Model F Simulation

From a portion of a probability distribution, you read that P(demand = 0) is 0.05 and P(demand = 1) is 0.10. The cumulative probability for demand = 1 would be which of the following?

.15

What is the cumulative probability of selling 4 tires? tires sold: 0, 1, 2, 3, 4, probablity: .1, .2, .15, .3, .25

1

Identify the seven steps involved in using simulation.

1. Define the problem. 2. Introduce the important variables associated with the problem. 3. Construct a numerical model. 4. Set up possible courses of action for testing by specifying values of variables. 5. Run the experiment. 6. Consider the results (possibly modifying the model or changing data inputs). 7. Decide what course of action to take.

A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time. This distribution has been prepared for Monte Carlo analysis. The first four random numbers drawn are 07, 60, 77, and 49. What is the average service time of this simulation?

13.5 min

A distribution of lead times in an inventory problem indicates that lead time was 1 day 20 percent of the time, 2 days 30 percent of the time, 3 days 30 percent of the time, and 4 days 20 percent of the time. This distribution has been prepared for Monte Carlo analysis. The first four random numbers drawn are 06, 63, 57, and 02. What is the average lead time of this simulation?

2 days

The number of tires sold at a car garage varies randomly between 0 and 4 each hour, with equally probability for each possible outcome. What set of random numbers (on the 01-100 scale) would tire sales of 2 be assigned?

41 through 60

A distribution of service times at a waiting line indicates that service takes 6 minutes 30 percent of the time, 7 minutes 40 percent of the time, 8 minutes 20 percent of the time, and 9 minutes 10 percent of the time. In preparing this distribution for Monte Carlo analysis, the service time of 8 minutes would be represented by what random number range?

71 through 90

A distribution of service times at a waiting line shows that service takes 6 minutes 30 percent of the time, 7 minutes 40 percent of the time, 8 minutes 20 percent of the time, and 9 minutes 10 percent of the time. This distribution has been prepared for Monte Carlo analysis. The first two random numbers drawn are 53 and 74. The simulated service times are ________ minutes, then ________ minutes.

7;8

There are four possible outcomes for a Monte Carlo simulation variable (A, B, C, and D). The random numbers 02, 22, 53, and 74 correspond to the variables ________, respectively, if each possible outcome has an equivalent chance of occurring.

A A C C

What are the advantages and disadvantages of simulation models?

Advantages: • It can be used to analyze large and complex real-world situations that cannot be solved by conventional operations management models. • Simulation allows for inclusion of real-world complications that most OM models cannot permit. • "Time compression" is possible with simulation. • Simulation allows "what if __?" types of questions. • Simulations do not interfere with the real-world system under study. Disadvantages: • Good simulation models can take a long time to develop. • Simulation does not generate optimal solutions. • Managers must generate all the conditions and constraints for the solutions that they want to examine. • Each simulation model is unique. Its solutions and inferences are not usually transferable to other problems

Explain what is meant by the statement: "simulation is not limited to using the standard probability distributions."

Correct "Standard models" include normal, binomial, beta, uniform, Poisson, exponential, and other probability distributions. Each has a specific set of assumptions and parameters. Real-world (empirical) systems can have any distribution imaginable. Simulation can mimic these real-world distributions by the use of random number intervals based on real-world behavior, and can therefore generate more realistic models than would occur if a standard model were used in place of a system-specific one.

Identify, in order, the five steps required to implement the Monte Carlo simulation technique.

Correct (1) Setting up a probability distribution for important variables. (2) Building a cumulative probability distribution for each variable. (3) Establishing an interval of random numbers for each variable. (4) Generating random numbers. (5) Actually simulating a series of trials.

State the three-fold idea behind simulation.

Correct (1) to imitate a real-world situation mathematically; (2) then to study its properties and operating characteristics; and (3) finally, to draw conclusions and make action decisions based on the results of the simulation.

From a portion of a probability distribution, you read that P(demand = 0) is 0.05, P(demand = 1) is 0.10, and P(demand = 2) is 0.20. What are the two-digit random number intervals for this distribution beginning with 01?

Correct 01 through 05, 06 through 15, and 16 through 35

From a portion of a probability distribution, you read that P(demand = 0) is 0.25, and P(demand = 1) is 0.30. What are the random number intervals for this distribution beginning with 01?

Correct 01 through 25, and 26 through 55

From a portion of a probability distribution, you read that P(demand = 1) is 0.05, P(demand = 2) is 0.15, and P(demand = 3) is .20. The cumulative probability for demand = 3 would be which of the following?

Correct Cannot be determined from the information given.

Explain how Monte Carlo simulation uses random numbers.

Correct First, a cumulative probability distribution is set up for the element being modeled. From this, a set of random number intervals is established. A random number is generated and matched against the set of intervals. The random number will fall into only one interval, and that determines the value for the element being modeled.

Provide a small example illustrating how random numbers are used in Monte Carlo simulation.

Correct For example, demand can be 0, 40% of the time, or 1, 60% of the time. The cumulative distribution is demand = 0, 0.40, and demand = 1, 1.00. The random number intervals are 01 through 40 for demand = 0, and 41 through 00 for demand = 1. A random number of 36 indicates demand = 0. Examples will vary.

Explain the difference between random numbers and random number intervals.

Correct Random numbers are a series of digits that have been selected by a totally random process. Random number intervals are numbers used to represent each possible value or outcome in a computer simulation. During simulation, a particular random number is matched against the random number intervals to determine the value for the element being modeled that particular time.

Define simulation.

Correct Simulation is the attempt to duplicate the features, appearance, and characteristics of a real system, usually via a computerized model.

Explain what is meant by the concept of "time compression" in simulation modeling.

Correct The effects of OM policies over many months or years can be obtained by computer simulation in a short time.

Identify five applications of simulation.

Correct The five applications of simulation can be picked from a list in Table F.1. Some examples are: traffic-light timing, bus scheduling, plant layout, production scheduling, inventory planning, and assembly-line balancing.

One of the disadvantages of simulation is that it:

Correct is a repetitive approach that may produce different solutions in different runs. mayy be very time consuming to develop Correct produces solutions and inferences that are not usually transferable to other problems.

"Time compression" and the ability to pose "what-if?" questions are elements of:

Correct the advantages of simulation.

Similar to mathematical and analytical models, simulation is restricted to using the standard probability distributions.

F

Simulation provides optimal solutions to problems.

F

Complete the following table in preparation for a Monte Carlo simulation. The expected demand is 3.52. demand: 0,2, 3, 4 blank probablity: blaknk cumulative prob: .1, blank, .5 blank, blank interval of random numbers: blank, 11-23, blank, blank, 86-00

Students should have only moderate difficulty filling in the table, save for the demand column. To do this they must set up the equation for the expected demand and solve for the missing component. .13(2) + .27(3) + .35(4) + .15(X) = 3.52 so X = 7

Random number intervals are based on cumulative probability distributions.

T

Results of simulation experiments with large numbers of trials or long experimental runs will generally be better than those with fewer trials or shorter experimental runs.

T

Simulation models that are based on the generation of random numbers may fail to give the same solution in repeated use to any particular problem.

T

Which of the following is a necessity for common EOQ methodology but not simulations?

constant lead time

A(n) ________ is a series of digits that have been selected by a totally random process.

cumulativie probablity distrubtion

A warehouse manager needs to simulate the demand placed on a product that does not fit standard models. The concept being measured is "demand during lead time," where both lead time and daily demand are variable. The historical record for this product suggests the following probability distribution. Convert this distribution into random number intervals. demand during lead time 100, 120, 140, 160, 180, 200 probablity: .02, .15, .25, .15, .13, .30

demand during lead time 100, 120, 140, 160, 180, 200 probablity: .02, .15, .25, .15, .13, .30 cumulative probablitiy: .02, .17, .42, .57, .70, 1.00 random number intervals: 01-02, 03-17 , 18-42 , 43-57, 58-70, 71-00

Historical records on a certain product indicate the following behavior for demand. The data represent the 288 days that the business was open during 2000. Convert these data into random number intervals. (Round each probability used to 2 decimal places, e.g., 0.36.) demand in cases: 7,8,9,10,11,12 number of occuranc: 52,9,14,39,72,102

demand in cases: 7,8,9,10,11,12 number of occuranc: 52,9,14,39,72,102 probablility: .18, .03, .05. .14, .25, .35 cumulative probab: .18, .21, .26, .40, .65, 1.0 random number intercals: 01-18, 19-21, 22-26, 41-65, 66,00

Complete the following table in preparation for a Monte Carlo simulation. demand: 0, 1, 2, 3 ,4 probablity: .1, .15 , .4, .15, .2 cumulative probablity: intervales of random numbers:

demand: 0, 1, 2, 3 ,4 probablity: .1, .15 , .4, .15, .2 cumulative probablity: .1, .25, .65, .8, 1 intervales of random numbers: 1-10, 11-25, 26-65, 66-80, 81-00

Suppose the following random numbers (1, 34, 22, 78, 56, 98, 00, 82) were selected during a Monte Carlo simulation that was based on the chart below. What was the average demand per period for the simulation? What is the expected demand? demand: 0,1,2,3,4 probablity: .1, .15, .4, .15, .2 cumprob: blank interval of random: blank

demand: 0,1,2,3,4 probablity: .1, .15, .4, .15, .2 cumprob: .1, .25, .65,.8, 1 interval of random: 1-10, 11-25, 26-65, 66-80, 81-00. Tires sold sum is given by 0 + 2 + 1 + 3 + 2 + 4 + 4 + 4 = 20 over 8 periods. Thus the average demand was 20/8 = 2.5 tires. The expected demand is simply the EV, or .1(0) + .15(1) + .4(2) + .15(3) + .2(4) = 2.2 tires per period.

The Las Vegas method is a simulation technique that uses random elements when chance exists in their behavior.

f

A simulation is "Monte Carlo" when the elements of a system being simulated exhibit chance in their behavior.

false

The ________ method is a simulation technique that uses random elements when chance exists in their behavior.

monte carlo

A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time. In preparing this distribution for Monte Carlo analysis, the service time 13 minutes would be represented by what random number range?

none of these; 13 minutes is not a possible outcome

The effects of OM policies over many months or years can be obtained by computer simulation in a short time. This phenomenon is referred to as ________. The effects of operations management policies over many months or years can be obtained by computer simulation in a short time. What is this phenomenon called?

time compression

By starting random number intervals at 01, not 00, the top of each range is the cumulative probability.

true

Despite the powerful simulation software available today, good simulation models can take a long time to develop.

true

In most real-world inventory problems, lead time and demand vary in ways that make simulation a necessity because mathematical modeling is extremely difficult.

true

One effective use of simulation is to study problems for which the mathematical models of operations management are not realistic enough.

true