Polyhedral Results for Some Constrained Arc-Routing Problems

Vehicle Routing Problems (VRPs) arise when routes must be devised for one or more vehicle(s) such that certain standards of efficiency are met and each route obeys one or more given restriction(s). VRPs are complex combinatorial optimisation problems and sophisticated algorithms are required in order to solve them. In this thesis, four particular VRPs are considered. All four are Arc Routing Problems, in which the vehicles are required to traverse certain edges (roads) of a network rather than visit certain vertices (customers). For each problem, an integer programming formulation is given and the convex hull of feasible solutions is studied to yield strong valid inequalities. For two of the problems, detailed optimisation algorithms are presented and tested.

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