Exact and Heuristic Approaches for the Covering Tour Location Routing Problem

Abstract: The Covering Tour Location Routing Problem (CTLRP) unites the well-known location routing problem with the possibility of covering customers through intermediary facilities. The objective is to select a subset of greenfield or brownfield depots and a subset of facilities, assign customers to suitable facilities, and design routes for a fleet of vehicles such that each customer's demand of a homogenous good can be satisfied and a given objective function is minimized. We focus particularly on the case when customers can not be directly visited, i.e. they have to pick up their orders from intermediary facilities, and the objective function consists of the strategic and operational costs, i.e. total routing costs plus costs for establishing or operating the selected depots and facilities. We introduce a mixed-integer programming model derived from a 2-commodity flow formulation, which can be seen as a baseline model for various applications. As such models are often impractical to solve for realistically-sized scenarios, a local search-based matheuristic to solve the problem at hand is developed. Furthermore, we construct benchmark instances for the CTLRP by expanding existing LRP instances to include information on facilities and customers. Extensive computational experiments on said instances with the aim of analyzing different heuristic configurations show that the proposed heuristic, if designed carefully, is able to produce very good results within a short period of time, while exact solving methods using the proposed MIP formulation frequently return highly suboptimal solutions and exhibit slow convergence speeds.