An example of solving mixed integer programming by rglpk (Ruby interface for GLPK)

rglpk-mip.rb

require "rglpk"

# An example of solving mixed integer programming by rglpk (Ruby interface for GLPK)
# Original C-language-version by Masahiro Sakai
# https://gist.github.com/msakai/2450935/32efeace1ce27b2259b9792e8731436d7b0bb523
# 
# rglpk must be installed
# https://en.wikibooks.org/wiki/GLPK/Ruby

# Maximize
# obj: x1 + 2 x2 + 3 x3 + x4
# Subject To
# c1: - x1 + x2 + x3 + 10 x4 <= 20
# c2: x1 - 3 x2 + x3 <= 30
# c3: x2 - 3.5 x4 = 0
# Bounds
# 0 <= x1 <= 40
# 2 <= x4 <= 3
# General
# x4
# End

p = Rglpk::Problem.new
p.name = "sample"
p.obj.dir = Rglpk::GLP_MAX

rows = p.add_rows(3)
rows[0].name = "c1"
rows[0].set_bounds(Rglpk::GLP_DB, 0.0, 20.0)
rows[1].name = "c2"
rows[1].set_bounds(Rglpk::GLP_DB, 0.0, 30.0)
rows[2].name = "c3"
rows[2].set_bounds(Rglpk::GLP_FX, 0.0, 0.0)

cols = p.add_cols(4)
cols[0].name = "x1"
cols[0].set_bounds(Rglpk::GLP_DB, 0.0, 40.0)
cols[1].name = "x2"
cols[1].set_bounds(Rglpk::GLP_LO, 0.0, 0.0)
cols[2].name = "x3"
cols[2].set_bounds(Rglpk::GLP_LO, 0.0, 0.0)
cols[3].name = "x4"
cols[3].set_bounds(Rglpk::GLP_DB, 2.0, 3.0)
cols[3].kind = Rglpk::GLP_IV

p.obj.coefs = [1.0, 2.0, 3.0, 1.0]

p.set_matrix([
 -1.0,  1.0, 1.0, 10.0,
  1.0, -3.0, 1.0,  0.0,
  0.0,  1.0, 0.0, -3.5
])

p.mip("presolve" => Rglpk::GLP_ON)

z = p.obj.mip
x1 = cols[0].mip_val
x2 = cols[1].mip_val
x3 = cols[2].mip_val
x4 = cols[3].mip_val

printf("z = %g; x1 = %g; x2 = %g; x3 = %g; x4 = %g\n", z, x1, x2, x3, x4)
#=> z = 122.5; x1 = 40; x2 = 10.5; x3 = 19.5, x4 = 3