Explain binding and nonbinding constraints How can you tell

Explain binding and non-binding constraints. How can you tell in the sensitivity report that a constraint is binding.

Solution

Please follow the data and the description :

Binding and Non - Binding Constraints :

These exist because ther are certain limitations that restrict the range of a variable\'s possible values. A constraint is considered to be binding if changing it also changes the optimal solution. Less severe constraints that do not affect the optimal solution are non-binding.

This is a constraint used in the stream of the linear programming equations whose value satisfies the optimal solution and if any minor changes in its value this reflects the respective changes in the optimal solution. And if once an optimal solution is obtained, then the managers or the organisers can relax the particular binding constraint so as to improve the solution by improving the objective function value. These should not be tighten or withheld the binding constraints as this degrades the value of the objective function.

Sensitivity Analysis :

This is a analysis or a report that can be performed to determine the sensitivity of the solution to the respective changes in parameters. MS-Excel can generates a sensitivity report in two parts namely a changing cells report and a constraints report.

For the Changing Cells report we have the columns namely :

Cell, Name, Final Value, Shadow Price, Constraint R.H. Side, Allowable Increase, Allowable Decrease.

The allowable increase and decrease refers to how much the objective function of the related product or the data of the decision variable coefficient can change without changing the values of any of the decision variables. However, the objective function value will have to change if a coefficient changes and the corresponding decision variable does not change variably.

And the shadow price column refers to the amount that the objective function value would change if the named constraint changed by one unit. This price is valid up to the allowable increase or decrease in the constraint. The shadow price after the constraint is changed by the entire allowable amount is unknown.

Now to determine if a constraint is binding, then we need to check or compare the Final Value with the Constraint R.H. Side. If a constraint is non-binding, its shadow price is zero.

Hope this is helpful.