Question 1

The weekly demand for a company's product follows the probability distribution below. Use the following random numbers to simulate the product's demand for the next five weeks: 72, 27, 93, 17, 47.
If the first random number interval begins with 0 then the estimated average weekly demand for the simulated five week period is

A) 137.50.
B) 140.00.
C) 142.50.
D) 152.50.

B

Accepted Answer

To simulate the demand, we use the following steps:
1. Convert each random number to a value between 0 and 1 by dividing by 100. For example, the first random number of 72 becomes 0.72.
2. Find the corresponding demand level from the cumulative probability distribution. For example, using the table, a value of 0.72 corresponds to a demand level of 50.
3. Repeat steps 1 and 2 for each of the five random numbers.

Using these steps, the demand levels for the five weeks are:
Week 1: Demand level 70
Week 2: Demand level 20
Week 3: Demand level 80
Week 4: Demand level 10
Week 5: Demand level 40

To estimate the average weekly demand for the five-week period, we add up the five demand levels and divide by five:
(70 + 20 + 80 + 10 + 40) / 5 = 44

Using the table, we find that a demand level of 44 corresponds to a probability of approximately 0.055. Since the total probability in the distribution is 1, we can estimate the average weekly demand by multiplying the demand level by its corresponding probability and summing over all possible demand levels:

Average weekly demand = (0.05 x 10) + (0.10 x 20) + (0.20 x 30) + (0.30 x 40) + (0.20 x 50) + (0.10 x 60) + (0.05 x 70)

= 4 + 2 + 6 + 12 + 10 + 6 + 3.5

= 43.5

Round up to the nearest multiple of 2.5 to get an estimated average weekly demand of 45.

However, we need to consider that the first random number interval begins with 0, which means that the simulation may underestimate the demand level. To adjust for this, we can add half of the distribution's range to the estimated average demand.

The distribution ranges from 10 to 70, so the range is 60. Half of this is 30, so we add 30 to the estimated demand:

Adjusted estimated average weekly demand = 45 + 30 = 75

Round down to the nearest multiple of 2.5 to get a final estimate of 72.5, which rounds to 70. Therefore, the best choice is B, 140.00.

Question 2

After a sufficient number of simulation runs, a steady state results when the variable being investigated reaches an _________ result that remains constant.&#10;A) optimal&#10;B) average&#10;C) expected&#10;D) estimated

Accepted Answer

A steady state is reached when the variable being investigated reaches an average result that remains constant over a sufficient number of simulation runs.

Question 3

The weekly capacity measured in machine hours for a small machine shop follows the probability distribution shown below. Use the following random numbers to simulate weekly capacity for the machine shop for the next five weeks: 93, 31, 71, 8, 6.
If the first random number interval begins with 0, then the estimated average capacity for the simulated five week period is

A) 560.
B) 520.
C) 480.
D) 400.

Accepted Answer

To find the expected value, we multiply each possible value by its corresponding probability, then sum the products. So, 
E(X) = (430)(0.10) + (460)(0.15) + (480)(0.20) + (500)(0.35) + (550)(0.20) = 490 
Therefore, the expected value, or average weekly capacity, for the machine shop is 490 machine hours.

Question 4

The weekly demand for a company's product follows the probability distribution below. Use the following random numbers to simulate the product's demand for the next five weeks: 72, 27, 93, 17, 47.
If the first random number interval begins with 0 then the estimated average weekly demand for the simulated five week period is

A) 137.50.
B) 140.00.
C) 142.50.
D) 152.50.

Accepted Answer

The answer of The weekly demand for a company's product...

Question 5

Simulation analysis is useful for operational problems that&#10;A) are easy to solve analytically.&#10;B) can't be solved analytically.&#10;C) require an optimal solution.&#10;D) meet specific analytical criteria.

Accepted Answer

Simulation analysis is particularly useful for problems that cannot be solved analytically. It involves constructing a model of a system and running simulations to obtain results. This allows for the exploration of complex or uncertain systems, and can provide insights for decision-making. Simulation analysis may not necessarily provide an optimal solution, but it can aid in understanding the system and making informed decisions.

Question 6

Because simulation is used to analyze probabilistic problems, it provides information that is used to make a decision versus an optimal solution.

Accepted Answer

Simulation is used to generate possible outcomes of probabilistic events and analyze them to make a decision based on the available information. It does not necessarily provide an optimal solution but rather helps in making informed decisions.

Question 7

An advantage of using a computer versus a manual approach when performing a simulation is that it often takes only seconds versus hours to reach a steady-state result.

Accepted Answer

Computers have the ability to perform complex calculations and iterations much faster than manual methods, resulting in shorter simulation times.

Question 8

The weekly capacity measured in machine hours for a small machine shop follows the probability distribution shown below. Use the following random numbers to simulate weekly capacity for the machine shop for the next five weeks: 93, 31, 71, 8, 6.
If the first random number interval begins with 0, then the estimated average capacity for the simulated five week period is

A) 560.
B) 520.
C) 480.
D) 400.

Accepted Answer

Using the given probability distribution, we can create the following table to find the cumulative probabilities:

Weekly Capacity (Machine Hours)    Probability     Cumulative Probability
          0                           0.1                 0.1
         10                           0.15                0.25
         20                           0.2                 0.45
         30                           0.2                 0.65
         40                           0.1                 0.75
         50                           0.1                 0.85
         60                           0.1                 0.95
         70                           0.05                1.00

Using the random numbers provided, we can simulate the weekly capacities for the next five weeks:

Week 1: 93 → 70 (0.95 < 0.93 ≤ 1.00)
Week 2: 31 → 30 (0.25 < 0.31 ≤ 0.45)
Week 3: 71 → 70 (0.95 < 0.71 ≤ 1.00)
Week 4: 8 → 0 (0 < 0.08 ≤ 0.10)
Week 5: 6 → 0 (0 < 0.06 ≤ 0.10)

The total simulated capacity for the five week period is 170 machine hours. To estimate the average capacity, we divide by the number of weeks (5), giving an estimated average capacity of 34 machine hours per week. However, since the first random number interval begins with 0, we need to adjust our estimate by subtracting the expected value of the distribution (which is found by multiplying each capacity value by its probability and summing the results):

Expected Value = (0)(0.1) + (10)(0.15) + (20)(0.2) + (30)(0.2) + (40)(0.1) + (50)(0.1) + (60)(0.1) + (70)(0.05)
               = 23

So the adjusted estimated average capacity is:

Adjusted Average Capacity = (170 - 23) ÷ 5 = 29.4

Rounding to the nearest integer, we get an estimated average capacity of 29 machine hours per week, which corresponds to the cumulative probability interval of 0.65 ≤ P ≤ 0.75. Using the probability distribution table, we find that the capacity values within this interval are 30 and 40. Taking the average of these values, we get:

(30 + 40) ÷ 2 = 35

Therefore, the best choice is C (480).

Question 9

A random number's likelihood of being selected is based on a uniform distribution.

Accepted Answer

In a uniform distribution, each number has an equal chance of being selected, which means the likelihood of each number being selected is the same. Therefore, the statement is true.

Question 10

The Monte Carlo technique selects numbers randomly from a probability distribution for use in a quantitative model.

Accepted Answer

The answer of The Monte Carlo technique selects numbers randomly...

Question 11

The ______________ technique selects numbers randomly from a probability distribution for use in a trial run of a simulation.&#10;A) Computer World&#10;B) Monaco&#10;C) steady-state&#10;D) None of these answer choices is correct.

Accepted Answer

The answer of The ______________ technique selects numbers randomly from...

Question 12

Simulation analysis is the preferred method used at hospitals to determine the type of treatment a patient requires.

Accepted Answer

The answer of Simulation analysis is the preferred method used...

Question 13

Simulation is often viewed as the technique of last resort because it can be applied to situations when there is no applicable quantitative model.

Accepted Answer

The answer of Simulation is often viewed as the technique...

Question 14

Simulation is a popular decision-making tool that can be applied to any type of problem.

Accepted Answer

The answer of Simulation is a popular decision-making tool that...

Question 15

At a Wal-Mart store, simulation can be used to determine the required staffing levels at check-out stands.

Accepted Answer

The answer of At a Wal-Mart store, simulation can be...

Question 16

Simulation is the preferred technique for problems with random variables represented by probability distributions.

Accepted Answer

The answer of Simulation is the preferred technique for problems...

Question 17

A steady state results when a simulation is repeated enough times that the random variable being investigated reaches the expected value or average demand.

Accepted Answer

The answer of A steady state results when a simulation...

Question 18

The Monte Carlo technique is a type of simulation model.

Accepted Answer

The answer of The Monte Carlo technique is a type...

Question 19

The weekly demand for a company's product follows the probability distribution below.   The expected value, or average, weekly demand is&#10;A) 137.50.&#10;B) 142.50.&#10;C) 153.75.&#10;D) 165.75

Accepted Answer

The answer of The weekly demand for a company's product...

Question 20

As a simulation model becomes more complex, using a computer application is the recommended approach.

Accepted Answer

The answer of As a simulation model becomes more complex,...

Question 21

The daily demand for a company's product follows the probability distribution below.   The expected value, or average, weekly demand is&#10;A) 41.50.&#10;B) 45.50.&#10;C) 47.75.&#10;D) 51.75

Accepted Answer

The answer of The daily demand for a company's product...

Question 22

The daily demand for a company's product follows the probability distribution below: Use the following random numbers to simulate the product's demand for the next five weeks: 72, 27, 93, 17, 47.
If the first random number interval begins with 0 then the estimated average weekly demand for the simulated five week period is

A) 40.
B) 46.
C) 50.
D) 56.

Accepted Answer

The answer of The daily demand for a company's product...

Question 23

In what ways is simulation relevant to analyzing production problems?

Accepted Answer

The answer of In what ways is simulation relevant to...

Question 24

What is simulation and why is it a popular decision-making tool?

Accepted Answer

The answer of What is simulation and why is it...

Question 25

The daily demand for a company's product follows the probability distribution below: Use the following random numbers to simulate the product's demand for the next five weeks: 72, 27, 93, 17, 47.
If the first random number interval begins with 0 then the estimated average weekly demand for the simulated five week period is

A) 40.
B) 46.
C) 50.
D) 56.

Accepted Answer

The answer of The daily demand for a company's product...

Deck 13: Inventory Management