Detailed simplex, branch and bound and transportation solvers for Julia

[fusion809]

I’m just wondering whether there are any Julia packages that show:

• detailed simplex tableaux for each iteration of the simplex method required to solve a linear programming problem;
• detailed information about the branch and bound iterations required to find the optimal solution to an integer programming problem; and
• detailed transportation tableaux for each iteration of the UV method as well as the initial feasible tableau generated using Vogel’s approximation method.

Naturally, I’m happy for answers that just mention a package that does one of these things and not all three. I know that JuMP is able to show the final solution to linear programming, integer programming and transportation problems, but I was wondering whether there’s a package that also shows the intermediate steps and completed tableaux, which are potentially useful for education purposes.

Thanks for your time.

[mtanneau]

As far as I know, not explicitly, no.

1. For simplex tableaux, you may take a look at the following Julia implementations of the simplex algorithm:

   • https://github.com/exanauts/Simplex.jl
   • https://github.com/JuliaLinearOptimizers/Simplex.jl (old)
   • https://github.com/IainNZ/RationalSimplex.jl (old)
   • https://github.com/mlubin/jlSimplex (very old)

   For playing around with simplex pivots, there is the very good simplex pivot tool. It is not in Julia, but I’ve used it in a course (as a student), and I liked it a lot.

2. For branch-and-bound, aside for Alpine.jl and Juniper.jl, I do not know of a Julia implementation of a general branch-and-bound scheme.
   AFAIK, the above two links were not designed for educational purposes.

[SonLe]

In terms of Branch-and-bound, you should take a look at Coluna.jl.