Test-Bank-for-Heizer-Operations-Management-9e

109.A crew of mechanics at the Highway Department garage repair vehicles which break down at an average of λ = 5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.

a.What is the probability that the system is empty?

b.What is the probability that there is precisely one vehicle in the system?

c.What is the probability that there is more than one vehicle in the system?

d.What is the probability of 5 or more vehicles in the system?

(a)P0 = 1 – 5/10 = 0.50; (b) Pn>1 =(5/10)2 = 0.25; the probability of exactly one is .50 -.25 = .25;

(c) 0.25 as previously calculated; (d) the probability of five or more is Pn>4 = (5/10)5 = 0.0313. (The variety of queuing models, moderate) {AACSB: Analytic Skills}

110.A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 11 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). What is the expected cost of this system?

The number of vehicles out of service is Ls = 8 / (11-8) = 8/3 = 2.667. The cost of waiting is $150 x Ls = $150 x 2.667 = $400. Server cost is $300 per day for a total of $700.

(The variety of queuing models, moderate) {AACSB: Analytic Skills}

111.A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.

a.What is the probability that the system is empty?

b.What is the probability that there is precisely one vehicle in the system?

c.What is the probability that there is more than one vehicle in the system?

d.What is the probability of 5 or more vehicles in the system?

(a) P0 = 1 – 8/10 = 0.20; (b) Pn>1 =(8/10)2 = 0.64; the probability of exactly one is .36 -.20 = .16;

(c) 0.64 as previously calculated; (d) Pn>4 = (8/10)5 = 0.32768. (The variety of queuing models, moderate) {ACSB: Analytic Skills}

112.A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 11 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). Which is cheaper, the existing system with one service crew, or a revised system with two service crews?

Ls for the single server is 8 / (11-8) = 8/3 = 2.667. The single-server system server cost is $300

per day; wait cost is $150 x 2.667 = $400, for a total of $700. For the two-server system, Ls = 0.8381. The two-server system will double the server cost to $600, but reduce the wait cost to $150 x .8381 = $125.72, for a total of $725.72. The single-server system is cheaper.

(The variety of queuing models, difficult) {AACSB: Analytic Skills}

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113.A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic is uniformly busy with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes.

a.What is the probability that the clinic is empty (except for the dentist)?

b.What percentage of the time is the dentist busy?

c.What is the average number of patients in the waiting room?

d.What is the average time a patient spends in the office (wait plus service)?

e.What is the average time a patient waits for service?

(a)Po = 1 – 3/4 = 0.25; (b) The dentist is busy when the clinic is not empty, or 1 - .25 = 0.75 or 75 percent of the time; (c) Lq = 3*3 / 4*(4-3) = 2.25; (d) Ws = 1 / (4-3) = 1 hour;

(e)Wq = 3 / 4*(4-3) = 0.75 hours. (The variety of queuing models, easy) {AACSB: Analytic Skills}

114.A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic arrivals follow a Poisson distribution with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes.

a. What is the probability that the clinic is empty (except for the dentist)? b. What is the probability that there are one or more patients in the system? c. What is the probability that there are four patients in the system?

d. What is the probability that there are four or more patients in the system?

(a)Po = 1 – 3/4 = 0.25; (b) The probability that there are one or more patients is Pn>0 = 3/4 or

.75; (c) The probability of exactly four patients is Pn>3 −Pn>4=.3164 – .2373 = .0791; (d) .3164

as previously calculated. (The variety of queuing models, moderate) {AACSB: Analytic Skills}

115.At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machines to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machines is at the rate of 100 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour.

a.What is the utilization rate of the system?

b.What is the average number of packages waiting to be sorted?

c.What is the average number of packages in the sorting system?

d.How long must the average package wait until it gets sorted?

e.What would Lq and Wq be if the service rate were exponential, not constant?

(a) The utilization rate is ρ = 100/150 = 0.67 or 67 percent; (b) Lq = 100*100 / (2*150*50) =

.67; (c) Ls = .67 + 100/150 = 1.33; (d) Wq = 100 / (2*150*50) = 0.0067 hours, or 0.4 minutes.

(e) Both values would be exactly doubled from the constant service rate results: Lq = 1.33 and Wq = .0133. (The variety of queuing models, moderate) {AACSB: Analytic Skills}

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116.At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machines to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machines is at the rate of 140 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour.

a.What is the utilization rate of the system?

b.What is the average number of packages waiting to be sorted?

c.What is the average number of packages in the sorting system?

d.How long must the average package wait until it gets sorted?

(a) The utilization rate is ρ = 140/150 = 0.9333 or 93.33 percent; (b) Lq = 6.53; (c) Ls = 7.47;

(d) Wq = 0.0467 hours, or less than 3 minutes. Parts (b)-(d) are supported by the excerpt from ExcelOM results below.

Results

(The variety of queuing models, moderate) {AACSB: Analytic Skills}

117.A waiting-line system that meets the assumptions of M/M/1 has λ = 1, μ = 4. Calculate Po. Build a table showing the probability of more than 0, 1, 2, 3, 4, 5, 6,and 7 units in the system. Round to six decimal places in your work

(The variety of queuing models, moderate) {AACSB: Analytic Skills}

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118.Genco, Inc., a small manufacturer of diesel-generator sets has four shearing machines. Because of the age of these machines, they need minor repairs after 30 hours of use. Analysis of previous breakdowns indicates that breakdowns follow a Poisson distribution. The facility employs one repairman specifically to repair these machines. Average repair time is two hours following an exponential distribution.

a.What is the service factor for this system?

b.What is the average number of these machines in service?

c.What is the impact of adding a second repairman?

(a) X = 2/(2+30) = .0625; (b) 4 - .2987 = 3.7123 machines; (c) 4 - .2514 = 3.7486, there is a slight improvement in availability of these machines. The table below summarizes the software results from ExcelOM.

(The variety of queuing models, difficult) {AACSB: Analytic Skills}

119.A finite population waiting line model with a single server has an average service time T of 200 minutes and an average time between service requirements U of 300 minutes. Calculate the service factor X. If the population consists of 5 elements, what are the average number waiting, the average number being serviced, and the average number running? Refer to Table D.7.

The service factor is X = T / (T + U) = 200 / (200 + 300) = 0.40. For a population of five, the table factors are D = .952 and F = 0.493. The number waiting is L = N*(1-F) = 5*(1-0.493) = 5*.507 = 2.535. The number being serviced is H = F*N*X = .493*5*.4 = 0.986. The number running is J = N*F*(1-X) = 5*.493*.60 = 1.479. (The variety of queuing models, moderate)

{AACSB: Analytic Skills}

120.A finite population waiting line model with a single server has an average service time T of 50 minutes and an average time between service requirements U of 350 minutes. Calculate the service factor X. If the population consists of 5 elements, what are the average number waiting, the average number being serviced, and the average number running? Refer to Table D.7.

The service factor is X = T / (T + U) = 50 / (50 + 350) = 0.125. For a population of five, the table factors are D = .473 and F = 0.920. The number waiting is L = N*(1-F) = 5*(1-0.920) = 5*.080 =0.400. The number being serviced is H = F*N*X = .920*5*.125 = 0.575. The number running is J = N*F*(1-X) = 5*.920*.875 = 4.025. (The variety of queuing models, moderate) {AACSB: Analytic Skills}

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MODULE E: LEARNING CURVES

TRUE/FALSE

1.Experience curves may be valid for industrial applications, but have no role in services such as health care procedures.

False (Introduction, easy)

2.Experience curves are the opposite of learning curves—as one rises, the other falls.

False (Introduction, easy)

3.Learning curves are based on the premise that people and organizations become better at their tasks as the tasks are repeated.

True (Introduction, moderate)

4.The earliest application of learning curves appears in the work of architect Frank Lloyd Wright.

False (Introduction, easy)

5.Learning curves can only be applied to labor.

False (Introduction, moderate)

6.If the learning rate for a process is 100 percent, then each unit in a series of units will have the same labor requirements.

True (Introduction, moderate)

7.If the first unit in a series of units takes 200 days to complete, and the learning rate is 80%, then the second unit will take 160 days.

True (Introduction, easy) {AACSB: Analytic Skills}

8.An 80% learning curve means that with each unit increase in production, labor requirements fall by 20%.

False (Introduction, moderate)

9.A 90% learning curve implies that each time the production volume is doubled the direct time per unit is reduced to 90% of its previous value.

True (Introduction, easy)

10.The learning rate in the steel industry and the learning rate in heart surgery have both been estimated at 79 percent.

True (Introduction, and Learning curves in services and manufacturing, moderate)

11.A project manager bases his time and labor estimates on a learning rate of 86%. The actual learning rate turns out to be 89%. The manager, because of the decreased learning, will complete his project in more time and with more labor use.

True (Learning curves in manufacturing and services, moderate)

12.The learning curve may not be permanent; it can be disrupted by changes in process, personnel, or product.

True (Learning curves in services and manufacturing, moderate)

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13.Learning curves can be used to establish budgets.

True (Learning curves in services and manufacturing, moderate)

14.The arithmetic approach (or successive doubling approach) to learning curve calculations allows us to determine the hours required for any unit.

False (Applying the learning curve, moderate)

15.The logarithmic approach to learning curve calculations allows us to determine the hours required for any unit.

True (Applying the learning curve, moderate)

16.The learning curve coefficient approach may be simpler to use than the logarithmic approach, but it requires the presence of a table of learning coefficients.

True (Applying the learning curve, moderate)

17.In the formula TN=T1Nb for the learning curve, the exponent b is the learning rate, expressed as a decimal.

False (Applying the learning curve, moderate)

18.A firm that successfully pursues a steeper-than-industry-average learning curve and manages costs down may still fail if, by underestimating a strong competitor, it fails to gain the added volume necessary for the learning curve to exist.

True (Strategic implications of learning curves, moderate)

19.On an ordinary graph, unit times decrease at a decreasing rate, but on a log-log graph, the learning "curve" appears as a straight line.

True (Strategic implications of learning curves, moderate)

20.Reevaluation of learning curves is inappropriate.

False (Limitations of learning curves, moderate)

MULTIPLE CHOICE

21.The fundamental premise underlying learning curve analysis is that

a.tasks can be easily learned in organizations

b.organizations and people become better at their tasks as the tasks are repeated

c.learning takes place when people in organizations change

d.total labor costs decrease as the number of production units increases

e.doubling output cuts labor requirements per unit in half

b (Introduction, moderate)

22.Which of the following best conveys the essence of learning curves?

a.As the number of repetitions increases, time per unit increases.

b.As the number of repetitions decreases, time per unit increases.

c.As the number of repetitions increases, time per unit decreases.

d.As the number of repetitions increases, time per unit remains constant.

e.As the number of repetitions increases, time per unit doubles.

c (Introduction, moderate)

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23.A learning curve

a.plots man-hours per dollar versus time

b.is mathematically described by a parabola

c.should be plotted on polar coordinate graph paper

d.is based on the premise that organizations learn from experience

e.follows a normal distribution

d(Introduction, easy)

24.Learning curves have a variety of purposes, which can be placed into these broad categories:

a.services, industry, and military

b.internal, external, and strategic

c.wholesale, distribution, and retail

d.arithmetic, logarithmic, and learning coefficients

e.positive learning, neutral learning, and negative learning

b (Introduction, easy)

25.Learning curves (or experience curves) were first applied to industry by _________ who was studying ________.

a.Frank Lloyd Wright; architecture

b.Frank Gilbreth; worker efficiency

c.T. P. Wright; air frame manufacture

d.Lilian Gilbreth; factory efficiency

e.Frederick W. Taylor; scientific management

c (Introduction, easy)

26.A job with a 90% learning curve required 20 hours for the initial unit. The fourth unit should require approximately how many hours?

a.16

b.16.2

c.18

d.20

e.54.2

b (Introduction, easy) {AACSB: Analytic Skills}

27.Learning curves can be applied to a variety of purposes internal to a firm, including

a.labor forecasting

b.scheduling

c.establishing costs

d.establishing budgets

e.all of these

e (Introduction, easy)

28.Which of the following statements regarding the usefulness of learning curves is false?

a.An external use of learning curves is in supply chain negotiations.

b.A strategic use of learning curves is in evaluating company and industry performance.

c.An internal use of learning curves is in establishing costs.

d.An internal use of learning curves is in labor forecasting.

e.A strategic use of learning curves is in establishing budgets.

e (Introduction, easy)

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29.The fact that human activities typically improve when they are done on a repetitive basis is described by a

a.normal distribution curve

b.binomial distribution curve

c.learning curve

d.Poisson distribution curve

e.exponential curve

c (Introduction, easy)

30.A 100% learning curve implies that

a.learning is taking place for all products and workers

b.learning is taking place at the best possible level

c.a 100% reduction in the direct labor time takes place each time the production is doubled

d.no learning is taking place

e.None of the above is true.

d (Introduction, moderate)

31.Which of the following statements is most appropriate with respect to a 70% learning curve?

a.There will be a 70% decrease in direct labor per unit each time the production volume doubles.

b.Each successive unit of production will take 70% of the direct labor of the previous unit.

c.There will be a 30% decrease in direct labor per unit each time production volume doubles.

d.Thirty percent of the production will be defective until full learning takes place.

e.None of the above is true.

c (Introduction, moderate)

32.The learning curve rate is

a.the percentage of time it will take to make each unit when the production rate doubles

b.the log-log of the annual rate change divided by the average unit cost

c.always based on constant value dollars

d.only considered valid after one year of data is accumulated

e.always based on a constant work force

a (Introduction, easy)

33.Which of the following statements comparing learning rates to improvement rates is true?

a.The learning rate is the same as the improvement rate.

b.The learning rate is a decimal value while the improvement rate is a percentage.

c.A 90 percent learning curve corresponds to a 10 percent rate of improvement.

d.Learning rates apply to labor only, while improvement rates apply to all resources.

e."Learning rates" is American usage, while "improvement rates" is British.

c (Learning curves in services and manufacturing, easy)

34.Learning curves are

a.the same for all products but different for different organizations

b.the same for all organizations but different for different products

c.the same for all organizations and all products

d.different for different organizations and different products

e.appropriate in services but not in manufacturing

d (Learning curves in services and manufacturing, moderate

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35.The learning rate depends on the characteristics of a company. Which one of the following companies usually has the lowest learning rate and, therefore, the most learning?

a.a product-focused company which produces high-volume products to stock

b.a process-focused company which accepts orders from different customers with different specifications

c.a company with a newly-installed flexible manufacturing system (FMS)

d.a continuous process company

e.a labor intensive company

e (Learning curves in services and manufacturing, difficult)

36.Which one of the following statements about learning curves is true?

a.A learning curve assumes that the direct labor requirements per unit will DECREASE at an INCREASING rate as cumulative production increases.

b.Learning at a capital intensive operation will usually be LESS than it is for a labor intensive operation.

c.Learning for simple products will usually be MORE than it is for complex products.

d.Learning curves can be used only for individuals, not for the whole organization

e.None of the above is true.

b (Learning curves in services and manufacturing, moderate)

37.The learning rate for a product is 80 percent. The first unit took 100 hours to complete. The manufacturer wants to determine how many hours the fifth unit will take by using the logarithmic method. The coefficient b for that calculation is approximately

a.-.0969

b.-.2231

c.-.3219

d. .80 e. 1.903

c (Learning curves in services and manufacturing, moderate) {AACSB: Analytic Skills}

38.The learning rate for a product is 90 percent. The first unit took 10 hours to complete. The manufacturer wants to determine how many hours the fourth unit will take by using the logarithmic method. The coefficient b for that calculation is approximately

a.-.1053

b.-.1520

c.-.3219

d. .6931 e. 8.1

b (Learning curves in services and manufacturing, moderate) {AACSB: Analytic Skills}

39.The first unit of a product took 832 hours to build, and the learning rate is 75%. How long will it take to make the 10th unit? (Use at least three decimals in the exponent if you use the logarithmic approach.)

a.less than 250 hours

b.from 251 to 275 hours

c.from 276 to 300 hours

d.from 301 to 325 hours

e.325 or more hours

d (Applying the learning curve, moderate) {AACSB: Analytic Skills}

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40.The first unit of a product took 832 hours to build, and the learning rate is 75%. How long will it take to make the 30th unit? (Use at least three decimals in the exponent if you use the logarithmic approach.)

a.less than 200 hours

b.from 200 to 225 hours

c.from 225 to 250 hours

d.from 2501 to 275 hours

e.275 or more hours

b (Applying the learning curve, moderate) {AACSB: Analytic Skills}

41.The first unit of a product took 832 hours to build, and the learning rate is 90%. How long will it take to make the 25th unit? (Use at least three decimals in the exponent if you use the logarithmic approach.)

a.time ≤ 500 hours

b.500 < time ≤ 525

c.525 < time ≤ 530

d.530 < time ≤ 550

e.time > 550

b (Applying the learning curve, moderate) {AACSB: Analytic Skills}

42.The first unit of a product took 50 hours to build, and the learning rate is 80%. How long will it take to make the third unit? (Use at least three decimals in the exponent if you use the logarithmic approach.)

a.under 30 hours

b.about 32 hours

c.about 35 hours

d.about 50 hours

e.about 75 hours

c (Applying the learning curve, moderate) {AACSB: Analytic Skills}

43.The first unit of a product took 50 hours to build, and the learning rate is 85%. How long will it take to make the 10th unit? (Use at least three decimals in the exponent if you use the logarithmic approach.)

a.less than 24 hours

b.from 25 to 30 hours

c.from 30 to 35 hours

d.from 35 to 40 hours

e.more than 40 hours

b (Applying the learning curve, moderate) {AACSB: Analytic Skills}

44.The first unit of a product took 1,000 hours to build and the learning curve is 85%. How long will it take to make the first 5 units? (Use Table E.3)

a.less than 4,005 hours

b.from 4,005 to 4,015 hours

c.from 4,015 to 4,025 hours

d.from 4,025 to 4,035 hours

e.from 4,035 to 4,045 hours

d (Applying the learning curve, moderate) {AACSB: Analytic Skills}

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