Operations Research 03E: Binding & Nonbinding Constraints

Operations Research 03E: Binding & Nonbinding Constraints

In this video, I’ll talk about binding and
nonbinding constraints in LP problems. A constraint is binding if the LHS and RHS
of the constraint are equal at the optimal solution. Otherwise, it is nonbinding. Let’s check this example. It has two constraints (C1 and C2) and two
sign restrictions (S3 and S4). Using the graphical method we can find that
the slope of the objective function is -3. If we move the line towards the top-right
corner, this is the last point before leaving the feasible region. So it is the optimal solution. x1=4.5 and x2=0. Let’s plug these values into the constraints
and sign restrictions. For C1, we have 2*4.5+0=9, which is equal
to the RHS. So C1 is binding. For C2, we have 4.5+2*0=4.5, which is less
than the RHS. So C2 is nonbinding. For S3, we have 4.5>0, which is the RHS. So S3 is nonbinding. For S4, we have 0=0, which is the RHS. So S4 is binding. We can also tell whether a constraint is binding
or not directly from this figure. If the optimal solution is on the constraint
line, then it’s binding. This optimal point is on C1 and S4, so they
are binding. The other two constraints are nonbinding. Okay, these are the concepts of binding and
nonbinding constraints. Thanks for watching.

Comments (7)

  1. that is very useful.

  2. In other words, binding means the constraint is active, while nonbinding means the constraint is inactive. An extreme point is the feasible solution that activates more than one constraints. This is a very important prerequisite for Simplex algorithm.

  3. This was so easy to understand! Thank you.

  4. Hi Guys, please comment and let me know what you think about this Operations Research Open Course. Your feedback is really appreciated. If you enjoy the video, please subscribe and share. All my replies here are only related to the content in my own videos. I am afraid I won't be able to answer other questions. Thanks for your understanding.

  5. thanks this is a really good video 🙂

  6. Thanks sir! I can understand easily 🙂

  7. Very easy to grasp

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