Advanced network connectivity features and zonal requirements in Covering Location problems

Abstract

Real-world facility planning problems often require to tackle simultaneously network connectivity and zonal requirements, in order to guarantee an equitable provision of services and an efficient flow of goods, people and information among the facilities. Nonetheless, such challenges have not been addressed jointly so far. In this paper we explore the introduction of advanced network connectivity features and spatial-related requirements within Covering Location Problems. We adopt a broad modelling perspective, accounting for structural and economic aspects of connectivity features, while allowing the choice for one or more facilities to serve the facility networks as depots, and containing the maximal distance between any active facility and such depot(s). A novel class of Multi-objective Covering Location problems are proposed, utilising Mixed Integer Linear Programming as a modelling tool. Aiming at obtaining efficiently the arising Pareto Sets and providing actionable decision-making support throughout real planning processes, we adapt to our problem the robust variant of the AUGMEnted ɛ-CONstraint method (AUGMECON-R). Furthermore, we exploit the mathematical properties of the proposed problems to design tailored Matheuristic algorithms which boost the scalability of the solution method, with particular reference to the case of multiple depots. By conducting a comprehensive computational study on benchmark instances, we provide a thorough proof of concept for the novel problems, highlighting the challenging nature of the advanced connectivity features and the scalability of the proposed Matheuristics. From a managerial standpoint, the suitability of the proposed work in responding effectively to the motivating needs is showcased.