The open capacitated arc routing problem

The Open Capacitated Arc Routing Problem (OCARP) is a NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours that services a subset of edges with positive demand under capacity constraints. This problem is related to the Capacitated Arc Routing Problem (CARP) but differs from it since OCARP does not consider a depot, and tours are not constrained to form cycles. Applications to OCARP from literature are discussed. A new integer linear programming formulation is given, followed by some properties of the problem. A reactive path-scanning heuristic, guided by a cost-demand edge-selection and ellipse rules, is proposed and compared with other successful CARP path-scanning heuristics from literature. Computational tests were conducted using a set of 411 instances, divided into three classes according to the tightness of the number of vehicles available; results reveal the first lower and upper bounds, allowing to prove optimality for 133 instances.