What is this BRATIO option in GAMS?

This is a note about BRATIO, a very exotic GAMS option related to providing an advanced basis to a Simplex-based LP (or NLP) solver. 

Inverting a matrix by LP

 The questions for this post are:

• Can we model the inversion of a matrix as an LP problem? (A: yes)
• Should we do that? (A: no)
• If we insist, can we make it a bit quicker (A: yes)

Parallel machine scheduling II, three more formulations

In [1] two formulations were discussed for a scheduling problem with multiple machines. Here we add a few more. Some of them are a bit strange. None of them really works better than the ones in [1].

So this is a collection of formulations that may sound reasonable at first, but are really not suited for this problem. If you want to read about good models, skip this post.

This is really a modeling issue

 In [1], the following scenario is described:

1. A MIP model is solved, delivering a feasible solution.
2. All integer variables are fixed to their levels.
3. The resulting LP model is solved in order to produce duals. This model turns out to be infeasible.