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
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