Main Principles in Sensitivity Analysis.

• Objective Function Coefficients(OFC)
  • When the Objective function coefficient (OFC) a variable changes this affects the slope of the contours only.
  • When OFC of the variable on the vertical axis increases the contours become flatter.
  • A change in the OFC may not be enough to affect the optimality of a solution.
  • If the change is sufficient to change the optimal point, the optimal point will shift to that adjacent corner where the variable that become more desirable will be used more.
  • Even if the change in OFC is not sufficient to move the optimal point, in general the OV will change.
  • The rate of change in the OV equals the value of the variable whose OFC is changing.

• Right Hand Sides (RHS)
  • When the RHS of constraints change, this shifts the constraint parallel to itself.
  • If the constraint is "<=" increasing the RHS loosens the constraint (makes the feasible region larger) and vice versa.
  • If the constraint is ">=" increasing the RHS tightens it and vice versa .
  • Loosening an inactive constraint will not affect the optimality of the current solution nor the OV. Only the associated slack/surplus will increase.
  • Tightening an inactive constraint by as much as the amount of slack/surplus will not affect the solution nor the OV, Only the associated slack/surplus will decrease.
  • when an inactive constraint is tightened by as much as the amount of slack/surplus the constraint becomes active.
  • In general, when the RHS of an active constraint is changed we are interested in the interval within which the same corner stays optimal.
  • Changing the RHS of an active constraint will, in general, change the values of the variables and the OV.
  • When the change is sufficiently large the solution shifts to a different corner (intersection of different constraints)
  • When the RHS of an active constraint is tightened, in general, the OV will deteriorate, while it will improve for changes that loosen the constraint.
  • The change in the objective function per unit of RHS change remains constant within the allowable interval. This is called the dual price of the constraint.
  • Dual price of an inactive constraint is zero.
  • A redundant constraint is one whose removal does not affect the feasible region.
  • In general, in terms of the sensitivity of the optimal solution, a redundant constraint behaves as do inactive constraints. However there are rare situations where a redundant constraint may also be active.