problems Example and some answers for chapter 9
Problems
1 Joe's Tasty Burger has determined that its production facility has a design capacity of
400 hamburgers per day. The effective capacity, however, is 250 hamburgers per day.
Lately Joe has noticed that output has been 300 hamburgers per day. Compute both
design and effective capacity utilization measures. What can you conclude?
Answer:
The utilization rates show that the facility's current output is below its design capacity
and considerably higher than its effective capacity. If the effective capacity is
realistically set, it is expected that the facility will operate over that level for a short
time.
2 A manufacturer of printed circuit boards has a design capacity of 1000 boards per day.
The effective capacity, however, is 700 boards per day. Recently, the production
facility has been producing 950 boards per day. Compute the design and effective
capacity utilization measures. What do they tell you?
3 Beth's Bakery can comfortably produce 60 brownies in one day. If Beth takes some
unusual measures, such as hiring her two aunts to help in the kitchen and work
overtime, she can produce up to 100 brownies in one day.
(a) What are the design and effective capacities for Beth's Bakery?
(b) If Beth is currently producing 64 brownies, compute the capacity utilization for
both measures. What can you conclude?
Answer:
(a) Effective capacity = 60 brownies
Design capacity = 100 brownies
(b)
The utilization rates show that the facility's current output is far below its
design capacity and higher than its effective capacity. The design capacity
occurs only with extra help.
4 The town barber shop can accommodate 35 customers per day. The manager has
determined that if two additional barbers are hired, the shop can accommodate 80
customers per day. What are the design and effective capacities for the barber shop?
5 The design and effective capacities for a local paper manufacturer are 1000 and 600
pounds of paper per day, respectively. At present, the manufacturer is producing 500
pounds per day. Compute capacity utilization for both measures. What can you
conclude?
Answer:
The computed utilization rates show that the facility's current output is below its
design and effective capacities. This illustrates that the manufacturer is not using
capacity to its fullest extent and there is room for improvement.
6 The design and effective capacities for a local emergency facility are 300 and 260
patients per day, respectively. Currently, the emergency room processes 250 patients
per day. What can you conclude from these figures?
7 The Steiner-Wallace Corporation has determined that it needs to expand in order to
accommodate growing demand for its laptop computers. The decision has come down
to either expanding now with a large facility, incurring additional costs and taking the
risk that the demand will not materialize, or expanding small, knowing that in three
years management will need to reconsider the question.
Management has estimated the following chances for demand:
The likelihood of demand being high is 0.60.
The likelihood of demand being low is 0.40.
Profits for each alternative have been estimated as follows:
Large expansion has an estimated profitability of either $100,000 or $60,000,
depending on whether demand turns out to be high or low.
Small expansion has a profitability of $50,000, assuming that demand is low.
Small expansion with an occurrence of high demand would require considering
whether to expand further. If the company expands at that point, the profitability
is expected to be $70,000. If it does not expand further, the profitability is
expected to be $45,000.
(a) Draw a decision tree showing the decisions, chance events, and their
probabilities, as well as the profitability of outcomes.
(b) Solve the decision tree and decide what Steiner-Wallace should do.
Answer:
(a)
(b)
Company should opt for the large expansion.
8 The owners of Sweet-Tooth Bakery have determined that they need to expand their
facility in order to meet their increased demand for baked goods. The decision is
whether to expand now with a large facility or expand small with the possibility of
having to expand again in five years.
The owners have estimated the following chances for demand:
The likelihood of demand being high is 0.70.
The likelihood of demand being low is 0.30.
Profits for each alternative have been estimated as follows:
Large expansion has an estimated profitability of either $80,000 or $50,000,
depending on whether demand turns out to be high or low.
Small expansion has a profitability of $40,000, assuming demand is low.
Small expansion with an occurrence of high demand would require considering
whether to expand further. If the bakery expands at this point, the profitability is
to be $50,000.
(a) Draw a decision tree showing the decisions, chance events, and their
probabilities, as well as the profitability of outcomes.
(b) Solve the decision tree and decide what the bakery should do.
9 Demand has grown at Dairy May Farms, and it is considering expanding. One option
is to expand by purchasing a very large farm that will be able to meet expected future
demand. Another option is to expand the current facility by a small amount now and
take a wait-and-see attitude, with the possibility of a larger expansion in two years.
Management has estimated the following chances for demand:
The likelihood of demand being high is 0.70.
The likelihood of demand being low is 0.30.
Profits for each alternative have been estimated as follows:
Large expansion has an estimated profitability of either $40,000 or $20,000,
depending on whether demand turns out to be high or low.
Small expansion has a profitability of $15,000, assuming that demand is low.
Small expansion with an occurrence of high demand would require considering
whether to expand further. If the company expands at that point, the profitability
is expected to be $35,000. If it does not expand further, the profitability is
expected to be $12,000.
(a) Draw a decision tree diagram for Dairy May Farms.
(b) Solve the decision tree you developed. What should Dairy May Farms do?
Answer:
(a)
(b)
Company should opt for the large expansion.
10 Spectrum Hair Salon is considering expanding its business, as it is experiencing a
large growth. The question is whether it should expand with a bigger facility than
needed, hoping that demand will catch up, or with a small facility, knowing that it
will need to reconsider expanding in three years.
The management at Spectrum has estimated the following chances for demand:
The likelihood of demand being high is 0.70.
The likelihood of demand being low is 0.30.
Estimated profits for each alternative are as follows:
Large expansion has an estimated profitability of either $100,000 or $70,000,
depending whether on demand turns out to be high or low.
Small expansion has a profitability of $50,000, assuming that demand is low.
Small expansion with an occurrence of high demand would require considering
whether to expand further. If the business expands at this point, the profitability
is expected to be $90,000. If it does not expand further, the profitability is
expected to be $60,000.
Draw a decision tree and solve the problem. What should Spectrum do?
11 Jody of Jody's Custom Tailoring is considering expanding her growing business. The
question is whether to expand with a bigger facility than she needs or with a small
facility, knowing that she will have to reconsider expanding in three years.
Jody has estimated the following chances for demand:
The likelihood of demand being high is 0.50.
The likelihood of demand being low is 0.50.
She has also estimated profits for each alternative:
Large expansion has an estimated profitability of either $200,000 or $100,000,
depending on whether demand turns out to be high or low.
Small expansion has a profitability of $80,000, assuming that demand is low.
Small expansion with an occurrence of high demand would require considering
whether to expand further. If the business expands at that point, the profitability
is expected to be $120,000. If it does not expand further, the profitability is
expected to be $70,000.
Draw a decision tree and solve it. What should Jody's Custom Tailoring do?
Answer:
(a)
(b)
Company should opt for the large expansion.
12 The owners of Speedy Logistics, a company that provides overnight delivery of
documents, are considering where to locate their new facility in the Midwest. They
have narrowed their search down to two locations and have decided to use factor
rating to make their decision. They have listed the factors they consider important and
assigned a factor score to each location based on a five-point scale. The information
is shown here. Using the procedure for factor rating, decide on the better location.
Factor Score at Each Location
Factor
Factor Weight
Location 1
Location 2
Proximity to airport
40
5
3
Proximity to road access
30
4
1
Proximity to labor source
10
3
5
Size of facility
20
2
4
13 Sue and Joe are a young married couple who are considering purchasing a new home.
Their search has been reduced to two homes that they both like, at different locations.
They have decided to use factor rating to help them make their decision. They have
listed the factors they consider important and assigned a factor score to each location
based on a five-point scale. The information is shown here. Using the procedure for
factor rating, complete the table and help Sue and Joe make their decision.
Factor Score at Each Location
Factor
Factor Weight
Location 1
Location 2
Proximity to Work
10
5
2
Proximity to family
20
4
2
Size of home
30
2
5
Transportation system
10
5
3
Neighborhood
30
3
5
Answer:
Weighted Score
Location 1 Location 2
50
20
80
40
60
150
Weighted Score
50
90
150
330
Total
30
390
Location 2 is the preferred one.
14 The Bakers Dozen Restaurant is considering opening a new location. It has
considered many factors and identified the ones that are most important. Two
locations are being evaluated based on these factors, using factor rating. Each location
has been evaluated relative to the factors on a five-point scale. These numbers are
shown here. Use factor rating to help the restaurant decide on the better location.
Factor Score at Each Location
Factor
Factor Weight
Location 1
Location 2
Proximity to customer
30
5
2
Proximity to competition
10
4
2
Proximity to labor
supply
30
2
5
Transportation system
20
5
3
Quality of life
10
3
5
15 Joe's Sports Supplies Corporation is considering where to locate its warehouse in
order to service its four stores in four towns: A, B, C, and D. Two possible sites for
the warehouse are being considered, one in Jasper and the other in Longboat. The
following table shows the distances between the two locations being considered and
the four store locations. Also shown are the loads between the warehouse and the four
stores. Use the load distance model to determine whether the warehouse should be
located in Jasper or in Longboat.
Town
Distance to
Jasper
Distance to
Longboat
Load between City and
Warehouse
A
30
12
15
B
6
12
10
C
10.5
30
12
Town
Distance to
Jasper
Distance to
Longboat
Load between City and
Warehouse
D
4.5
24
8
Answer:
Load-Distance ScoreJasper = lijdij = (30)(15) + (6)(10) + (10.5)(12) + (4.5)(8) = 672
Load-Distance ScoreLongboat = lijdij = (12)(15) + (12)(10) + (30)(12) + (24)(8) = 852
Warehouse should be located in Jasper.
16 Given here are the coordinates for each of the four towns to be serviced by the
warehouse in Problem 15. Use the information from Problem 15 and the center of
gravity method to determine coordinates for the warehouse.
Town
Coordinates (X,
Y)
A
(4, 18)
B
(12, 2)
C
(10, 8)
D
(8,15)
17 Shoeless Joe is a specialty retailer that is deciding where to locate a new facility. The
annual fixed and variable costs for each possible site have been estimated as follows:
Location Fixed Costs Variable Costs
A
$70,000
$1/unit
B
$34,000
$5/unit
C
$20,000
$8/unit
D
$50,000
$4/unit
If demand is expected to be 2000 units, which location is best?
Answer:
Location C is best.
18 The Quick Copy center for document copying is deciding where to locate a new
facility. The annual fixed and variable costs for each site it is considering have been
estimated as follows:
Location Fixed Costs Variable Costs
A
$85,000
$2/unit
B
$49,000
$7/unit
C
$35,000
$10/unit
D
$65,000
$6/unit
If demand is expected to be 3000 units, which location is best?
Example problems and answers for chapter 11
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Problems
1 Fresh Foods Grocery is considering redoing its facility layout. The fromto matrix showing
daily customer trips between departments is shown in Table 10-10, and their current layout is
shown in Figure 10-12. Fresh Foods is considering exchanging the locations of the dry
groceries department (A) and the health and beauty aids department (F). Compute the ld score
for Fresh Foods' current and proposed layouts. Which is better?
Table 10-10
FromTo Matrix for Fresh Foods
Trips between Departments
Department
A
A. Dry groceries
15 45 25 10 50
B. Bread
B
C
D
E
F
30 15 25 25
C. Frozen foods
34 15 20
D. Meats
40 10
E. Vegetables
20
F. Health and beauty aids
Figure 10-12 Current layout for Fresh Foods
Answer:
Current Layout
Proposed Layout
Departments
Number of
Trips(l)
Distance
(d)
LoadDistance
Score(ld)
Distance
(d)
LoadDistance
Score(ld)
AB
15
1
15
2
30
AC
45
2
90
1
45
AE
10
2
20
1
10
AF
50
3
150
3
150
BC
30
1
30
1
30