A capacitated mobile facility location problem with mobile demand: Recurrent service provision to en route refugees

Abstract

In this paper, we help humanitarian organizations provide service via mobile facilities (MFs) to migrating refugees, who attempt to cross international borders. Over a planning horizon, we aim to optimize number and routes and relocations of the MFs over a planning horizon. The problem is represented on a network where several refugee groups relocate in their predetermined paths throughout the periods. To incorporate continuity of service, each refugee group should be served at least once every fixed consecutive periods via capacitated MFs. We aim to minimize the total cost, consisting of fixed, service provision, and MF relocation costs, while ensuring the service continuity requirement. We formulate a mixed integer linear programming (MILP) model for this problem. We develop a matheuristic and an accelerated Benders decomposition algorithm as an exact solution method. The proposed model and solution methods are investigated over instances we extracted from the 2020 Honduras migration crisis.