Resumen de New models and algorithms for several families of arc routing problems
Some of the most common decisions to be taken within a logistic systems at an operational level are related to the design of the vehicle routes. Vehicle Routing Problems and Arc Routing Problems are well-known families of problems addressing such decisions. Their main difference is whether service demand is located at the vertices or the edges of the operating network.
In this thesis we focus on the study of several arc routing problems. We concentrate on three families of problems. The first family consists of Multi Depot Rural Postman Problems, which are an extension of Rural Postman Problems where there are several depots instead of only one. The second family of problems that we study are Location-Arc Routing Problems, in which the depots are not fixed in advance, so their location becomes part of the decisions of the problem. We finally study Target-Visitation Arc Routing Problems, where the service is subject to an ordering preference among the connected components induced by demand arcs. Different models are studied for each considered family. In particular, two different Multi Depot Rural Postman Problem models are considered, which differ in the objective function: the minimization of the overall transportation cost or the minimization of the makespan. Concerning Location-Arc Routing Problems, we study six alternative models that differ from each other in their objective function, whether there is an upper bound on the number of facilities to be located, or whether there are capacity constraints on the demand that can be served from selected facilities. Finally, two Target-Visitation Arc Routing Problem models are studied, which differ from each other in whether or not it is required that all the required edges in the same component are visited consecutively.
The aim in this thesis is to provide quantitative tools to the decision makers to identify the best choices for the design of the routes. To this end and for each considered problem, we first study and analyze its characteristics and properties. Based on them we develop different Integer Linear Programming formulations suitable for being solved trough branch-and-cut. Finally, all formulations are tested trough extensive computational experience. In this sense, for Multi Depot Rural Postman Problems and Location-Arc Routing Problems we propose natural modeling formulations with three-index variables, where variables are associated with edges and facilities. For some of the models we also present alternative formulations with only two-index variables, which are solely associated with edges. Finally, for the Target-Visitation Arc Routing Problems we propose three different formulations, two alternative formulations for the general case, and one for the clustered version, where all the edges in the same components are served sequentially, which exploits some optimality conditions of the problem.
