## Discrete Optimization IDiscrete Optimization I |

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0–1 programs 0–1 variables algorithm applications approach Balas branch and bound branching variable center problem cl conv client codes coefficients combinatorial considered constraints convex hull cost cutting planes cutting-plane defined discrete optimization disjunctive program dual problem duality efficient enumerative facets finite FMPS formulation Gomory graph heuristic implicit enumeration infeasible integer linear programming integer programming problem integer solution integer variables knapsack problem Lagrangean techniques location problems logical inequalities lower bound LP problem machine Management Sci Math mathematical programming median methods minimize minimum mixed integer programming nonlinear NP-hard objective function obtained Operations Res optimal solution optimum p-median problem P.L. Hammer penalties polynomial procedure pseudo-costs relaxation S1 set satisfying Sciconic Section set covering problem solved subadditive subadditive function subproblem Theorem travelling salesman problem upper bound valid inequalities vector vertex vertices weighted distance XDLA zero-one