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Multilevel Solution Methods
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activities adjustment phase applied Benders algorithm block-angular lp problem Chapter column commodity considered convex convex set coordinable corporate constraints corresponding cost coupling constraints Dantzig Dantzig-Wolfe decomposition method Dantzig-Wolfe method decision problem decomposition algorithm denoted dinamico discussed dynamic programming energeticos execution phase extremal problem extreme point extreme ray feasible solution headquarters hence heuristic hierarchical production planning implementation infimal subproblems instance integer programming itinerary Jennergren Kornai linear programming lower bound mathematical programming Maximize Minimize multilevel approach multilevel methods multilevel model multilevel systems analysis national economic planning network flow nonlinear nonlinear programming number of iterations objective function objective function coefficient obtained Operations Research optimal dual multipliers optimal solution value ordinary lp organizational subunits original problem overall problem paperboard planning problem planning procedure programming problem restricted master problem sector ship simplex method solved studies subblocks supremal subproblem two-level method upper bound variables