Innovative Applications of O.R.
Relief Aid Provision to En Route Refugees: Multi-Period Mobile Facility Location with Mobile Demand

https://doi.org/10.1016/j.ejor.2021.11.011Get rights and content

Highlights

  • Planning delivery of relief aid to en route refugees through mobile facilities.

  • Multi-period problem with mobile demand and service continuity consideration.

  • Objective is to minimize the total setup and travel costs of the mobile facilities.

  • A mathematical model and an adaptive large neighborhood search algorithm.

  • Case analysis on 2018 Honduras Migration Crisis.

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.

Introduction

The migration crisis can be considered one of the most urgent and distressing global challenges, partly because the worldwide displacement of people is now at the highest level ever recorded. According to the UN Refugee Agency (2020), by the end of 2019, 79.5 million individuals were forcibly displaced worldwide as a result of persecution, conflict, violence, or human rights violations. Out of the 79.5 million individuals, 26 million were refugees displaced globally, whereas 45.7 million were internally displaced people, the remaining 4.2 million and 3.6 million were asylum-seekers and Venezuelans displaced abroad, respectively.

According to the UN Refugee Agency (2018), a refugee is someone who has been forced to flee his or her country because of persecution, war, or violence. Having been exposed to traumatic events, refugees suffer from different medical problems: foremost mental disorders such as post-traumatic stress disorder, depression, and anxiety, followed by nutritional problems and chronic pain in addition to undiagnosed chronic conditions (Comellas et al., 2015). According to the World Health Organization, the health conditions of refugees who have fled to Europe contain more risks compared with the citizens of the country they reached (WHO, 2019). Providing medical care and other services during the arduous and often lengthened process of migration may alleviate these risks.

Mobile clinics are common for delivering health services in humanitarian emergencies (McGowan et al., 2020), where access of care is better addressed by mobile teams than regular clinics in circumstances with difficult access. Many humanitarian organizations aim to fulfill the requirements of en route refugee groups who are on their journey to cross borders. These requirements can be provided only with the aid of support units that can be easily mobilized (Shortall, Glazik, Sornum, & Pritchard, 2017). As an economical and practical solution, governments or non-governmental organizations provide essential services to en route refugees using mobile facilities (MRS, 2019). For instance, according to Gulland (2015), Medicins Sans Frontieres - Doctors Without Borders (MSF) set up a mobile clinic and served approximately 100 people daily in the Serbia-Hungary border, where approximately 2000 people pass by every day. In another case, over 850,000 refugees, asylum seekers, and migrants arrived in Greece in 2015. In response to an overwhelming demand for access to health care for them, Doctors of the World established the Refugee Ferry Project, which comprised of a clinic providing primary health care, and integrated mental health and psycho-social support onboard a commercial ferry (Shortall et al., 2017). The Office of the High Commissioner for Human Rights stated that the scarcity of the studies prepared for the refugee groups in transit creates a significant obstacle to providing effective, sustainable, and fair solutions (OHCHR, 2016).

In this paper, we aim to address one of the challenges encountered by the mass movement of people, namely the provision of mobile services to transiting refugees. In particular, we are concerned with the operational problem of deciding the number and routes of mobile facilities on the paths of transiting refugees. We envision a mobile facility location problem (MFLP) in which over time, as refugees are en route, service demand progresses on a network towards destination nodes, while new demand enters the network at various source nodes. Service should be provided intermittently to mobile demand while minimizing total travel and setup costs of the facilities.

We consider the service requirement as continuity of care which is defined by WHO as the degree to which a series of discrete health care events is experienced by people as coherent and interconnected over time and consistent with their health needs and preferences (WHO, 2018). There are several studies (e.g., Barker, Steventon, Deeny, 2017, Christakis, Mell, Koepsell, Zimmerman, Connell, 2001, Deeny, Gardner, Al-Zaidy, Barker, Steventon, 2017, Gray, Sidaway-Lee, White, Thorne, Evans, 2018) in healthcare literature that emphasize the importance of continuity of care. From a migration perspective, continuity of care is an important facilitator to build trusting relationships with refugees (Robertshaw, Dhesi, & Jones, 2017). Health experts state that frequency for a health service depends on its type and can have different values (Salman, Yücel, Kayı, Turper-Alışık, & Coşkun, 2021). Service continuation is provided by serving each demand point at least once in the maximum number of days for each service type between two consecutive visits. For instance, the maximum number of days between two consecutive visits is determined as 4 weeks and 2 weeks for child-care vaccination and reproductive health, respectively (Salman et al., 2021). Aiming to provide service in the form of general aid (food, water, health supplies and healthcare services) to moving refugees and considering stocking options of general aid supplies, an adequate service frequency can be determined to satisfy continuity of service. For example, if only water supply service is to be provided, then service frequency should be determined considering that on average, a person cannot survive for three days without water supply (Johnson & Luo, 2021).

We model this problem considering a multi-period planning horizon and a network associated with the paths of refugees. Refugee groups may enter and exit the network in different periods and follow different paths. While the network topology does not change from period to period, the demand at the nodes may vary as refugees follow their paths and move from one node to an adjacent one in their predetermined path. That is, in each period, demand at a node moves on a path from its origin node to its destination node. Multiple mobile service facilities are available and each facility should be located at a node of the network in a period to provide service to the people located there. In any period, a facility may be relocated to another node or remain at the same node. We operationalize continuity of care with a constraint which ensures that each refugee group is required to be served by a facility at least once every predetermined number of periods. A refugee receives a service from a facility if both are at the same node in the same period. The aim is to determine the locations, and thus the routes, of the mobile facilities during the planning horizon to satisfy the refugee service requirements while refugees follow their paths. The objective is to minimize the sum of the total travel costs of the facilities and the fixed costs required to set up the mobile facilities and prepare for the service. Because of these properties, we call this problem the multi-period mobile facility location problem with mobile demand (MM-FLP-MD) and present it to the facility-location literature as a new problem.

In the next section, we examine the related literature and identify the differences of our problem from the well-known problems. We formally define the problem in Section 3 and provide an explanatory example. Section 4 presents a mathematical programming formulation, and Section 5 proposes an adaptive large neighborhood search algorithm to solve the problem. Section 6 provides computational experiments and derives managerial insights to decision-makers on a real-life case, namely the 2018 Honduras Migration Crisis for which we extracted data. Finally, Section 7 presents the concluding remarks.

Section snippets

Literature Review

Owing to its nature, our problem can be classified as a facility location problem (FLP). FLPs have been extensively studied in the literature with many different variations over the years (Laporte, Nickel, & da Gama, 2015). In these problems, the challenge involves locating facilities to the best locations, according to one or more criteria, to serve demand points (Laporte et al., 2015). The FLP can be divided into two categories, static and dynamic, based on the time dimension of the problem (

Problem Definition

In this section, we provide a formal description of the MM-FLP-MD together with an illustrative example and prove its computational complexity. To facilitate the problem description, we provide explanations of some important problem features below.

Network: MM-FLP-MD is defined on a directed network G=(V,A), where moving refugee groups and mobile facilities form two subnetworks. The network of refugee groups is represented by Gρ=(V,Aρ). The node sets of Gρ and G are the same, and correspond to

Mathematical Model

We propose the following mathematical model to solve the MM-FLP-MD problem.

Sets:

PSet of refugee paths
VSet of nodes
VνSet of nodes that mobile facilities can visit, where VνV
ASet of arcs
AρArc set of the refugee network, where AρA
AνArc set of the mobile facility network, where AνA
MSet of mobile facilities
TSet of periods

Parameters:

dpt1, if a refugee group enters path p in period t; 0, otherwise, pP,tT
ai1, if a mobile facility can be located at node i, i.e. if iVν; 0, otherwise, iV
lpnumber

Adaptive Large Neighborhood Search Algorithm Implementation

The MM-FLP-MD rapidly becomes intractable as the number of refugee groups entering the network and the number of nodes in the paths increase. To avoid the computational complexity, we developed an adaptive large neighbourhood search (ALNS) algorithm with problem-specific moves.

Case Study

We applied the proposed solution approach to the real-life case of the Honduras Migration Caravan Crisis in 2018. In October 2018, a refugee movement began from Central America to the USA. People from Honduras, Guatemala, and Nicaragua gathered to leave their countries because of various reasons such as poverty, crime rates, and political pressures; they sought a new life with better living conditions and better jobs. On October 12, the group began their march with 160 people from San Pedro

Conclusions

In this study, we defined a multi-period mobile facility location problem in which demand is also mobile (MM-FLP-MD). This problem emanates from the provision of humanitarian aid to refugee groups who are on their journey. The aim is to provide services to these vulnerable groups in the most effective manner and with the most efficient use of the resources. An important characteristic of the problem is that service must be provided frequently. Therefore, each refugee group must be served at

Acknowledgments

This research was supported by TUBITAK [Grant number 119M229].

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