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A computer help desk receives new daily customer arrivals-(Answered)

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Question

  • A computer help desk receives new daily customer arrivals according to the following probability distribution:

# Arrivals

Probability

Random #

0

0.05

01-05

1

0.2

06-25

2

0.3

26-55

3

0.2

56-75

4

0.15

76-90

5

0.1

91-00

The number of customers that the help desk has the capability to serve per day is based on the following probability distribution:


# Served

Probability

Random #

3

0.5

01-50

4

0.3

51-80

5

0.2

81-00


If the number of arrivals exceeds the # served capability, the customers will receive top priority the next day. The random numbers drawn for a 5-day simulation are as follows:


Arrival Random #

Service random #

19

95

34

95

39

92

90

33

97

85


What will the average number of delays be for the 5-day simulation?

0.9/day

1.2/day

None of the alternatives are correct.

0.4/day

2.1/day

Demand per day

0

1

2

3

4

Lead

Time

1

2

Probability

0.15

0.2

0.3

0.2

0.15

0.80

0.20

Random #

01-15

16-35

36-65

66-85

86-00

01-80

81-00



The store orders 4 refrigerators per day to have in stock to meet demand. They are trying to maintain low inventory levels. The holding cost is $5/unit/day. The ordering cost is $20 per order. The lost sale cost is $10/unit. A simulation is to be developed to estimate the average daily inventory cost over 5 days. The table below shows the random numbers to be used for refrigerator demand and lead time on orders:

demand random number

lead time random number

day 1

88

54

day 2

27

94

day 3

32

44

day 4

36

75

day 5

54

71


Assuming that beginning inventory is equal to 5 with no prior orders in transit, what is the overall average daily cost of inventory for the 5 days?

$32.

$53

24

None of the alternatives are correct.

$45

  • A certain grocery store has noted the following figures with regard to the number of people who arrive at its three checkout stands ready to check out, and the time it takes to check out the individuals.

Arrivals/Min.

Frequency

Service Time

in Min

Frequency

0

0.3

1

0.1

1

0.5

2

0.3

2

0.2

3

0.4

4

0.2


Create an appropriate table of interval of random numbers for both variables.
Answer:

Arrivals

Interval of

Random #s

Service Time

Interval of

Random #s

0

01-30

1

01-10

1

31-80

2

11-40

2

81-00

3

41-80

4

81-00


The time between arrivals at a drive-through window of a fast-food restaurant follows the distribution given below. The service time distribution is also given in the table below. Use the random numbers provided to simulate the activity of the first five arrivals. Assume that the window opens at 11:00 a.m. and the first arrival after this is based on the first interarrival time generated.


Time Between

Arrivals

Probability

Service Time

Probability

1

0.2

1

0.3

2

0.3

2

0.5

3

0.3

3

0.2

4

0.2




Random numbers for arrivals: 14, 74, 27, 03
Random numbers for service times: 88, 32, 36, 24


What times does the fourth customer leave the system?

11:06.

None of the alternatives are correct.

11:09

11:04.

11:08.

  • The table below represents the probability distribution for machine breakdowns in a day of operation.

Number of breakdowns

Probability

Interval of

Random Numbers

0

0.20

1-20

1

0.30

21-50

2

0.35

51-85

3

0.15

86-00



According to the table, if a random number of 00 is drawn, what would the simulated number of breakdowns be?

Not enough information provided

2

0

3

1

  • The table below represents the probability distribution for machine breakdowns in a day of operation.

Number of breakdowns

Probability

Interval of

Random Numbers

0

0.20

1-20

1

0.30

21-50

2

0.35

51-85

3

0.15

86-00




According to the table, what is the probability of at least one breakdown?

0.5

0.8

0.3

0.2

0.85


1. A computer help desk receives new daily customer arrivals according to the following

 

probability distribution:

 

# Arrivals Probability

 

0

 

0.05

 

1

 

0.2

 

2

 

0.3

 

3

 

0.2

 

4

 

0.15

 

5

 

0.1

 


 

Random #

 

01-05

 

06-25

 

26-55

 

56-75

 

76-90

 

91-00

 


 

The number of customers that the help desk has the capability to serve per day is based on the

 

following probability distribution:

 

# Served

 

3

 

4

 

5

 


 

Probability

 

0.5

 

0.3

 

0.2

 


 

Random #

 

01-50

 

51-80

 

81-00

 


 

If the number of arrivals exceeds the # served capability, the customers will receive top priority

 

the next day. The random numbers drawn for a 5-day simulation are as follows:

 

Arrival

 

Random #

 

19

 

34

 

39

 

90

 

97

 


 

Service

 

random #

 

95

 

95

 

92

 

33

 

85

 


 

What will the average number of delays be for the 5-day simulation?

 

0.9/day

 

1.2/day

 

None of the alternatives are correct.

 

0.4/day

 

2.1/day

 


 

2. The demand for refrigerators at an appliance store adheres to the following probability

 

distribution:

 

Demand per

 

day

 

Probability

 

Random #

 


 

Lead

 

0

 

1

 

2

 

3

 

4

 

Time 1

 

2

 

0.15 0.2

 

0.3

 

0.2

 

0.15

 

0.80 0.20

 

01-15 16-35 36-65 66-85 86-00

 

01-80 81-00

 


 

The store orders 4 refrigerators per day to have in stock to meet demand. They are trying to

 

maintain low inventory levels. The holding cost is $5/unit/day. The ordering cost is $20 per

 

order. The lost sale cost is $10/unit. A simulation is to be developed to estimate the average daily

 

inventory cost over 5 days. The table below shows the random numbers to be used for

 

refrigerator demand and lead time on orders:

 


 

day

 

day

 

day

 

day

 

day

 


 

1

 

2

 

3

 

4

 

5

 


 

deman

 

d

 

rando

 

m

 

numbe

 

r

 

88

 

27

 

32

 

36

 

54

 


 

lead

 

time

 

rando

 

m

 

numbe

 

r

 

54

 

94

 

44

 

75

 

71

 


 

Assuming that beginning inventory is equal to 5 with no prior orders in transit, what is the

 

overall average daily cost of inventory for the 5 days?

 

$32.

 

$53

 

24

 

None of the alternatives are correct.

 

$45

 


 

3. A certain grocery store has noted the following figures with regard to the number of people

 

who arrive at its three checkout stands ready to check out, and the time it takes to check out

 


 

the individuals.

 

Arrivals/Mi

 

n.

 

0

 

1

 

2

 


 

Frequency

 

0.3

 

0.5

 

0.2

 


 

Service Time

 

Frequency

 

in Min

 

1

 

0.1

 

2

 

0.3

 

3

 

0.4

 

4

 

0.2

 


 

Create an appropriate table of interval of random numbers for both variables.

 

Answer:

 

Arrivals

 

0

 

1

 

2

 


 

Interval of

 

Random

 

#s

 

01-30

 

31-80

 

81-00

 


 

Service Time

 


 

Interval of

 

Random #s

 


 

1

 

2

 

3

 

4

 


 

01-10

 

11-40

 

41-80

 

81-00

 


 

The time between arrivals at a drive-through window of a fast-food restaurant follows the

 

distribution given below. The service time distribution is also given in the table below. Use the

 

random numbers provided to simulate the activity of the first five arrivals. Assume that the

 

window opens at 11:00 a.m. and the first arrival after this is based on the first interarrival time

 

generated.

 

Time

 

Between

 

Arrivals

 

1

 

2

 

3

 

4

 


 

Probability Service Time Probability

 

0.2

 

0.3

 

0.3

 

0.2

 


 

1

 

2

 

3

 


 

0.3

 

0.5

 

0.2

 


 

Random numbers for arrivals: 14, 74, 27, 03

 

Random numbers for service times: 88, 32, 36, 24

 


 

What times does the fourth customer leave the system?

 

11:06.

 

None of the alternatives are correct.

 

11:09

 

11:04.

 

11:08.

 


 

4. The table below represents the probability distribution for machine breakdowns in a day of

 

operation.

 

Number of

 

breakdowns

 

0

 

1

 

2

 

3

 


 

Probability

 

0.20

 

0.30

 

0.35

 

0.15

 


 

Interval of

 

Random Numbers

 

1-20

 

21-50

 

51-85

 

86-00

 


 

According to the table, if a random number of 00 is drawn, what would the simulated number of

 

breakdowns be?

 

Not enough information provided

 

2

 

0

 

3

 

1

 


 

5. The table below represents the probability distribution for machine breakdowns in a day of

 

operation.

 

Number of

 

breakdowns

 

0

 

1

 


 

Probability

 

0.20

 

0.30

 


 

Interval of

 

Random Numbers

 

1-20

 

21-50

 


 

2

 

3

 


 

0.35

 

0.15

 


 

51-85

 

86-00

 


 

According to the table, what is the probability of at least one breakdown?

 

0.5

 

0.8

 

0.3

 

0.2

 

0.85

 


 

 

Paper#9209244 | Written in 27-Jul-2016

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