ABSTRACT Title of dissertation: MODELING AND SOLVING ARC ROUTING PROBLEMS IN STREET SWEEPING AND SNOW PLOWING

In arc routing problems, the goal is to determine an optimal path, or set of paths, that traverse a required subset of arcs on a graph with respect to a set of constraints and objective function. The Chinese Postman Problem (CPP) forms the basis for many arc routing problems. Let graph G = (V,A), where V is a set of vertices and A = {(i, j)|i, j ∈ V} is a set of arcs that each connect exactly two vertices, each with its own cost of traversal cij. The objective of the CPP is to construct a least cost path that traverses each arc in A at least once. There are many practical applications for variants of the CPP, including winter street maintenance, and street sweeping that incorporate: Rural Instances Rural Postman Problems (RPP) stipulate that only a subset AR ⊂ A require traversal, allowing for non-servicing traversal on the rest of the graph. In the context of street sweeping, a street sweeper isn’t responsible for sweeping all the streets. Windy Graphs In the CPP, the cost of traversal of an arc is the same, regardless of the direction of traversal. In the Windy Postman Problem (WPP), the cost of traversa