SCM Chapter 11 Monte Carlo Simulation

The Excel formula "=RAND( )" will generate a random number between

0 and 1.

Suppose we used the probability distribution and the interval of assigned random numbers, shown below, to represent the number of minutes it takes for a customer to complete the checkout process at a big box retailer. For example, "1" means that it takes 1 minute to checkout a customer. That happens approximately 20% of the time. We would like to simulate the checkout process for several shoppers to determine how many customers we could expect to assist per hour. Suppose we drew a random number to represent the length of time needed to check out a particular customer. If the random selection process yielded the value 0.11, how many minutes would that "customer" take to checkout?

2 -- The value 0.11 would correspond to a 2-minute long checkout process because the value 0.11 falls in the interval [0.1, 0.4).

The cooling time required in a production process varies according to the following distribution. The table above represents the simulated cooling time for a step in a manufacturing process. The simulated cooling time associated with the random number 0.08 is _______ minutes.

3 -- The random number 0.08 falls in the interval [0, 0.14), which corresponds to 3 minutes of required cooling time.

Suppose we used the probability distribution and the interval of assigned random numbers, shown below, to represent the number of minutes it takes for a customer to complete the checkout process at a big box retailer. For example, "1" means that it takes 1 minute to checkout a customer. That happens approximately 20% of the time. We would like to simulate the checkout process for several shoppers to determine how many customers we could expect to assist per hour. Suppose we drew a random number to represent the length of time needed to check out a particular customer. If the random selection process yielded the value 0.55, how many minutes would that "customer" take to checkout?

3 -- The value 0.55 would correspond to a 3-minute long checkout process because the value 0.55 falls in the interval [0.4, 0.8).

The required cooling time in a production process varies according to the following distribution. Compute the mean cooling time, in minutes.

4.82 -- The Expected Value or mean can be calculated using the Excel formula =SUMPRODUCT(A2:A6,B2:B6) = 4.82 minutes.

The cooling time required in a production process varies according to the following distribution. The table above represents the simulated cooling time for a step in a manufacturing process. The simulated cooling time associated with the random number 0.88 is _______ minutes.

6 -- The random number 0.88 falls in the interval [0.71, 0.89), which corresponds to 6 minutes of required cooling time.

The table below gives 4 popular State Routes in a particular state. Time represents the number of minutes it can be expected to take to travel between exits. What is the average travel time, in minutes, between exits on State Route 9?

6.3 -- The average travel time, in minutes, between exits on State Route 9 is 6.3 minutes. This is calculated as follows: (5)(0.3) + (6)(0.2) + (7)(0.4) + (8)(0.1) = 6.3 minutes.

The table below gives 4 popular State Routes in a particular state. Time represents the number of minutes it can be expected to take to travel between exits. What is the average travel time, in minutes, between exits on State Route 99?

7.6 -- The average travel time, in minutes, between exits on State Route 99 is 7.6 minutes. This is calculated as follows: (6)(0.2) + (7)(0.2) + (8)(0.4) + (9)(0.2) = 7.6 minutes.

A distribution of a random variable for which values extremely larger or smaller than the mean are increasingly unlikely can possibly be modeled by an exponential probability distribution.

False

The outcome of a simulation experiment is a probability distribution for one or more input measures.

False

Which of the following inferences can be drawn about the weekly sales? *looks like normal cuve (has 54 in middle)

The average weekly sales is $54,000.

Which of the following inferences can be drawn from the graph given below? *looks like soccer goal, starts @5 and ends @25

The variable is equally likely to take any value between 5 and 25.

A Monte Carlo simulation uses repeated random sampling to represent uncertainty in a model representing a real system and that computes the values of model outputs.

True

If values were independent, we would expect to see no pattern in a scatter plot.

True

The Excel function "=VLOOKUP( )" can be used when you need to find an exact match in a table or a range by row.

True

When an analyst knows little about the likelihood of values of a random variable, but the range of values can be ascertained, the use of the continuous or discrete (integer) uniform distribution is recommended.

True

____________ is the process of determining that a simulation model provides an accurate representation of a real system.

Validation

____________ is the process of determining that the computer procedure that performs the simulation calculations is logically correct.

Verification

An airport traffic controller notes that the number of incoming planes needing to use a runway is typically 0, 1, or 2 with probabilities 0.3, 0.5, and 0.2 respectively. The table above shows the assignment of random numbers to represent the event of 0, 1, or 2 incoming airplanes needing to use a runway. What interval of random numbers should be assigned to represent the event of 1 airplane arriving to use the runway?

[0.3, 0.8) -- The probability of zero airplanes arriving for landing is 30%, so 30% of the interval (0, 1) should be assigned to this outcome. That translates to an interval of [0, 0.3). The probability of one airplane arriving for landing is 50%, so the numbers [0.3, 0.8) represent this outcome.

A certain big box retailer has noted that the time it takes to complete checkout is 1 minute 20% of the time, 2 minutes 40% of the time, 3 minutes 20% of the time, and 4 minutes 20% of the time. The table above shows the assignment of random numbers to represent the event of a 1- and 2- minute checkout. What interval of random numbers should be assigned to represent the event of a 3-minute checkout process?

[0.6, 0.8)

When using a simulation, the analyst must be conscious of the ____________ of the model in order to understand its limitations.

assumptions

In a _____________ probability distribution, a random variable can take any value specified.

continuous

After reviewing the simulation results, the analyst is often able to make decision recommendations for the _____ that address not only the average output, but also the variability of the output.

controllable input

An input to a simulation model that is selected by the decision maker is known as a

controllable input.

Graph that looks like an average curve

normal.

If we were to list all possible outcomes in a given scenario as well as the probability of each outcome, we would be constructing a

probability distribution.

Promus receives monthly deliveries from its supplier and replenishes its inventory to a predetermined level at the beginning of each month. This predetermined inventory level is referred to as (the) _____.

replenishment level

Decision makers are interested in quantifying the likelihood and magnitude of undesirable outcomes. This is known as

risk analysis.

The Excel function "=RANDBETWEEN(1,6)" could be used to simulate

rolling a fair six-sided die.

The Excel function "=RANDBETWEEN(1,7)" could be used to simulate

selecting a random day of the week.

A simulation model extends spreadsheet modeling by replacing the use of ________ for parameters with a range of possible outcomes.

single values

Question Content Area In comparing the simulation approach to the manual what-if approach, we observe that much more information is obtained using which method?

the simulation approach -- In comparing the simulation approach to the manual what-if approach, we observe that much more information is obtained using the simulation approach.

Graph that looks like a soccer goal |-|

uniform.

In a ____________, the output is determined by assuming the most likely values for the random variables of a model.

worst-case scenario