**Discussion 1**

What are some benefits of using decision trees?

In what ways can decision trees be used for business decisions? Name some real-world examples

**Discussion 2**

How does the science of probability affect decisions? Why?

**Discussion 1**

Why do we use pseudorandom numbers in simulations?

How do pseudorandom numbers affect the accuracy of a simulation?

**Discussion 2**

What is the role of statistical analysis in simulation?

**Discussion 1**

Choose one of the forecasting methods and explain the rationale behind using it in real-life.

Describe how a domestic fast food chain with plans for expanding into China would be able to use a forecasting model.

**Discussion 2**

What is the difference between a causal model and a time- series model? Give an example of when each would be used. What are some of the problems and drawbacks of the moving average forecasting model? How do you determine how many observations to average in a moving average model? How do you determine the weightings to use in a weighted moving average model?

What is the difference between a causal model and a time- series model? Give an example of when each would be used.

**Discussion Week 4**

- Choose one of the forecasting methods and explain the rationale behind using it in real-life.
- Describe how a domestic fast food chain with plans for expanding into China would be able to use a forecasting model.
- What is the difference between a causal model and a time- series model? Give an example of when each would be used.
- What are some of the problems and drawbacks of the moving average forecasting model?
- How do you determine how many observations to average in a moving average model? How do you determine the weightings to use in a weighted moving average model?

**Discussion 1**

What are some business uses of a linear programming model? Provide an example.

**Discussion 2**

In the graphical method, how do you know when a problem is infeasible, unbounded, or when it has multiple optimal solutions?

What are the essential ingredients of an LP model? Why is it helpful to understand the characteristics of LP models?

**Discussion 3**

Not very many real world examples use only two variables, and those that do can usually be solved much more easily by guess and check methods rather than LP models. Why then do we study the graphical method? Be specific.

**Discussion 4**

Distinguish between a minimization and maximization LP model. How do you know which of these to use for any given problem?

**Discussion 5**

Give examples of both a minimization LP model and a maximization LP model. Every minimization model has a related maximization model. In what way do you think they are related?

- ___________ is a technique for selecting numbers randomly from a probability distribution.
- Monte Carlo is a technique for selecting numbers randomly from a probability distribution.

- Analogue simulation replaces a physical system with an analogous physical system that is _____________ to manipulate.
- Variable costs are independent of volume and remain constant.

- Regret is the difference between the payoff from the best decision and all other decision payoffs.

- Deterministic techniques assume that no uncertainty exists in model parameters.
- A continuous random variable may assume only integer values within a given interval.
- A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
- A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches A table of random numbers must be normally distributed and efficiently generated.

**DISCUSSION 1**

What does the shadow price reflect in a maximization problem? Please explain

How do the graphical and computer-based methods of solving LP problems differ? In what ways are they the same? Under what circumstances would you prefer to use the graphical approach?

What does the shadow price reflect in a maximization problem? Please explain.

How do the graphical and computer-based methods of solving LP problems differ? In what ways are they the same?

Under what circumstances would you prefer to use the graphical approach?

**DISCUSSION 2**

How does sensitivity analysis affect the decision making process? How could it be used by managers?

How does sensitivity analysis affect the decision making process?

**DISCUSSION 3**

In many ways, shadow prices are far more important results of an LP model then the optimal solution. Explain. Make sure that your answer provides context to the nature and utility of shadow prices.

**DISCUSSION 1**

What is the relationship between decision variables and the objective function?

What is the difference between an objective function and a constraint?

What is the relationship between decision variables and the objective function?

What is the difference between an objective function and a constraint?

**DISCUSSION 2**

Does the linear programming approach apply the same way in different applications? Explain why or why not using examples.

**DISCUSSION 3**

Many LP models can be viewed through the lens of a Transpotation model. Choose one of the following types of problem and explain how to see it as a Transpotation problem. That is, explain what the “goods” we are shipping are, what the “roads” we are shipping along are, what the costs of “shipping” are, what the supply” and “demand” are:

**DISCUSSION 1**

Explain how the applications of Integer programming differ from those of linear programming. Why is “rounding-down” an LP solution a suboptimal way to solve Integer programming problems?

Explain how the applications of Integer programming differ from those of linear programming.

Why is “rounding-down” an LP solution a suboptimal way to solve Integer programming problems?

**DISCUSSION 2**

Explain the characteristics of integer programming problems. Give specific instances in which you would use an integer programming model rather than an LP model. Provide real-world examples.

Explain the characteristics of integer programming problems.

Give specific instances in which you would use an integer programming model rather than an LP model. Provide real-world examples.

**DISCUSSION 3**

Do you think Integer Programming or Linear Programming has more real world applications? Why? If Integer Programming is more prevalent, why do we focus so much on Linear Programming in this course? If Linear Programming is more prevalent, what do you think the challenges are facing Linear Programmers (since software like QM can handle all the computations)?

**DISCUSSION 4**

Explain the characteristics of integer programming problems. Give specific instances in which you would use an integer programming model rather than an LP model. Provide real-world examples.

**DISCUSSION 1**

Can we apply transshipment models to inventory applications? Why or why not?

Is the transportation model an example of decision making under certainty or decision making under uncertainty? Why?

Can we apply transshipment models to inventory applications? Why or why not?

Is the transportation model an example of decision making under certainty or decision making under uncertainty? Why?

**DISCUSSION 2**

Explain the assignment model and how it facilitates in solving transportation problems.

What benefits would be gained from using this model?

Explain the assignment model and how it facilitates in solving transportation problems.

What benefits would be gained from using this model?

- In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.
- In a transshipment problem, items may be transported from destination to destination and from source to source.
- Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality.
- A cycle is an up and down movement in demand that repeats itself in less than 1 year.
- If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

** **

- Fractional relationships between variables are not permitted in the standard form of a linear program.
- In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.
- Excel can be used to simulate systems that can be represented by both discrete and continuous random variables.
- In a transshipment problem, items may be transported from destination to destination and from source to source.
- In a total integer model, all decision variables have integer solution values.

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