QBA 5330 Exam 3
Is the change in right hand side of a constraint within the allowable range? (No)
We cannot use the shadow price to predict. We must solve the linear program using the updated constraint to find the new solution.
Is the change in an objective function coefficient within the allowable range? (No)
We must solve the model with the updated objective function to find the new optimal values of the decision variables
Four steps with building a linear model/optimization
1) Identify the decision variables 2) Identify the objective function 3) Identify the constraints 4) Write the objective function and constraints as mathematical expressions
Basic properties of linear optimization
1) the objective function and all constraints are linear functions of the decision variables 2) all variables are continuous
Cannot Exceed constraint
<=
Must contain exactly constriant
=
At least constraint
>=
Binding constraints
A constraint for which the cell value is equal to the right hand side value of the constraint. The constraint is satisfied as a strict equality.
Reduced cost
A number that tells us how much the objective function coefficient needs to be reduced for a non-negative variable that is zero in the optimal solution to become positive
What occurs if a shadow price is negative?
A one unit increase in the right hand side of the associate constraint results in a decrease in the optimal objective function value
What occurs if a shadow price is positive
A one unit increase in the right hand side value of the associated constraint results in an increase in the optimal objective function value
Unbounded solution
A solution that has allowed the value of the objective function to be increase or decreased without bound and without violating any of the constraints
Feasible solution
Any solution that satisfies all constraints of an optimization problem
What are limits, requirements, or other restrictions that are imposed on any solution?
Constraints
What is a function of the decision variable?
Constraints
What are all variables with linear optimization?
Continuous variables
Non-negative constraints format
Decision variable >= 0
What are the unknown values that an optimization model seeks to determine?
Decision variables
What are constraints a function of?
Decision variables in the problem
What can decision variables be denoted by?
Descriptive name, abbreviations, subscripted letters
How are constraints expressed?
Expressed mathematically as algebraic inequalities or equations with all variables on the left side and constant terms on the right
shadow price
How much the value of the objective function will change as the right hand side of a constraint is increased by one unit
What does the sensitivity report provide?
How optimal objective function value and optimal decision variable values are affected by: 1) changes in the objective function coefficients 2) changes in certain decision variables 3) changes in the constraint resource limitation or requirements
Constraints
Limitations, requirements, or other restrictions that are imposed on any solution either from practical or technology considerations
What are the objective function and constraints?
Linear funtions of the deicison variables
Infeasible problem
No feasible solution exists. There is no way to satisfy all of the constraints in the problem simultaneously
What is a constraint to always remember to include?
Non-negative constraint
Is the change in an objective function coefficient within the allowable range? (Yes)
Optimal values of decision variables will not change, recalculate the value of the objective function using the new coefficient value
Alternate optimal solution
Solutions that results in a maximum (or minimum) objective function value by more than one combination of decision variables
What to do with shadow price to analyze effects of decreases in right hand side values?
Switch the sign of the shadow price
Examples of constraints
The amount of money spent on research and development projects cannot exceed the assigned budget, materials available
What is the quantity that is to minimized or maximized?
The objective function
Optimization
The process of finding a set of values for decision variables that minimize or maximize some quantity of interest and the most important tool for predictive analytics
objective function
The quantity that is to be minimized or maximized
Decision variables
The unknown values that an optimization model seeks to determine
Is the change in right hand side of a constraint within the allowable range? (Yes)
Use shadow price to predict how the objective function value will change. Solve the model with the updated constraint to find the new values of the decision variables
Unique optimal solution
there is exactly one solution that will result in the maximum or minimum of the objective function
Slack
refers to the difference between the left and right hand sides of the constraints for the optimal solution
