Simplex minimization

Question

I've noticed that my OR book doesn't talk much about minimization with Simplex. I've read some things online but it's still a bit messy in my head. If I have greater or equal restraints, if I set min Z = max -Z then it feels like I'll end up with an unlimited problem. If I have a mix of greater than or equal or less than or equal to restraints will I be able to solve min Z using the max -Z technique?

Minimization seems like a bit of a mess to me with Simplex. Why can't I just use additional variables $y_1,y_2,\text{...},y_n\geq0$ and subtract them from greater than or equal restraints to obtain equality restraints?

Answer 1

I can see why you are confused many people seem to use different approaches online .
One way you can work is this: turn the minimization problem into standard form. That is :

• replacing the objective function z by -z and
• asking for maximisation while at the same time you make sure you have constraints in the form of $a_ix_i \leq b_i$

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But I have seen people solving it as such as well :
Keep the objective function as it is and apply those rules:

• For the pivot column you look for the most positive (instead of the most negative) coefficient in the line corresponding to the objective function
• compute the min ratio as usual