How to Solve a Linear Programming Problem Using the Dual Simplex Method

In this lesson we learn how to solve a linear programming problem using the dual simplex method.

Note: You don't need to write the dual formulation of a problem to use the dual simplex. The Dual simplex is to solve the dual of given problem without actually writing its dual formulation. Sometime solving the dual problem is more economic (time -efficient) than primal problem. Since according to the dual theorem the value of primal and dual programming are the same at the optimal solution, we prefer to solve the dual instead of the original problem.
In general, to solve a linear programming problem, assuming that RHS is greater than or equal to zero, you can solve the problem Using
1- Regular simplex when all constraints are in from of less than or equal.
2- Big M or two phase when there are equal or greater than or equal constraints.
Problems of type 2, can also be solved using dual simplex if certain conditions are true for the problem : optimality condition and infeasibility.

Two conditions to solve a problem using dual simplex:
Optimality: recall that the optimal condition is when all values in the row of Z of the simplex table are positive or zero for a max problem and when all values of z-row of the simplex table are negative or zero for a min problem

Infeasibility: It means that you have to have at least one negative in the RHS of your initial table.

So, if any the above two conditions are not true you cannot use the dual simplex to solve the problem. You might instead use the big-M or two-phase to solve the problem.

[aleroux]

The amount of times I have rather watched this video than work through all the theory is uncountable - thank you for the great video :)

[FPrimeHD]

Great explanation, I definitely appreciate the work you put into this! Linear Programming is hands down the easiest math explained in the most complicated way lol.

[kimbryanduenas]

If I could upvote this video a thousand times I would.

[parthajitmazumdar]

Was confused before watching this video as to what the heck has dual of an LPP got to do with the Dual Simplex method...This video made it clear the start itself..Too good :)

[mouhamethfadalmarabyaidara]

Flawless explanation. I appreciated the prelusion you made by first explaining the usefulness of this method before getting through the different steps of this lesson

[babakkhajavi]

Really appreciate your awesome in detailed teaching. I couldn't find better than your description for dual simplex. Iranian proud of you. Many Thanks Shokoufeh Jan.

[feyza]

I was so confused, now it all makes sense. Thank you very much!

[AbhishekSingh-ycdp]

The best video out there for understanding Dual Simplex Method... Great work

[giovannybuitron]

so what do you do when the objective function doesnt satisfy the requirements, eg a max function has all positive coef.?

[kunaldesarda]

Mam great explanation, it has really helped me. I have a doubt after making the tabulae if the question is of maximization type do we still to minimum test or we take the maximum of the ratios and key column?

[manindermanish]

ur voice is soo sweet i think i can never forget this dual simplex

[ada]

It's very satisfying to watch your videos. Everything is summarized and simplified in a format that it's very easy to understand the concepts that I struggled with a lot during classes. Also, the handwriting is nice on the eyes and your voice is very soothing to the ears. Thanks for your effort, appreciated it a lot!

[MrOnizukakira]

VOUS ETES SPECTACULAIRE.... BRAVO..i barely can understand english and i understood this lesson :D thanks .

[kuromimi_]

thank u for this short yet concise explanation and i love your calm accent hehe

[chrisjfox]

Thanks for the very clear video and explanation! I am a bit confused about something though [and the more I try to write out my question then the more turned around I get haha...]

I see the caption clarification that you don't actually have to use the Dual formulation [despite you taking the time to show its setup] in order to perform the Dual Simplex Method. I get that using the Dual table can sometimes be the more time-efficient approach, which may be done whether the conditions necessary for the Dual Simplex Method are met or not...?

I understand the conditions of being allowed to use the Dual Simplex Method (DSM), but what distinguishes the method itself from the Regular Simplex Method (RSM) using the Primal and from the RSM using the Dual...if conditions for being allowed to use the DSM are not so? Around the 3:05 mark, I believe what you're getting at is that you're using the Primal to perform the DSM to avoid the need to have to work out the Dual, but was that much work really saved here?

[apprentice]

Are the elements in the z row, the reduced costs? If yes, in order to have the optimality for a minimization problem should be greater or equal than 0 not negative.

[marcellacella]

Do we need to consider the negative sign when we need to find the ratio in maximum problem?

[mathsandstatswithsajidrehm]

One Question Plz, if the Coefficients in MAX objective function are negative ( or at least one) then can it be solved as you told coefficients in objective function should be Postive. Ans plz today...

[SagarmayBiswas]

Thank you ma'm. You nailed it in just 10 minutes. Helped me a lot for my exam

[BBoyXy]

Thank you so much. Compliments from Portugal!