## Graph Theory in Operations Research |

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### Contents

Some Basic Concepts | 13 |

Branchandbound Methods | 47 |

Shortest Route Problems | 69 |

Copyright | |

9 other sections not shown

### Common terms and phrases

1-centre algorithm FF AND-OR tree arc ij assigned bounding function branching capacity clearly complete enumeration tree considered constraints Corollary corresponding crash customers cycle defined Definition denote depot directed graph distance edges Euler path exercise facilities feasible flow feasible solution Find a minimal flow augmenting chain flow of value function given global optimum graph G graph theory heuristic integer integer linear programming knapsack problem labelled leads lower bound maximal flow maximise maximum minimal cost flow minimise multi-commodity flow network flow network of figure node Numbers alongside obtained optimal solution points possible problem of example project duration Proof reduced resource result routing problem scheduled search tree selected sequence set covering problem shortest path shown in figure solved Step 1 Setup subset terminate Theorem tour travelling salesman problem undirected units of flow updated variable vehicle vertex numbers vertex set zero