A naive pure-Ruby implementation of the Simplex algorithm for solving linear programming problems. Solves maximizations in standard form.

1.2: Raises Simplex::UnboundedProblem if the problem is unbounded.

I wrote this because I needed to solve some small allocation problems for a web game I'm writing, and there didn't seem to be any Ruby 2.0 bindings for the "pro" solver libraries, and anyway they are hard to install on Heroku.

• Use it for: small LP problems, with feasible origins, when you have trouble loading native or Java solvers, and when you can accept not that great performance.
• Don't use it for: large LP problems, problems with infeasible origins,when you have access to native solvers, when you need very fast solving time.

To solve the linear programming problem:

max x +  y

  2x +  y <= 4
   x + 2y <= 3

   x, y >= 0

Like this:

> simplex = Simplex.new(
  [1, 1],       # coefficients of objective function
  [             # matrix of inequality coefficients on the lhs ...
    [ 2,  1],
    [ 1,  2],
  ],
  [4, 3]        # .. and the rhs of the inequalities
)
> simplex.solution
=> [(5/3), (2/3)]

You can manually iterate the algorithm, and review the tableau at each step. For instance:

> simplex = Simplex.new([1, 1], [[2, 1], [1, 2]], [4, 3])
> puts simplex.formatted_tableau
 -1.000   -1.000    0.000    0.000            
----------------------------------------------
 *2.000    1.000    1.000    0.000  |    4.000
  1.000    2.000    0.000    1.000  |    3.000

> simplex.can_improve?
=> true
> simplex.pivot
=> [0, 3]

> puts simplex.formatted_tableau
  0.000   -0.500    0.500    0.000            
----------------------------------------------
  1.000    0.500    0.500    0.000  |    2.000
  0.000   *1.500   -0.500    1.000  |    1.000

The asterisk indicates what will be the pivot row and column for the next pivot.