## Integer programmingLinear programming; Integer programming graphs; Enumeration methods; Cutting plane methods; The knapsack problem; Integer programming over cones; The set covering and partitioning problems; Approximate methods; Integer nonlinear programming; Computational experience. |

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### Contents

Linear Programming | 25 |

Integer Programming and Graphs | 62 |

Enumeration Methods | 108 |

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algorithm of Section approximate method assignment problem augmenting path basic feasible solution basis matrix binary bound algorithm branch and bound choose composite cut computational Consider convex hull cutting plane deleted dual feasible edges element entering variable enumeration algorithm example Exercise exists extreme point fathomed given in Table go to Step go.o Gomory graph group knapsack problem Hermite Normal Form ILP's ILPC implicit enumeration implies integer forms integer programming integer solution linear programming max x0 method of integer MILP monotone nonincreasing Nemhauser nonbasic nonnegative Note objective function obtained optimal solution partition polyhedron primal feasible prime cover recursion return to Step satisfies Set Covering Problem simplex algorithm slack variable Smith Normal Form solved source row subtour surrogate constraint tableau Theorem totally unimodular traveling salesman problem upper bound vertex vertices xu x2 yields