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49) Which of the following is not considered one of the 5 steps of Monte Carlo Simulation?
A) establishing probability distributions for important input variables
B) generating random number
C) building a cumulative probability distribution for each input variable
D) establishing an objective function
E) simulating a series of trials
50) The logic in a simulation model is presented graphically through which of the following?
A) scatterplot
B) flowchart
C) blueprint
D) decision tree
E) None of the above
51) The use of simulations in competitive situations is called
A) Monte Carlo simulation.
B) systems simulation.
C) operational gaming.
D) virtual reality.
E) None of the above
52) The process of comparing a model to the real system that it represents to make sure it is accurate is called
A) validation.
B) verification.
C) simulation.
D) experimentation.
E) None of the above
53) The process of determining that the computer model is internally consistent and following the logic of the
conceptual model is called
A) validation.
B) verification.
C) simulation.
D) experimentation.
E) None of the above
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Topic: OTHER SIMULATION ISSUES
54) The number of cars arriving at a self–service gasoline station during the last 50 hours of operation are as
follows:
# of Cars
Arriving Frequency
6 10
7 14
8 18
9 8
Create an appropriate table of interval of random numbers.
55) Customer arrivals adhere to the following probability distribution:
# Arrivals Probability
0 0.1
1 0.2
2 0.3
3 0.2
4 0.1
5 0.1
Create an appropriate table of interval of random numbers.
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56) Consider the interval of random numbers presented below. The following random numbers have been
generated: 99, 98, 26, 09, 49, 52, 33, 89, 21, 37. Simulate 10 hours of arrivals at this gas station. What is the average
number of arrivals during this period?
# of Cars Interval of
Random Numbers
6 01–20
7 21–48
8 49–84
9 85–00
57) The number of machine breakdowns in a day is 0, 1, or 2, with probabilities 0.6, 0.3, and 0.1, respectively. The
following random numbers have been generated: 13, 10, 02, 18, 31, 19, 32, 85, 31, 94. Use these numbers to
generate the number of breakdowns for 10 consecutive days. What proportion of these days had at least one
breakdown?
58) 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.
59) A certain grocery store has created the following tables of intervals of random numbers 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. Simulate the utilization rate of the three checkout stands over four minutes using the following
random numbers for arrivals: 07, 60, 49, and 95. Use the following random numbers for service: 77, 76, 51, and
16. Describe the results at the end of the four–minute period.
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
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Topic: MONTE CARLO SIMULATION
60) Average daily sales of a product are 8 units. The actual number of sales each day is either 7, 8, or 9, with
probabilities 0.3, 0.4, and 0.3, respectively. The lead time for delivery of this averages 4 days, although the time
may be 3, 4, or 5 days, with probabilities 0.2, 0.6, and 0.2. The company 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) and 52, 78, 13, 06, 99, 98, 80, 09, 67, 89, 45 (set 2). Use set 1 of
these to generate lead times and use set 2 to simulate daily demand. Simulate 2 ordering periods with this and
determine how often the company runs out of stock before the shipment arrives. Assume 32 units on–hand and
an order was just placed.
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61) 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?
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62) Henry has a newspaper stand where he sells papers for $0.50 each. The papers cost him $0.30 each, giving
him a 20–cent profit on each one he sells. From past experience, Henry knows that
20% of the time he sells 100 papers
20% of the time he sells 150 papers
30% of the time he sells 200 papers
30% of the time he sells 250 papers
Assuming that Henry believes the cost of a lost sale is 10 cents and any unsold papers cost him $0.30, simulate
Henry’s profit outlook over 5 days if he orders 175 papers for each of the 5 days. Use the following random
numbers: 52, 06, 50, 88, 53.
63) A local computer store is running a sale on the first 99 flat panel monitors sold. There is an equally likely
chance of 0–99 units being sold. Each monitor cost $250, and profit is $10 per monitor sold. That is, profit equals –
$250 + $10X, where X = the number of monitors sold. The mean amount you would expect to sell is 49.5 units.
(a) Calculate the expected profit.
(b) Simulate the sale of 10 items, using the following double digit random numbers: 47, 77, 98, 11, 02, 18, 31, 20,
32, 90.
(c) Calculate the average profit in (b) above, and compare with the results of (a) above.
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64) The demand for refrigerators at an appliance store adheres to the following probability distribution:
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?
65) 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?
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66) What are the seven steps of simulation?
67) List the major advantages of simulation techniques.
68) List the major disadvantages of simulation techniques.
69) Explain what is meant by a Monte Carlo simulation.
70) Explain what is meant by operational gaming and give one example.