COB 291 Final
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