Relief aid provision to en route refugees: Multi-period mobile facility location with mobile demand

Abstract

Many humanitarian organizations aid en route refugee groups who are on their journey to cross borders using mobile facilities and need to decide the number and routes of the facilities. We define a multi-period facility location problem in which both the facilities and demand are mobile on a network. Refugee groups may enter and exit the network in different periods and follow various paths. In each period, a refugee group moves from one node to an adjacent one in their predetermined path. Each facility should be located at a node in each period and provides service to the refugees at that node. Each refugee should be served at least once in a predetermined number of consecutive periods. The problem is to locate the facilities in each period to minimize the total setup and travel costs of the mobile facilities, while ensuring the service requirement. We call this problem the multi-period mobile facility location problem with mobile demand (MM-FLP-MD) and prove its NP-hardness. We formulate a mixed integer linear programming (MILP) model and develop an adaptive large neighborhood search algorithm (ALNS) to solve large-size instances. We tested the computational performance of the MILP and the metaheuristic algorithm by extracting data from the 2018 Honduras Migration Crisis. For instances solved to optimality by the MILP model, the proposed ALNS determines the optimal solutions faster and provides better solutions for the remaining instances. By analyzing the sensitivity to different parameters, we provide insights to decision-makers.