Exam 16: 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

Simulation models that must take into account how the system changes or evolves over time are referred to as dynamic simulation models.

Computer-generated random numbers are not technically random.

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution. Minutes Relative Frequency 3 .14 4 .30 5 .27 6 .18 7 .11 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?

When events occur at discrete points in time

Simulation allows the user to specify certain desired results (for example,profit or service level values),and then the necessary model parameters and operating policies are determined.

The degree of risk is associated with the probability or magnitude of loss.

For the past 50 days,daily sales of laundry detergent in a large grocery store have been recorded (to the nearest 10). Units Sold Number of Times 30 8 40 12 50 15 60 10 70 5 a.Determine the relative frequency for each number of units sold. b.Suppose that the following random numbers were obtained using Excel:.12.96.53.80.95.10.40.45.77.29Use these random numbers to simulate 10 days of sales.

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? Freeway 5 63 88 55 46 55 Freeway 57 59 09 57 87 07 Freeway 55 71 95 83 44 34 Freeway 91 51 79 09 67 15

As the owner of a rent-a-car agency you have determined the following statistics: Potential Rentals Daily Probability Rental Duration Probability 0 .10 1 day .50 1 .15 2 day .30 2 .20 3 days .15 3 .30 4 days .05 4 .25 The gross profit is $40 per car per day rented.When there is demand for a car when none is available there is a goodwill loss of $80 and the rental is lost.Each day a car is unused costs you $5 per car.Your firm initially has 4 cars. a.Conduct a 10-day simulation of this business using Row #1 below for demand and Row #2 below for rental length. Row \#1: 63 88 55 46 55 69 13 17 36 81 Row \#2: 59 09 57 87 07 92 29 28 64 36 b.If your firm can obtain another car for $200 for 10 days, should you take the extra car?

Values for the probabilistic inputs to a simulation

The number of units expected to be sold is uniformly distributed between 300 and 500.If r is a random number between 0 and 1,then the proper expression for sales is

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

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

Each simulation run provides only a sample of how the real system will operate.

A static simulation model is used in situations where the state of the system affects how the system changes or evolves over time.

Attendees at the National Management Science Society (NMSS)Conference register by first standing in line to pay their fees.They then proceed to a designated line based on the first letter of their last name to collect their conference materials. At the conference,it is planned to have three different parallel lines for the collection of materials: one each for people whose last names begin with A-H,I-Q,and R-Z respectively. During each minute of the morning registration period it is anticipated that attendees will arrive to pay their fees according to the following distribution: Number of Arrivals Probability 0 .30 1 .30 2 .30 3 .10 The time to pay one's fees is either one minute or two minutes depending upon whether one uses a check or credit card.The probability of a one-minute time is .60. After paying his fees,an attendee then goes to the correct line for the conference materials.At this year's conference 35% of the attendees have last names beginning with A-H,36% with last names beginning with I-Q,and 29% with last names beginning with R-Z.The time required to pick up conference materials is fixed at 2 minutes. a. Simulate the waiting line for the first 10 minutes of the morning registration that begins at 8:00 AM. Use the following random numbers to generate:Number of arrivals in any given minute: 71, 95, 83, 44, 34, 49, 88, 56, 05, 39Registration fee service time: 51, 79, 09, 67, 15, 58, 04, 78, 30, 56First letter of the last name: 15, 08, 19, 45, 76, 42, 38, 47, 82, 37 b. What is the average size of the waiting line to pay fees (not including the person being served), and the average customer waiting time to pay fees based on this simulation?

The parameters of a simulation model are the controllable inputs.

In comparing different policies using simulation,one should use the same set of random numbers whenever possible.

A graphical tool that helps describe the logic of the simulation model is a