Chapter 3 Flashcards
Sensitivity Analysis
study of how changes in coefficients of optimization model (min or max) affect optimal solution
What do we want to determine with sensitivity analysis?
How much these changes will affect optimal solution of LPM
Two questions answered with sensitivity analysis
how will change in coefficient of objective function affect optimal solution?
how will change in right side value of constraint affect optimal solution
Feasible solution satisfies all….
solution that satisfies all constraints
feasible set or region
set of all feasible solutions
Optimal solution
feasible solution that produces the best objective function of all feasible solutions
When does sensitivity analysis begin
after original optimal solution of LP model is estalished
sensitivity analysis is also known as
post-optimality analysis
Binding constraints
constraints satisfied exactly at optimal solution, S=0
Binding constraints are constraints whose intersection…….
determines optimal solution to LP Model
Non binding constraints
constraints that are satisfied at the optimal solution but have surplus -S and slack +S whose value is not zero
Range of optimality
range of values for each variable of objection function coefficient which current solution will remain optimal
Range of optimality changes to variables at a time
only one variable coefficient change at a time
Does increase or decrease of a objection function coefficient change the values of decision variables in optimal solution
no they cannot if in optimal range
what if coefficient change for objection function is outside range
Manage will have to resolve linear program model, change should not be allowed, would result in new optimal solution, cannot guarantee optimality for other variables
Shadow price
amount by which optimal objection value will change if right hand side of constraint is increase or decreased by one unit
Other terms for Shadow Price
marginal value or dual price
Shadow price is equal to
different in values of objective function between new and original problem
Shadow price for non-binding constraint is….
zero
negative shadow price indicates
objective function will not improve if RHS is increased
Range of Feasibility
range of values over which a right hand side value may vary without changing the value and interpretation of shadow price
Any change to right hand side of binding constraint will……
change the optimal solution
Any change to right hand side of non-binding constraint that is less than slack or surplus will……
will cause no change to optimal solution as S is zero
Reduced Cost
minimum amount by which objective coefficient of a variable should change in order to affect optimal solution
Case Maximization: If reduced cost is < 0
cost of consumed is higher than profit, activity should not be undertaken
Case maximization: Reduced cost =
per unit profit of activity - cost of consumed resource per activity
* per unit of resource is priced at shadow price
Case Maximization: if reduced cost >= 0
cost of consumed is lower/equal to profit, activity is economically attractive
Case minimization: Reduced cost =
per unit cost of activity - cost of consumed resource per activity
* per unit of resource is priced at shadow price
Case Minimization: If reduced cost is > 0
cost of consumed is higher than cost of activity so it should not be undertaken
Case Minimization: If reduced cost is <= 0
cost of consumed is lower than or equal to cost of activity is economically attractive
Variable value increase indication of worse objective value.
- Maximization
- Minimization
Maximization: R is negative and objective decrease
Minimization: R is Positive and objective increase
