1. How are the uncertain variables in the GF Auto example modeled?

The uncertain variables are modeled by using normal distribution.

2. What is the basis for selecting the underlying probability distributions?

All uncertain variables in the example are independent. They can be any numbers with the same probability. According to Central Limit Theorem, the distribution of the sum of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution.

3. How can the uncertainty in these variables be modeled more accurately?

One of the disadvantages of simulation is that results are sensitive to the accuracy of input data. The results deriving from using inaccurate input data will be of no use to the decision-making. To improve the accuracy of input data, we can collect more historical data to get the underlying distribution.

4. How are the results of simulation utilized in selecting between decision alternatives?

Simulation produces all possible outcomes that result from uncertain variables and probability distributions of the outcomes. We can choose the best possible outcome among decision alternatives based on its value and probability.

5. Compare the purpose of conducting sensitivity, scenario and simulation analyses? Using the GF Auto example, provide examples of each of these analyses.

In GF example, 4 uncertain factors affect GF's NPV, fixed cost, variable production cost, demand, and production factor.

If we change only one factor of them, say fixed cost, and keep all others constant, the change in NPV will be the result of sensitive analysis. Sensitive analysis tells us how sensitive the dependent variable responds to the the change of one independent variable.

If we change several independent variables - say fixed cost, demand, and production cost - simultaneously while keep others constant and observe the effect on NPV, this process is called scenario analysis.

From the above discriptions of applications of sensitive analysis and scenario analysis, we can observe that these two analyses have certain limitations: 1) time consuming since you are only able to run one test at a time; 2) only good for a relatively simple model with a few variables because of limited computing power; 3) failure to incorporate the real-world uncertainty in the model.

Here simulation analysis comes to play.

Simulation analysis builds uncertainty of the variables into the GF model by using distributions of all possible values for all independent variables. NPV varies as a function of varying inputs.

6.What is the overall purpose for conducting Monte-Carlo simulation analysis?

Monte-Carlo simulation is a computer model that imitates a real-life situation. It explicitly build uncertainty in one or more inputs by modeling uncertain variables using probability distributions. It allows decision makers to see how the outputs vary as a function of the varying inputs. Advantages of Monte-Carlo simulation include:

* inexpensive to evaluate decisions before implementation

* revealing critical components of the system

* excellent tool for selling the need for change.

7. Using the GF Auto example, illustrate how the overall objective is accomplished using simulation.

In GF Auto example, GF is trying to determine what type of compact car to develop. 10-year net present value of the gross profits from the car is the determinant of whether the car should fly. NPV is greatly influenced by fixed cost of developing car, variable production cost, and demand. All these variables have inherited uncertainties. @Risk incorporates the uncertainties by using normal distribution for each variable. After running @Risk, we obtain the distribution of NPV as the result of varying variables.

Examining the summary output, we can see that the more cars GF produces, the bigger NPV will be. The possibilities of making money for three simulations are 79.93%, 80.57%, and 80.96% respectively. This indicates that GF has a better chance to making profits from developing this car.