Results

The optimal solution to our small test problem has the objective function value 18.1852. Our program produces the following output, showing that the problem is solved to optimality with 3 iterations (looping around steps 1 and 2) of the decomposition algorithm:

**** Start solution: 4,056
  u: 0,741 1,185 2,13 0
  x: 0,611 0,167 0,111

**** Iteration: 1
Step 1: -1.146,15
  y: 1000 0 0
  Slack: 0
Step 2: 1007
  u: 0 1 0 0
  x: 0 251,75 0
Test optimality: -3.146,15 = 1007 : false

**** Iteration: 2
Step 1: 17,018
  y: 3 0 0
  Slack: 0 -1,019
Step 2: 12,5
  u: 0 1 2,5 0
  x: 0,5 2,5 0
Test optimality: 11,018 = 12,5 : false

**** Iteration: 3
Step 1: 18,185
  y: 2 0 0
  Slack: 0 -5,185 -0,185
Step 2: 14,185
  u: 0,741 1,185 2,13 0
  x: 1,037 2,222 0,037
Test optimality: 14,185 = 14,185 : true

**** Solution (Benders): 18,185
  x: 1,037 2,222 0,037   y: 2 0 0