be lower cost solutions.
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4.
The American Company has two factories, A and B, located in Wilmington, Delaware, and
San Francisco, California. Each has a production capacity of 550 units per week.
American’s markets are centered in Los Angeles, Chicago, and New York City. The
demands of these markets are for 150, 350, and 400 units, respectively, in the coming
week. A matrix of shipping distances is prepared. Determine the shipping schedule that
minimizes total shipping distance. Estimates of shipping distances (in miles) are shown in
the following matrix, along with supply and demand.
Matrix of Shipping Distances in Miles
Los Angeles
Wilmington
3,000
San Francisco 400
Demand
150
Chicago
1,000
2,000
350
New York City Supply
300
550
3,000
550
400
Solution:
Markets
Factory
Wilmington
San Francisco
Los Angeles
Chicago
0
150
150
200
New York
City
400
0
Total Shipping Distance: 730,000.
See Excel File “SMCh10 problems 4, 5 and 6”, worksheet problem 4 for detailed calculations.
Transportation Model of Linear Programming, discussed in Appendix A of the book, has been
used to solve this problem.
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5.
Using the load-distance model, determine a good arrangement for work centers at locations
for the numbers given in the following matrices.
Distance Matrix: Distances (feet) between locations A, B, C, D, and E from row i to column j.
i/j A B C D E
A
0
10 20 32 40
B
10 0
C
20 16 0
D
32 18 12 0
E
40 20 15 10 0
16 18 20
12 15
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Number of units flowing between work centers 1, 2, 3, 4, and 5 from row i to column j:
i/j 1
2
3
4
5
1
x
50 60 80 20
2
40 x
3
80 90 x
4
50 10 40 x
5
60 5
50 10 90
5
60 30
70
30 x
If the cost of a unit moving one foot is one dollar ($1 per unit-foot traveled), what is the total
daily work-flow cost of the solution obtained?
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Solution:
The first row of the distance matrix is monotonically increasing. That is, the distance from A increases
going from B; similarly going from B to C and then to D and then to E. Since you want to assign large
flow units to small distances (to keep the sum of the products small), let’s make the first row of the flows
monotone decreasing, which is the sequence 1,4,3,2,5. This will lead to the matching: A1, B4, C3, D2,
E5. To perform the calculations, multiply the ABCDE distance matrix term-by-term with the unit flow
matrix below. This yields total unit-feet traveled which is then multiplied by $1 per unit-foot traveled.
i\j
1
4
3
2
5
1
x
80
60
50
20
4
50
x
40
10
70
3
80
60
x
90
30
2
40
10
50
x
90
5
60
30
5
5
x
Total Cost = (10)(80) + (20)(60) + (32)(50) + . . . + (20)(30) + (15)(5) + (10)(5) = $17,295.
See Excel File “SMCh10 problems 4, 5 and 6”, worksheet problem 5 for detailed calculations.
12
6. Consider the data given in the table below. This table gives various factors to be considered in
a location decision. Four alternatives under consideration are also listed in the table. The table
also includes the score for each factor for each location. Calculate the total score for each
location. What is the best location?
Scoring Model
Location Alternatives
Chile Mexico Honduras Brazil
Factor Name
Weight
Score out of 10
Labor Productivity
0.06
8
7
3
6
Nearness to Markets
0.08
4
6
9
7
Nearness to Sources of Raw Material
0.15
3
5
2
8
Infrastructure Facilities
0.19
7
3
4
4
Transportation Facilities
0.09
6
6
7
9
Power Availability
0.07
5
8
6
7
Political Climate
0.04
9
9
8
8
Labor Unions
0.03
3
4
3
3
Labor Cost
0.04
6
5
5
5
Material Cost
0.25
7
2
1
2
1.00
5.91
4.50
3.87
5.29
Total
Solution: Chile has become the winner with the highest score of 5.91. Brazil comes in 2nd with
5.29. Honduras is still in last place with 3.87. Mexico is in 3rd place with 4.5. For convenience,
these numbers have also been entered in the table totals.
See Excel File “SMCh10 problems 4, 5 and 6”, worksheet problem 6 for detailed calculations.
13
7. There are five jobs, Job 1 through Job 5. The number of units to be produced of each
job is given in the column “Load” in the table below. There are six processing
departments (work centers) that are labeled as A, B, C, D, E and F. The sequences in
which these processing departments are required to produce these jobs are also given in
the table below. For example, 200 units of Job 2 are to be produced and the sequence of
the processing departments is C-A-B-D-B-E-F-D.
Load and Processing Sequence for a Five-job Problem
Processing Sequence - Operation Number
Jobs
Load
1
2
3
4
5
6
7
8
Job 1
100
A
B
C
A
C
D
F
E
Job 2
200
C
A
B
D
B
E
F
D
Job 3
300
C
B
A
B
C
D
E
F
Job 4
50
B
A
C
D
F
E
F
C
Job 5
150
A
B
D
C
E
F
D
C
Each one of these processing departments A, B, C, D, E and F requires 400 square feet. The
plant in which these departments will be located has six rooms labeled as Room 1, Room 2,
Room 3, Rooms 4, Room 5 and Rooms 6. The size of each of these rooms is 20 feet x 20 feet
(400 square feet).
The figure below shows the floor plan of the building with the six rooms. The problem is to find
which processing department should be located in which room. Assume that the movement of
the material takes place only in horizontal and vertical directions from the center of the rooms.
For example see the two arrows showing movements between Room 1 and Room 2 and Room 3
and Room 6; the distance between Room 1 and Room 2 will be 20 feet (center of Room 1 to
center of Room 2).
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Floor Plan
Room 1
Room 3
Room 2
Room 4
Room 5
Room 6
Find the total unit-feet traveled for the following three room assignments. Which one is the best?
a. Assignment 1
Room
Department
Room 1 Room 2 Room 3 Room 4 Room 5 Room 6
A
B
C
D
Answer
Total Load x Distance = 175,000
15
E
F
b. Assignment 2
Room
Department
Room 1 Room 2 Room 3 Room 4 Room 5 Room 6
A
C
B
D
E
F
Answer
Total Load x Distance = 186,000
c. Assignment 3
Room
Department
Room 1 Room 2 Room 3 Room 4 Room 5 Room 6
A
C
D
B
E
Answer
Total Load x Distance = 155,000
See Excel File “SMCh10 problem 7” for detailed calculations.
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F
8 The Columbus Technology Corporation (CTC) plans to add an extension to its current
manufacturing plant. CTC will locate four departments, each of size 30 feet x 30 feet in
the following configuration.
Department 1
30 feet x 30 feet
Department 2
30 feet x 30 feet
Department 3
30 feet x 30 feet
Department 4
30 feet x 30 feet
Sequences of processing assembled products through these departments are given in the
following table.
Sequence of Processing Assemblies Through Departments
Assembly SKU Sequence of Departments
Units Produced per year
Q655
1-3-2-4
1,800
Z432
2-4-3-1
600
T691
1-2-3-4
2,200
K518
2-1-3
850
a. Complete the Volume (also called Load) Matrix.
b. Complete the Distance Matrix.
c. What is the total unit-feet traveled per year?
d. What is the total unit-feet traveled per year if departments 1 and 3 are interchanged?
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In the following solution:
Department 1 is designated as A.
Department 2 is designated as B.
Department 3 is designated as C.
Department 4 is designated as D.
Answer 8(a)
Load Matrix
TO
FROM
A
A
B
C
D
850
600
B
2200
C
2650
2200
1800
D
2400
2200
600
See Excel File: “SMCh10 Problem 8” Worksheet Problem 8a Load Matrix.
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Answer 8(b)
Problem 8 (b)
Distance Matrix
TO
A
B
C
0
30
30
30
0
60
30
60
0
60
30
30
FROM
A
B
C
D
D
60
30
30
0
Answer 8(c)
Problem 8 (c)
Load-Distance Matrix
FROM
TO
Total Load Distance
A
B
C
D
A
B
C
D
0
66000 79500
0
25500
0
132000 72000
18000 108000
0
66000
0
0
18000
0
585000
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Answer 8(d)
Problem 8 (d): Locations of A and C have been interchanged.
FROM
A
B
C
D
A
0
60
30
30
Distance Matrix
TO
B
C
60
30
0
30
30
0
30
60
FROM
From Problem 8 (a)
Load Matrix
TO
A
B
C
A
2200
2650
B 850
2200
C 600
1800
D
600
D
30
30
60
0
D
2400
2200
Load-Distance Matrix
FROM
TO
Total Load Distance
A
B
C
D
A
B
C
D
0
132000 79500
0
51000
0
66000 72000
18000 54000
0
132000
0
0
36000
0
640500
See Excel File: “SMCh10 Problem 8” Worksheet Problem 8b, c, d for detailed calculations.
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