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applied assignment associated assumed Balas basic solution basic variables binary variables branch-and-bound branching coefficients computational condition Consider continuous optimum continuous solution convex cutting methods cutting-plane methods defined determined developed dual feasible dual method equation Example extreme point fathomed feasible integer feasible solution follows formulation free variables given Glover's go to step heuristic implicit enumeration infeasible integer model integer problem integer programming integer solution integer variables iteration j e NB jeNB knapsack problem Land-Doig algorithm LIFO linear program lower bound matrix maximize minimize node nonbasic variables nonnegative number of variables objective function optimal optimum objective value optimum solution partial solution penalties primal procedure relaxed problem result satisfied SC problem Section selected set covering problems simplex algorithm simplex method slack variable solution space solving source row subtour surrogate constraint Theorem traveling salesman problem upper bound yields zero level zero-one problem zmin