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a b s t r a c tThe aim of this paper is to introduce the periodic capacitated arc routing problem with irregular services. Some applications can be found in road maintenance operations and road network surveillance. The problem consists of determining a set of routes to cover a given network over a time horizon. The roads must be serviced a number of times in sub-periods over the time horizon, according to a hierarchy of arc classes. We present a mathematical model and a heuristic solution approach.

The Rural Postman Problem with Time Windows for the undirected case is introduced. The problem occurs in the monitoring of roads for black‐ice detection. Different formulations are proposed and tested on sets of instances adapted from the literature. A cutting plane algorithm based on valid inequalities for the Traveling Salesman Problem (TSP) with Time Windows and the Precedence Constrained TSP is presented as solution method and tested on a set of real‐life networks. Computational results show that this approach is able to solve to optimality instances with up to 104 required edges. At the end of the article the formulations for the undirected case are extended to the directed case. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 64(3), 169–180 2014

In this paper, the rescheduling arc routing problem is introduced. This is a dynamic routing and scheduling problem that considers adjustments to an initial routing itinerary when one or more vehicle failures occur during the execution stage and the original plan must be modified. We minimize the operational and schedule disruption costs. Formulations based on mixed‐integer programming are presented to compare different policies in the rerouting phase. A solution strategy is developed when both costs are evaluated and it is necessary to find a solution quickly. Computational tests on a large set of instances compare the different decision‐maker policies.

The rural postman problem with time windows is the problem of serving some required edges with one vehicle; the vehicle must visit these edges during established time windows. This article presents a competitive adaptive large neighborhood search algorithm to solve the problem. Computational experiments are performed on a large set of instances with up to 104 required edges. The results show that this approach is efficient, significantly reducing the computational time on large instances and achieving good solutions: the algorithm is able to solve to optimality 224 of 232 instances. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 44–59 2017