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Exam 12: Simulation

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Question 21

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On a visit to an amusement park you pass someone who has just ridden a roller coaster and asks you for directions to the First Aid Station. Realizing that traffic at the First Aid Station would be something to study with simulation, you gather some information. Two EMTs staff the station, and patients wait and go to the first one available. People coming there can be divided into two groups: those who need something minor (e.g. Tylenol, a band-aid) or those who need more help. Assume those in the first group constitute 25% of the patients and take 5 minutes to have their problem solved. Those in the second group need an uncertain amount of time, as given by a probability distribution. Develop a flowchart for this simulation problem.

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Let
i = patient counter
AT(i) = arrival ...

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Question 22

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For the past 50 days, daily sales of laundry detergent in a large grocery store have been recorded (to the nearest 10). $\begin{array} { c c } \text { Units Sold } & \text { Number of Times } \\\hline 30 & 8 \\40 & 12 \\50 & 15 \\60 & 10 \\70 & 5\end{array}$ a.Determine the relative frequency for each number of units sold. b.Suppose that the following random numbers were obtained using Excel: .12 .96 .53 .80 .95 .10 .40 .45 .77 .29 Use these random numbers to simulate 10 days of sales.

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Question 23

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Simulation

Seventy-five percent of calls arriving at a help line can be handled by the person who answers the phone, but the remaining 25% of them will need to be referred to someone else. Assume that every call requires one minute of attention by the person who answers the phone (either to answer the question or to figure out how the referral should be handled). Calls that are referred need an additional amount of time, as given in the table below. $\begin{array} { c c } \text { Time Required } & \text { Probability } \\\hline 3 \text { minutes } & .25 \\5 \text { minutes } & .35 \\10 \text { minutes } & .40\end{array}$ Callers are served on a first come, first served basis, and are put on hold until the line is free. Use the random numbers to simulate what happens to 10 callers. (Use the random numbers in order -- from left to right, first row first -- as you need them.) What percentage of your callers needs to be referred? Of those who had to be referred, what is the average referral time? $\begin{array} { l }.82&.39&.16&.79&.56&.62&.13&.04&.42&.81\\.85&.32&.64&.90&.73&.02&.76&.03&.86&.67\end{array}$

In a Monte Carlo simulation, each simulation trial is dependent upon the result of a previous trial.

A discrete-event simulation reviews the status of the system periodically, whether or not an event occurs.

Values for the probabilistic inputs to a simulation

The word "uniform" in the term "uniform random numbers" means

Which of the following statements is INCORRECT regarding the advantages of simulation?

If customer 2 has a service time of 1.6, and if customer 3 has an interarrival time of 1.1 and a service time of 2.3, when will customer 3's service be completed?

The parameters of a simulation model are the controllable inputs.

Arrivals to a truck repair facility have an interarrival time that is uniformly distributed between 20 and 50 minutes. Service times are normally distributed with mean 30 minutes and standard deviation 10 minutes. Develop a spreadsheet model to simulate the arrival of 100 trucks. Collect information on the time the repair facility is idle and on the average waiting time for trucks.

When events occur at discrete points in time

A quantity that is difficult to measure with certainty is called a

Computer-generated random numbers are not technically random.

Greenfields is a mail order seed and plant business. The size of orders is uniformly distributed over the interval from $25 to $80. Use the following random numbers to generate the size of 10 orders. .41 .99 .07 .05 .38 .77 .19 .12 .58 .60

Computer-generated random numbers are normally distributed over the interval from 0 to 1.

Using simulation to perform risk analysis is like playing out many what-if scenarios by randomly generating values for the probabilistic inputs.

A simulation model uses the mathematical expressions and logical relationships of the

Simulation is to be used to study customer waiting patterns at several branches of an organization. Acknowledging that arrivals and service times follow different distributions over the branches, of what use is the development of a general simulation model?