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: 4.05556
  u: 0.740741 1.18519 2.12963 0
  x: 0.611111 0.166667 0.111111

**** Iteration: 1
Step 1: -1146.15
  y: 1000 0 0
  Slack: 0
Step 2: 1007
  u: 0 1 0 0
  x: 0 251.75 0
Test optimality: -3146.15 = 1007 : false

**** Iteration: 2
Step 1: 17.0185
  y: 3 0 0
  Slack: 0 -1.01852
Step 2: 12.5
  u: 0 1 2.5 0
  x: 0.5 2.5 0
Test optimality: 11.0185 = 12.5 : false

**** Iteration: 3
Step 1: 18.1852
  y: 2 0 0
  Slack: 0 -5.18519 -0.185185
Step 2: 14.1852
  u: 0.740741 1.18519 2.12963 0
  x: 1.03704 2.22222 0.037037
Test optimality: 14.1852 = 14.1852 : true

**** Solution (Benders): 18.1852
  x: 1.03704 2.22222 0.037037   y: 2 0 0