Question: Consider solving the following MILP by Benders Decomposition Algorithm 13E. Treat the y variables as the complicating ones, and begin with y102 = 10, 02.

Consider solving the following MILP by Benders Decomposition Algorithm 13E. Treat the y variables as the complicating ones, and begin with y102 = 10, 02.

max 60x1 + 50x2 - 25y1 - 100y2 s.t. 20x1 + 17x2 - 60y1 - 30y2 … 10 11x1 + 13x2 - 30y1 - 60y2 … 10 x1, x2 Ú 0;

y1, y2 [0, 10] and integer

(a) Treating y variables as the complicating ones, formulate the corresponding Benders Primal and Benders Dual subproblems

(definition 13.19 ).

(b) Starting with all yi = 0, optimize the instance by Algorithm 13E. Use class optimization software to solve sub- and master problems when they become inconvenient for solution by inspection.

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