On a routing and scheduling problem concerning multiple edge traversals in graphs

Abstract

Practical vehicle routing problems generally have both routing and scheduling aspects to consider. However, few heuristic methods exist that address both these complicated aspects simultaneously. We present heuristics to determine an efficient circular traversal of a weighted graph that requires a subset of its edges to be traversed, each a specified (potentially different) number of times. Consecutive time instances at which the same edge has to be traversed should additionally be spaced through a scheduling time window as evenly as possible, thus introducing a scheduling consideration to the problem. We present a route construction heuristic for the problem, based on well-known graph theoretic algorithms, as well as a route improvement heuristic, that accepts the solution generated by the construction heuristic as input and attempts to improve it in an iterative fashion. We apply the heuristics to various randomly generated problem instances, and interpret these test results.

Recent results on Arc Routing Problems: An annotated bibliography

“…In Groves et al [90], another generalization of the RPP is considered. Now, it is no longer required that each edge be traversed at least once, but rather that each edge be traversed at least a given number of times and that the positions within the closed walk at which consecutive traversals of the same edge occur should be spread over the whole closed walk as evenly as possible, for all edges.…”

Forty years of periodic vehicle routing

“…They often arise in residential waste collecting and street sweeping applications. Chu et al , Groves et al , and Mei et al also consider the periodic arc routing problem.…”