Lecture 5: Sensitivity Analysis

Optimal solutions to LP problems have been found under…

Deterministic assumptions

What is Deterministic Assumption?

We assume complete certainty in the data and relationships of a problem

What is Sensitivity Analysis?

Determines how the optimal solution is affected by changes within specified ranges in…

• the objective function coefficients

• the right-hand side (RHS) values in the constraints

What type of questions does Sensitivity Analysis allow managers to as about a problem?

What-if questions

What may not change the current Optimal Solution?

Modest incr and decr in objective function

What does the Allowable Increases & Allowable Decreases indicate?

How much one coefficient in the objective could change before the optimal solution would change

What is Right-Hand-Side (RHS)

values of the constraints often represent resources available to the firm

What happens when there are changes in the Right-Hand-Side (RHS) values?

It often changes the optimal solution, thus might change the optimal objective value

What is the Shadow Price for a constraint?

The improvement in the objective function value that results from a one-unit incr in the right-hand-side (RHS) of the constraint

What is the Allowable Increase & Allowable Decrease for Shadow Price?

Conditions for applying the shadow price

If the change in RHS is increased or decreased beyond the allowable increase or decrease, what happens?

Then the objective function would no longer increase by the shadow price

What are four difficulties that arise when using the graphical approach?

• Alternate Optimal Solutions

• No Feasible Solution

• Unboundedness

• Redundancy

What is the Redundant Constraint?

the constraint that does not affect the feasible solution region