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Introduction to Integer Programming
Dual Fractional Integer Programming
Convergence Using the Dantzig Cut
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appears arcs Balas Balinski basic variables branch and bound Chapter coefficients converge corresponding cosets cost cutting plane dangling nodes defined discussed dual feasible dynamic programming element enumerative equation equivalent extreme point feasible region fixed charge problem fractional free variables Glover Gomory cut group minimization problem group problem hyperplane inequality integer constrained integer cut Integer Linear Programming integer point integer variables knapsack problem Land and Doig lexicographically linear programming solution Management Science matrix maximize mixed integer program nonbasic variables nonnegative integer objective function obtain Operations Research optimal integer solution optimal linear programming optimal solution pivot column pivot row plant location problem primal procedure programming algorithm result Salkin satisfied Section set covering problem set partitioning problem simplex tableau slack variables solve the integer Spielberg subproblem Suppose surrogate constraint technique Theorem Traveling Salesman Problem upper bound vector xJ(J yields zero zero-one