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Module F Internet Homework Problems

F.23 Adventure Rafting runs rafts on the Colorado River. It has eight rafts in itsinventory. The demandfor rafts during the busy months of June and July has been either 4, 5, 6, 7 or 8, withprobabilities of

0.1, 0.3, 0.3, 0.2, or 0.1 respectively. Use Table F.4 to simulate the number of raftsthecompany will need for 10 consecutive days. Start at the top of column number 4(random number =88) and move down in the table (second number = 02) to locate the remainingnumbers.

F.24 The number of cars arriving at Mark Coffins self-service gasoline station during the last 50 hours of

operation are as follows:

Number of Cars ArrivingFrequency

6

107

12

8

20

9

8

The following random numbers have been generated: 44, 30, 26, 09, 49, 13, 33, 89, 13, and 37. Simulate 10

hours of arrivals. What is the average number of arrivals during this period?

F.25 Average daily sales of a product in Paul Jordans store are 8 units. The actual number of sales each

day is either 7, 8, or 9, with probabilities 0.3, 0.4, or 0.3, respectively. The lead time for delivery averages 4

days, although the time may be 3, 4, or 5 days, with probabilities of .2, .6, and .2. Jordan plans to place an

order when the inventory level drops to 32 units (based on the average demand and average lead time). The

following random numbers have been generated:

60, 87, 46, 63 (set 1)

52, 78, 13, 06, 99, 98, 80, 09, 67, 89, 45 (set 2)

Use set 1 to generate lead times and set 2 to simulate daily demand. Simulate two ordering periods and

determine how often the company runs out of stock before an order arrives.

F.26 Woodworth Property Management is responsible for the maintenance, rental, and day-to-day

operation of a large apartment complex in El Paso. Bruce Woodworth is especially concerned about thecost projections for replacing air conditioner compressors. He would like to simulate the number of

compressor failures each year over the next 20 years. Using data from a similar apartment building that he

also manages, Woodworth establishes the following table of relative frequency of failures during a year:

Number of A.C. ProbabilityCompressor Failures (relative frequency)

0 .061 .13

2 .25

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3 .28

4 .20

5 .07

6 .01

He decides to simulate the 20-year period by selecting 2-digit random numbers from column 3 of Table F.4

(starting with the random number 50). Conduct the simulation for Woodworth. Is it common to have 3 or

more consecutive years of operation with 2 or fewer compressor failures per year?

F.27 Refer to Example F2 in the textbook. An increase in the size of the barge-unloading crew at the Port

of New Orleans has resulted in a new probability distribution for daily unloading rates. In particular, Table

F.6 in that example may be revised as shown here:

Daily Unloading Rate Probability

1 .03

2 .12

3 .40

4 .28

5 .12

6 .05

a) Resimulate 15 days of barge unloading and compute the average number of barges

delayed, average number of nightly arrivals, and average number of barges unloaded

each day. Draw random numbers from the bottom row of Table F.4 (on p. 854) to

generate daily arrivals and from the second-from-the-bottom row to generate daily

unloading rates.

b) How do these simulated results compare to those in the Example F2?

F.28 Laurie MacDonald, a Ph.D. student at Northern Virginia University, has been having problems

balancing her checkbook. Her monthly income is derived from a graduate research assistantship; in most

months, however, she also makes extra money by tutoring undergraduates in a quantitative analysis course.

In the following table, her chances of various income levels are shown on the left.

MacDonalds expenditures also vary from month to month, and she estimates that they will follow thedistribution on the right.

Monthly Income Probability Monthly ExpensesProbability

$350 .40 $300 .10$400 .20 $400 .45

$450 .30 $500 .30

$500 .10 $600 .15

Assume that MacDonalds income is received at the beginning of each month and that she begins her final

year with $600 in her checking account. Simulate the entire year (12 months) and discuss MacDonalds

financial picture.

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F.29 Helms Aircraft Co. operates a large number of computerized plotting machines. The machines are

highly reliable, with the exception of the 4 sophisticated built-in ink pens. The pens constantly clog and

jam in a raised or lowered position. When this occurs, the plotter is unusable.

Currently, Helms replaces every pen as it fails. The service manager, however, has proposed replacing all 4

pens every time one fails. This practice, he contends, should cut down the frequency of plotter failures. At

present, it takes 1 hour to replace 1 pen. All 4 pens could be replaced in 2 hours. The total cost of an

unusable plotter is $50 per hour. Each pen costs $8.If only 1 pen is replaced each time a clog or jam occurs, the following breakdown data are thought to be

valid:

Hours between PlotterFailures if One Pen Is

Replaced during a Repair Probability

10 .05

20 .15

30 .15

40 .20

50 .20

60 .15

70 .10

Based on the service managers estimates, if all 4 pens are replaced each time 1 pen fails, the probability

distribution between failures is as follows:

Hours between PlotterFailures if All Four Pens

Are Replaced during a RepairProbability

100

.15

110

.25

120

.35

130.20

140

.05

a) Simulate Helmss problem and determine the best policy. Should the firm replace 1 pen

or all 4 pens each time a failure occurs?

b) Develop a second approach to solving this problem (this time without simulation).

Compare the results. How does it affect the policy decision that Helms reached using

simulation?

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