Exam 12: Simulation

Computer-generated random numbers are not technically random.

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?

Susan Winslow has two alternative routes to travel from her home in Olport to her office in Lewisburg. She can travel on Freeway 5 to Freeway 57 or on Freeway 55 to Freeway 91. The time distributions are as follows: ​ Do a five-day simulation of each of the two combinations of routes using the random numbers below. Based on this simulation, which routes should Susan take if her objective is to minimize her total travel time?

Simulation is a trial-and-error approach to problem solving.

An airline reservation system first asks customers whether they want to schedule a domestic or an international flight. Sixty-five percent of the reservations are for domestic flights. The time distribution of advance sales is also important, and it is given below. ​ a. Place the appropriate random number ranges in the tables above. b. Set up and perform a simulation for three customers. Determine whether they want a domestic or international flight, and how far in advance the reservation is being made. Use random numbers from this list: .632 .715 .998 .671 .744 .021

To use Excel to generate a normally distributed random variable, you must know the mean and standard deviation of the distribution and have a random number between 0 and 1.

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.

Simulation is an optimization technique.

Validation determines that the computer procedure is operating as it is intended to operate.

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.

The process of generating probabilistic inputs and computing the value of the output is called

Three airlines compete on the route between New York and Los Angeles. Stanton Marketing has performed an analysis of first class business travelers to determine their airline choice. Stanton has modeled this choice as a Markov process and has determined the following transition probabilities. ​ a. Show the random number assignments that can be used to simulate the first class business traveler's next airline when her last airline is A, B, and C. b. Assume the traveler used airline C last. Simulate which airline the traveler will be using over her next 25 flights. What percent of her flights are on each of the three airlines? Use the following random numbers, going from left to right, top to bottom.

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

​Why would one want to use a general purpose programming language rather than a spreadsheet to develop a simulation?

A simulation model used in situations where the state of the system at one point in time does not affect the state of the system at future points in time is called a

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. 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?

​How can historical information be used to create discrete probability distributions?

Verification is the process of ensuring that the simulation model provides an accurate representation of the real system.

For the past 50 days, daily sales of laundry detergent in a large grocery store have been recorded (to the nearest 10). ​ 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.

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution. ​ a. Compute the mean drying time. b. Using these random numbers, simulate the drying time for 12 processes. .33 .09 .19 .81 .12 .88 .53 .95 .77 .61 .91 .47 c. What is the average drying time for the 10 processes you simulated?