The Mobile Facility Routing Problem

Abstract

In many applications, ranging from cellular communications to humanitarian relief logistics, mobile facilities are used to provide a service to a region with temporal and spatially distributed demand. This paper introduces the mobile facility routing problem (MFRP), which seeks to create routes for a fleet of mobile facilities that maximizes the demand serviced by these mobile facilities during a continuous-time planning horizon. In this setting, demand is produced by discrete events at rates that vary over time. Mobile facilities can be positioned at discrete locations to provide service to nearby events. In addition, mobile facilities can be relocated at any time, although the relocation times are significant in relation to the length of the planning horizon. The demand serviced by a mobile facility depends on the arrival and departure times at each location it visits. Although the MFRP is NP-hard, the optimal route for a single mobile facility can be computed in polynomial time. We describe three heuristics for creating routes for the fleet of mobile facilities and evaluate their performance. Our results demonstrate that these heuristics produce high-quality routes for mobile facilities, especially in scenarios where the demand for service changes significantly over time.