COB 291 Final

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Mathematical Functions are called Linear Functions if

1. Each variable appears in a separate term 2. Each variable is raised to the first power

Calculate the optimal solution point

1. Identify the constraint equations that intersect at the optimal point 2. Solve these equations simultaneously to find the optimal values for x, and y

Redundant Constraint

A constraint that can be removed from the model without changing the feasible region.

Feasible Solution

A solution point that satisfies all the constraints simultaneously

R-squared vs adjusted R-squared

Because R2 never decreases when independent variables are added to a regression, it is important to multiply it by an adjustment factor when assessing and comparing the fit of a multiple regression model. This adjustment factor compensates for the increase in R2 that results solely from increasing the number of independent variables. Adjusted R2 is provided in the regression output. It is particularly important to look at Adjusted R2, rather than R2, when comparing regression models with different numbers of independent variables.

Exponential smoothing

Choose high values of 𝛼when the underlying average is likely to change

EVwPI

Choose the best decision alternative for the state of nature, and multiply its payoff by the probability of the state of nature

The expected value of perfect information

EVPI = EVwPI - EVwoPI

Find the optimal solution by enumerating the corner points of the feasible region

If an LP problem has a unique optimal solution, that solution is one of the corner points of the feasible region

Alternative Optimal Solutions

If the level curve (objective function) is parallel with any constraint line, we may have multiple optimal solutions, but it is not guaranteed

Optimal Objective Function Value

In a maximization (minimization) problem, the optimal value is the least upper (largest lower) bound of the objective function values over the entire feasible solutions.

slack

LHS + slack = RHS

surplus

LHS - surplus = RHS

Optimal Solution

The feasible solution that provides the best possible value of the objective function.

unbounded solution

The objective function can be made infinitely large or small

Change in the LHS coefficient is beyond the allowable range

The optimal solution and optimal objective function will change

The change in RHS is within the allowable range and constraint is binding

The optimal solution will change The change in the optimal objective function value can be exactly calculated

The change in RHS is beyond the allowable range

The optimal solution will change The general pattern of the change in the optimal objective function value can be predicted

Change in the LHS coefficient is within the allowable range

The optimal solution will not change The optimal objective function value will change

The change in RHS is within the allowable range and constraint is non-binding

The optimal solution will not change, and The shadow price is zero, and the optimal objective function value will not change

EVwoPI

Use the prior probabilities

LP is used when

we have a set of decision variables

binding constraint

a constraint where some optimal solution is on the line for the constraint. Thus, if this constraint were to be changed slightly (in a certain direction), this optimal solution would no longer be feasible.

a circle node

chance/event node SUM

Posterior probabilities

conditional probabilities when the result of the sample information is given

a square node

decision node MAX/MIN

If an LP model has more than one optimal solution

it has an infinite number of alternate optimal solutions.

Prior Probabilities

marginal probabilities in the join probability table

Infeasible problems

no point can satisfy all the constraints at the same time

unbounded feasible region

open graph that goes on forever- contains max or min but NEVER both -an unbounded feasible region does not necessarily mean that the problem is unbounded

Objective Function Coefficients

represent the marginal profits (or costs) associated with the decision variables


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