Deck 14: Simulation

Question 1

A table of random numbers must be normally distributed and efficiently generated.

Answer 1

False

Question 2

In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution.

Answer 2

True

Question 3

Starting conditions have no impact on the validity of a simulation model.

Answer 3

False

Question 4

Simulation results will always equal analytical results if 30 trials of the simulation have been conducted.

Question 5

The Monte Carlo process is analogous to gambling devices.

Question 6

In computer mathematical simulation, a system is replicated with a mathematical model that is analyzed with the computer.

Question 7

It's often difficult to validate that the results of a simulation truly replicate reality.

Question 8

Simulations should always be started with an empty system.

Question 9

When using Excel to simulate a system, it is necessary to compute only the probability (relative frequency) distribution.

Question 10

Random numbers are equally likely to occur.

Question 11

Monte Carlo is a technique for selecting numbers randomly from a probability distribution.

Question 12

Random numbers generated by a mathematical process instead of a physical process are pseudorandom numbers.

Question 13

Excel can only be used to simulate systems that can be represented by continuous random variables.

Question 14

Simulation applies mathematical models to determine optimal solutions to business problems.

Question 15

Random numbers are typically generated on the computer using a numerical technique.

Question 16

Developing the cumulative probability distribution helps to determine random number ranges.

Question 17

A long period of real time can be represented by a short period of simulated time.

Question 18

In Excel the VLOOKUP function is used to determine values for continuous random variables.

Question 19

Manual simulation is limited because of the amount of real time required to simulate even one trial.

Question 20

Validation of a simulation model occurs when the true steady state average results have been reached.

Question 21

Simulation models must be ________ to make sure they are accurately replicating the system being simulated.

Question 22

Developing the ________ probability distribution helps to determine random number ranges.

Question 23

In a continuous probability function, the area under the curve represents the probability of occurrence of the random variable.

Question 24

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

Determine the drying time for these 5 random numbers: 0.13, 0.09, 0.19, 0.81, and 0.12.

Question 25

The ________ command is used in generating the random numbers with Excel.

Question 26

Cumulative probabilities are analogous to the discrete ranges of random numbers used in the Monte Carlo process.

Question 27

Consider the following distribution and random numbers:
If a simulation begins with the first random number, what would the first simulation value would be ________.

Question 28

In order to determine the value of discrete demand in a simulation model using Excel, the ________ function is used to associate a specific value of demand with a random number.

Question 29

________ is a technique for selecting numbers randomly from a probability distribution.

Question 30

________ is a risk analysis and forecasting program that uses Monte Carlo simulation.

Question 31

Random numbers of a mathematical process instead of a physical process are ________ numbers.

Question 32

Applications of simulation models reflecting continuous distributions are more common than those of models employing discrete distributions.

Question 33

A table of random numbers must be ________ distributed, efficiently generated, and absent of patterns.

Question 34

The Monte Carlo process is analogous to and derives its name from ________.

Question 35

________ are numbers equally likely to be chosen from a large population of numbers.

Question 36

A long period of real time is represented by a short period of ________.

Question 37

Integrating a function from zero to any value of a random variable x is an important step in determining the cumulative probability of that value of x.

Question 38

________, ________, and ________ are common applications of simulation.

Question 39

A random number table features numbers that are derived from a(n) ________ process.

Question 40

In the Monte Carlo process, values for a random variable are generated by sampling from a(n) ________.

Question 41

After plowing through contracts for a decade, the contract writer knew about how long it took to crank out the material necessary to satisfy a contract's requirements. The distribution could be modeled using the data provided in this table.

If each contract is worth $4000 but it costs $200 per week to work on a contract, what is the profit resulting from a simulation drawing of the numbers 72, 36, 8, 71, and 94?

Question 42

After plowing through contracts for a decade, the contract writer knew about how long it took to crank out the material necessary to satisfy a contract's requirements. The distribution could be modeled using the data provided in this table.

If the ten numbers generated are 87, 84, 99, 18, 81, 75, 32, 87, 46, and 35, what is the resultant expected average completion time?

Question 43

If f(x) = 2x, what is the equation for generating x, given the random number r?

Question 44

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

Determine the drying time for these 5 random numbers: 0.53, 0.95, 0.97, 0.96, and 0.07.

Question 45

George Pourbabaee owns a gas station. The cars arrive at the gas station according to the following inter-arrival time distribution. The time to service a car is given by the following service time distribution.

Using the following random number sequence: 92, 44, 15, 97, 21, 80, 38, 64, 74, 08, estimate the average customer waiting time, average idle time of the assistant, and the average time a car spends in the system.

Question 46

After plowing through contracts for a decade, the contract writer knew about how long it took to crank out the material necessary to satisfy a contract's requirements. The distribution could be modeled using the data provided in this table.

If each contract is worth $5000 but it costs $300 per week to work on a contract, what is the profit resulting from a simulation drawing of the numbers 72, 36, 8, 71, and 94 to represent contract durations?

Question 47

A graduate research assistant "moonlights" at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers have to wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he's cooking an order, they have to wait until he's completed the current order. He is working on the simulation and a portion is shown below.
Complete the table below and determine the average customer wait time.

Question 48

Consider the following manual simulation of machine breakdowns and repair.

What operating charactistics can be obtained from this simulation?

Question 49

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
Compute the mean drying time.

Question 50

A business professor wishes to model the duration of his commute through the busy streets of Bangalore. He decides to model it based on the number of auto-rickshaws that he passes during the first ten minutes of the drive. The continuous probability distribution 7x - 2 serves as a good model.
What is the integral from 0 to 4 for this distribution?

Question 51

A newsboy sells newspapers and his goal is to maximize profit. He kept a record of his sales for 125 days with the following result:
His ordering policy is to order an amount each day that is equal to the previous day's demand.
A newspaper costs the carrier 50 cents and he sells it for $1.00. Unsold papers are returned and he receives 25 cents (for a loss of 25 cents).
Develop the cumulative distribution table and the corresponding random numbers.

Question 52

An answering service for a doctor's office wants to evaluate the service by simulation calls. They used past data to determine the distributions for the time between calls and the time spent on the phone with patients.
Use the table below to manually simulate 8 calls. The time of the call and the service time have already been determined.

Calculate the average waiting time per customer.
Calculate the utilization of the operator.

Question 53

The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours of operation is observed to be the following:
Based on the above frequencies, use two-digit random numbers, start with random number 00, and determine the random number ranges for the data set given above.

Question 54

A graduate research assistant "moonlights" at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers have to wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he's cooking an order, they have to wait until he's completed the current order. He is working on the simulation and a portion is shown below.
Complete the table and determine the average customer waiting time and the utilization of the cook.

Complete the table and determine the average customer waiting time and the utilization of the cook.

Question 55

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
What is the average drying time if you simulate 10 trials using these random numbers:
0.13, 0.09, 0.19, 0.81, 0.12, 0.53, 0.95, 0.97, 0.96, and 0.07.

Question 56

A normal distribution has a mean of 500 and a standard deviation of 50. A manager wants to simulate two values from this distribution and has drawn these random numbers: -0.6 and 1.4. What are the two values, respectively?

Question 57

After plowing through contracts for a decade, the contract writer knew about how long it took to crank out the material necessary to satisfy a contract's requirements. The distribution could be modeled using the data provided in this table.

If the first four random numbers are 17, 33, 64, and 8, what is the average number of weeks?

Question 58

Assume that order prep time is based on the following distribution:

Complete the following table given that the random numbers for order prep time for customers 3, 4, and 5 are 62, 93, and 26, respectively.

What is the average customer waiting time and the graduate student's utilization?

Question 59

Given the following random number ranges and the following random number sequence: 62, 13, 25, 40, 86, 93, determine the average demand for the following distribution of demand.

Question 60

The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours of operation is observed to be the following:
Determine the probability distribution of car arrivals.

Question 61

Random numbers generated by a ________ process instead of a ________ process are pseudorandom numbers.

A) physical, physical
B) physical, mathematical
C) mathematical, physical
D) mathematical, mathematical

Question 62

A newsboy sells newspapers and his goal is to maximize profit. He kept a record of his sales for 125 days with the following result:
His ordering policy is to order an amount each day that is equal to the previous day's demand.
A newspaper costs the carrier 50 cents and he sells it for $1.00. Unsold papers are returned and he receives 25 cents (for a loss of 25 cents).
Use the information and random numbers given in the table below to simulate the sale of newspapers for 10 days.

After completing the simulation, determine his total revenue for the ten days as well as monetary losses that result from unmet demand and unsold papers.

Question 63

________ numbers are numbers derived from a mathematical process that appear to be random.

A) Random
B) Pseudorandom
C) Randomized
D) Semi-random

Question 64

The ________ process is analogous to gambling devices.

A) Simulation
B) Monte Carlo
C) Monaco
D) none of the above

Question 65

A table of random numbers must be

A) in descending order.
B) efficiently generated.
C) normally distributed.
D) in ascending order.

Question 66

Which of the following would not be considered a limitation of simulation modeling?

A) Models are typically unstructured.
B) Validation of simulation models can be difficult.
C) The cost of building simulation can be prohibitive.
D) Simulation allows flexibility in analyzing systems.

Question 67

________ is not part of a Monte Carlo simulation.

A) Analyzing results
B) Analyzing a real problem
C) Finding an optimal solution
D) Evaluating the results

Question 68

Pseudorandom numbers exhibit a ________ in order to be considered truly random.

A) limited number of possible outcomes
B) uniform distribution
C) detectable pattern
D) detectable run of certain numbers

Question 69

Analogue simulation replaces a physical system with an analogous physical system that is ________ to manipulate.

A) harder
B) easier
C) equally difficult
D) more expensive

Question 70

Consider the following frequency of demand and random numbers:
$$\begin{array}{l}\begin{array} { c c } &\text { Relative }\\\text { Demand } & \text { Frequency } \\\hline 0 & 0.15 \\1 & 0.30 \\2 & 0.25 \\3 & 0.15 \\4 & 0.15\end{array}\end{array}$$ Random numbers: 0.13, 0.81, 0.53.

-If the simulation begins with the second random number, the simulated value for demand would be:

A) 1
B) 2
C) 3
D) 4

Question 71

In assigning random numbers to probabilistic events in a simulation,

A) several events are associated with the same random number.
B) every random number is associated with a particular event.
C) every event is associated with the same random number.
D) the events dictate the seed number of the random number stream.

Question 72

Simulations are normally done

A) manually.
B) in a casino.
C) by a spreadsheet.
D) on the computer.

Question 73

Consider the following frequency of demand and random numbers:
$$\begin{array}{l}\begin{array} { c c } &\text { Relative }\\\text { Demand } & \text { Frequency } \\\hline 0 & 0.15 \\1 & 0.30 \\2 & 0.25 \\3 & 0.15 \\4 & 0.15\end{array}\end{array}$$ Random numbers: 0.13, 0.81, 0.53.

-If the simulation begins with the third random number, the simulated value for demand would be:

A) 0
B) 1
C) 2
D) 3
E) 4

Question 74

Consider the following frequency of demand and random numbers:
$$\begin{array}{l}\begin{array} { c c } &\text { Relative }\\\text { Demand } & \text { Frequency } \\\hline 0 & 0.15 \\1 & 0.30 \\2 & 0.25 \\3 & 0.15 \\4 & 0.15\end{array}\end{array}$$ Random numbers: 0.13, 0.81, 0.53.

-If the simulation begins with the first random number, the simulated value for demand would be:

A) 0
B) 1
C) 2
D) 3

Question 75

________ are the values that express the state of the system being modeled at the beginning of the Monte Carlo simulation.

A) Outputs
B) Random events
C) Initial conditions
D) Random numbers

Question 76

________ is a technique for selecting numbers randomly from a probability distribution.

A) Marseille
B) Monaco
C) Monte Carlo
D) Analogue simulation

Question 77

Simulation does not usually provide recommended decisions. Instead it provides

A) operating characteristics.
B) optimal solutions.
C) realistic results.
D) system parameters.

Question 78

For the following frequency distribution of demand, the random number 0.23 would be interpreted as a demand of: $$\begin{array} { c c } \hline \text { Demand } & \text { Frequency } \\\hline 0 & 32 \\1 & 26 \\2 & 24 \\3 & 18\end{array}$$

A) 0
B) 1
C) 2
D) 3

Question 79

In the Monte Carlo process, values for a random variable are generated by ________ a probability distribution.

A) sampling from
B) running
C) integrating
D) implementing

Question 80

A seed value is a(n)

A) steady state solution of a simulation experiment.
B) number used to start a stream of random numbers.
C) first run of a simulation model.
D) analytic solution of a simulation experiment.