Homework answers / question archive / Harran University - Yeniehir Campus STAT 201 Chapter 14 Simulation Modeling 1)Simulation of a business or process is generally performed by building a mathematical model to represent the process or system

Harran University - Yeniehir Campus STAT 201 Chapter 14 Simulation Modeling 1)Simulation of a business or process is generally performed by building a mathematical model to represent the process or system

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Harran University - Yeniehir Campus

STAT 201

Chapter 14 Simulation Modeling

1)Simulation of a business or process is generally performed by building a mathematical model to represent the process or system.

 

2)            Simulation models are designed to generate optimal solutions, which can then be applied to real-world situations.

 

3)            A major advantage of using simulation techniques is to be able to study the interactive effect of individual components/variables.

 

4)            Despite the power of simulation, less than 20% of the largest U.S. corporations use simulation in corporate planning.

 

5)            One of the major advantages of simulation is "time compression," i.e., the ability to study in a relatively short period, activities that would, in reality, take place over a period of days, months, or even years.

 

6)            To "simulate" is to try to duplicate the features, appearance, and characteristics of a real system.

 

7)            While it is powerful, simulation is not considered to be a flexible quantitative analysis tool.

8)            Simulation can use any probability distribution that the user defines; it does not require standard distributions.

 

9)            One disadvantage of simulation is that it does not allow for "what-if?" types of questions.

10)          Simulation models may contain both deterministic and probabilistic variables.

 

11)          Monte Carlo simulation was developed as a quantitative technique by the great mathematician John von Neumann during World War I.

 

12)          Simulation models are limited to using standard probability distributions such as Poisson, exponential, normal, etc.

 

13)          The Monte Carlo simulation is used with variables that are probabilistic.

14)          When using a random number generator, one should never start in the middle of the table of random numbers.

 

15)          If we are using a Monte Carlo simulation model, we should expect the model to produce the same results for each set of random numbers used.

 

16)          The four disadvantages of simulation are cost, its trial-and-error nature, time compression, and uniqueness.

 

17)          The wider the variation among results produced by using different sets of random numbers, the longer we need to run the simulation to obtain reliable results.

 

18)          Simulation is very flexible. Thus, its solutions and inferences are usually transferable to other problems.

 

19)          Simulation models are useful for economic order quantity problems with probabilistic demand and lead time.

 

20)          A flow diagram is helpful in the logical coding procedures for programming a simulation process.

Answer:  TRUE

21)          If, in a simple queuing or waiting line problem, we wish to know the maximum likely waiting time, or the maximum likely length of the line, we must use a simulation model.

22)          If, for a simple queuing or waiting line problem, we compare the solution from an analytical model with that from a simulation, we will typically find them to be exactly the same.

 

23)          The advantage of simulation over queuing or waiting line models is that simulation allows us to relax our assumptions regarding arrival and service distributions.

24)          Simulation of maintenance problems can help management analyze various staffing strategies based on machine downtime and labor cost.

 

25)          When establishing a probability distribution based on historical outcomes, the relative frequency for each possible outcome of a variable is found by dividing the frequency of each outcome by the total number of observations.

 

26)          Operational gaming involves a single player competing with the computer simulated game.

 

27)          There are three categories of simulation models: Monte Carlo, operational gaming, and systems simulation.

Answer:  TRUE

28)          Validation relates to building the right model.

 

29)          The following is not an advantage of simulation:

A) It allows for the study of what-if questions. B) Each simulation model is unique.

C)            It allows the study of interaction of components or variables to determine which are important.

D)           It allows time compression.

 

E)            None of the above

 

30)          Simulation can be effectively used in many

A)           inventory problems.

B)            plant layout problems.

C)            maintenance policy problems.

D)           sales forecasting problems. E) All of the above

 

31)          Monte Carlo simulation was developed by           . A) John von Neumann

B)            Eric von Brock

C)            A.K. Erlang

D)           P.K. Poisson

E)            J.D. Monte Carlo

 

32)          In assigning random numbers in a Monte Carlo simulation, A) it is important to develop a cumulative probability distribution.

B)            it is important to use a normal distribution for all variables simulated.

C)            it is not important to assign probabilities to an exact range of random number intervals.

D)           All of the above

E)            None of the above

Table 14-1

A new young mother has opened a cloth diaper service. She is interested in simulating the

number of diapers required for a one-year- old. She hopes to use this data to show the cost effectiveness of cloth diapers. The table below shows the number of diapers demanded daily and the probabilities associated with each level of demand.

 

Daily Demand   

Probability          Interval of

Random Numbers

5              0.30        01-30

6              0.50        31-80

7              0.05        81-85

8              0.15        86-00

33)          According to Table 14-1, if the random number 40 were generated for a particular day, what would the simulated demand be for that day?

A) 5 B) 6

C)            7

D)           20

E)            None of the above

 

34)          According to Table 14-1, if the random number 96 were generated for a particular day, what would the simulated demand be for that day?

A)           5

B)            6

C)            7 D) 8

E) None of the above

 

35)          According to Table 14-1, what is the cumulative probability that demand is less than or equal to 7?

A) 0.85

B) 0.95

C) 0.80

D) 0.15

E) None of the above

Table 14-2

A pharmacy is considering hiring another pharmacist to better serve customers. To help

 

analyze this situation, records are kept to determine how many customers will arrive in any 10-minute interval. Based on 100 ten-minute intervals, the following probability distribution has been developed and random numbers assigned to each event.

Number of

Arrivals

Probability          Interval of

Random Numbers

6              0.2          01-20

7              0.3          21-50

8              0.3          51-80

9              0.1          81-90

10           0.1          91-00

 

36)          According to Table 14-2, the number of arrivals in any 10-minute period is between 6 and 10, inclusive. Suppose the next three random numbers were 18, 89, and 67, and these were used to simulate arrivals in the next three 10-minute intervals. How many customers would have arrived during this 30-minute time period?

A) 22 B) 23

C)            24

D)           25

E)            None of the above

 

37)          According to Table 14-2, the number of arrivals in any 10-minute period is between 6 and 10, inclusive. Suppose the next three random numbers were 20, 50, and 79, and these were used to simulate arrivals in the next three 10-minute intervals. How many customers would have arrived during this 30-minute time period?

A)           18

B)            19

C)            20 D) 21

E) None of the above

 

38)          According to Table 14-2, the number of arrivals in any 10-minute period is between 6 and 10 inclusive. Suppose the next 3 random numbers were 02, 81, and 18. These numbers are used to simulate arrivals into the pharmacy. What would the average number of arrivals per 10-minute period be based on this set of occurrences?

A) 6 B) 7

C)            8

D)           9

E)            None of the above

 

Table 14-3

A pawn shop in Arlington, Texas, has a drive-through window to better serve customers. The

following tables provide information about the time between arrivals and the service times required at the window on a particularly busy day of the week. All times are in minutes.

Time Between

Arrivals

Probability         

Interval of Random Numbers

1              0.1          01-10

2              0.3          11-40

3              0.4          41-80

4              0.2          81-00

                               

Service Time      Probability          Interval of Random Numbers

1              0.2          01-20

2              0.4          21-60

3              0.3          61-90

4              0.1          91-00

 

The first random number generated for arrivals is used to tell when the first customer

 

arrives after opening.

 

39)          According to Table 14-3, the time between successive arrivals is 1, 2, 3, or 4 minutes. If the store opens at 8:00 a.m., and random numbers are used to generate arrivals, what time would the first customer arrive if the first random number were 02?

A) 8:01

B) 8:02

C) 8:03

D) 8:04

E) None of the above

 

40)          According to Table 14-3, the time between successive arrivals is 1, 2, 3, or 4 minutes. The store opens at 8:00 a.m., and random numbers are used to generate arrivals and service times. The first random number to generate an arrival is 39, while the first service time is generated by the random number 94. What time would the first customer finish transacting business?

A) 8:03

B) 8:04

C) 8:05

D) 8:06

E) None of the above

 

41)          According to Table 14-3, the time between successive arrivals is 1, 2, 3, or 4 minutes. The store opens at 8:00 a.m., and random numbers are used to generate arrivals and service times. The first 3 random numbers to generate arrivals are 09, 89, and 26. What time does the third customer arrive?

A) 8:07

B) 8:08

C) 8:09

D) 8:10

E) None of the above

 

42)          According to Table 14-3, the time between successive arrivals is 1, 2, 3, or 4 minutes. The store opens at 8:00 a.m., and random numbers are used to generate arrivals and service times. The first two random numbers for arrivals are 95 and 08. The first two random numbers for service times are 92 and 18. At what time does the second customer finish transacting business?

A) 8:07

B) 8:08

C) 8:09

D) 8:10

E) None of the above

 

Table 14-4

 

Variable Value   Probability          Cumulative Probability

0              0.08        0.08

1              0.23        0.31

2              0.32        0.63

3              0.28        0.91

4              0.09        1.00

 

Number of

Runs     

200

Average Value  2.10

 

43)          According to Table 14-4, which presents a summary of the Monte Carlo output from a simulation of 200 runs, there are 5 possible values for the variable of concern. If this variable represents the number of machine breakdowns during a day, what is the probability

 

that the number of breakdowns is 2 or fewer? A) 0.23

B) 0.31

C) 0.32

D) 0.63

E) None of the above

 

44)          According to Table 14-4, which presents a summary of the Monte Carlo output from a simulation of 200 runs, there are 5 possible values for the variable of concern. If this variable represents the number of machine breakdowns during a day, what is the probability that the number of breakdowns is more than 4?

A) 0

B) 0.08

C) 0.09

D) 1.00

E) None of the above

 

45)          According to Table 14-4, which presents a summary of the Monte Carlo output from a simulation of 200 runs, there are 5 possible values for the variable of concern. If random numbers between 01 and 100 are used to generate values, then a random draw of 72 would produce a variable value of       .

A)           0

B)            1

C)            2 D) 3

E) 4

 

46)          Which of the following represents the primary reason simulation cannot be used for the classic EOQ model?

A)           too many parameters involved

B)            too many decision variables

C)            EOQ models are probabilistic D) EOQ models are deterministic

E) None of the above

 

47)          Which of the following scenarios would require simulation for a queuing model?

A)           Poisson arrival process

B)            exponential service time

C)            deterministic arrival process

D)           deterministic service time E) None of the above

 

48)          Simulation models can be broken down into which of the following three categories?

A)           Monte Carlo, queuing, and inventory

B)            queuing, inventory, and maintenance policy

C)            Monte Carlo, operational gaming, systems simulation

D)           inventory, systems simulation, and operational gaming

E)            None of the above

 

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

 

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 Probabilit

y

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.

 

 

 

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

 

 

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.

 

 

 

 

 

 

 

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?

 

 

 

 

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.

 

 

 

 

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?

 

 

 

 

 

 

 

 

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.