By Begoña Vitoriano, Adán Rodríguez-Martínez, and María Teresa Ortuño
Natural disasters affect countless individuals each year, leading to deaths and injuries, environmental destruction, and lost livelihoods. The logistics of disaster management are quite challenging and comprise a broad and interdisciplinary research area. Humanitarian logistics refers to the process of planning, implementing, and controlling the efficient, cost-effective flow and storage of goods, materials, and related information from the point of origin to the point of consumption. These actions meet the end beneficiary’s requirements and alleviate the suffering of vulnerable people.
In the context of disaster management, a hazard refers to a threatening event or the potential occurrence of a damaging phenomenon within a given period and area. Such episodes may be natural or human-made. Naturally occurring physical phenomena can include sudden or slow-onset events that are geophysical, hydrological, climatological, meteorological, or biological in nature (e.g., earthquakes, landslides, tsunamis, volcanic activity, cyclones, floods, extreme temperatures, droughts, wildfires, epidemics, animal plagues, and famines). Conversely, human-made or technological events are caused by people and occur in (or close to) human settlements (e.g., industrial accidents or transport accidents). Complex emergencies, which stem from human activity but constitute a separate class, relate to conflicts with huge numbers of displaced populations, violence against civilians, risks to humanitarian operations, and limited access to the affected zone.
Humanitarian logistics differentiates between emergencies, disasters, and catastrophes. An emergency is a situation that poses an immediate risk to health, life, property, or the environment. Emergencies arise regularly in communities and are sometimes, but not always, managed by local entities. A disaster disrupts the normal functioning of a system or community and has a strong impact on people, structures, and the environment that surpasses local response capacity. Finally, a catastrophe is an extremely large-scale disaster.
In light of a disaster, two factors determine a society’s consequences: vulnerability and resilience. Vulnerability pertains to hazard exposure and a disaster’s impact on the affected population, while resilience relates to the population’s response capacity and recovery. Given these terms, disaster risk reduction (DRR) aims to prevent new disaster risks, reduce existing ones, and help strengthen resilience. DRR embodies the concept and practice of risk reduction through systematic efforts to analyze and regulate the causal factors of disasters, such as reducing exposure to hazards, lessening the vulnerability of people and property, wisely managing land and the environment, and improving preparedness for adverse events [1].
The disaster management cycle considers pre-event activities—like prevention and mitigation—to reduce hazard exposure and prepare for disaster response, as well as post-event activities—like response and recovery—that only begin once the emergency commences. Researchers generate mathematical models for the different phases of disaster management based on their unique characteristics. Here, we present a model that we developed for the preparedness phase of humanitarian logistics [2].
Many countries feel the impact of recurrent natural disasters, and authorities must provide relief aid to affected communities under immense time-related pressure. The local individuals and organizations that comprise first response teams are critical to disaster response, especially in the first 72 hours (the average minimum time until international support arrives). Large amounts of relief aid must be transported to affected populations in an extremely short time period, which means that the strategic pre-positioning of humanitarian assistance is crucial.
Our model focuses on strategic and tactical planning. Strategic decisions consider where to place the warehouses, when to build them, and what their capacities must be. Tactical decisions address the amount of pre-positioned humanitarian aid, the location of storage, and the appropriate budget for facilities and response. When evaluating these decisions, stakeholders must account for the potential responses to future disasters under various scenarios. Operational decisions about the transportation of necessary goods, the amount of humanitarian aid that an emergency will require, and the level of necessary post-disaster restocking all depend on the nature of the disaster in question and previous preparedness decisions.
Figure 2. Pareto frontier between unmet demand and budget deviations. Figure courtesy of [2].
We developed a stochastic programming model with a time horizon of several years and divided it into periods based on seasons. Our model includes a transport network with nodes for demand, supply, and transit that are connected by links that represent roads and paths. We generated a set of disaster scenarios for each season that were defined by the affected people and areas (the demand in each node), as well as road conditions for the distribution of relief aid (capacities of the links). We also associated each scenario with a probability of occurrence that depended on the season.
To assess the effectiveness of different plans, we considered the following criteria: response time, unmet demand, and cost. A constraint on response time prevented us from pulling supplies from distant warehouses that are too far from a particular demand node. Unmet demand is a stochastic criterion that depends on the scenario; we measured it by the expected value in each season. Finally, cost constitutes a deterministic cost that is associated with strategic decisions (i.e., facilities building and maintenance) and a stochastic cost that is contingent upon the scenario. We measure stochastic cost as the expected value of the deviations to the proposed budget, acknowledging that excess costs often arise during disasters. To manage these criteria, we utilized a multi-objective approach to obtain the Pareto frontier.
We applied our model to data from Mozambique, a country in Africa that experiences recurrent natural disasters in the form of floods, storms, droughts, and epidemics. We combined information about historical disasters from two databases—the Emergency Events Database and DesInventar—and collected in situ data on the transportation network.
Figure 3. The installed warehouse capacity per year, which depends on the importance of cost versus unmet demand. Figure courtesy of [2].
To obtain scenarios from historical cases, we conducted a five-step procedure:
(i) Obtain a discrete distribution for the total demand of each type of disaster. For a pre-determined number of scenarios, minimize the sum of deviations of the discrete distribution’s moments (average, standard deviation, and skewness) to the estimated moments of the continuous distribution.
(ii) Perform fuzzy classification to allocate historical cases to the discrete distribution’s classes.
(iii) Find geographical scenarios for each class based on a defined distance measure between cases, then obtain representative scenarios.
(iv) Merge the obtained scenarios of different disaster types (several disasters can arise in the same season); we obtained 1,647 scenarios.
(v) Perform scenario reduction by clustering with the defined distance; doing so yielded 91 scenarios.
We applied our model to the Nampula province in Mozambique (see the bolded border in Figures 1b and 1c), which resulted in a case with 21 nodes (districts), 78 links, and 35 scenarios for a five-year horizon with four seasons per year. The subsequent mathematical programming model has 183,733 constraints and 259,288 variables, including 105 binary variables. The Pareto frontier in Figure 2 illustrates the tradeoff between the objectives of unmet demand and budget deviations.
Figure 4. Average installed capacity in the Nampula province. The district with the highest capacity is the capital. Figure courtesy of [2].
The installed capacity varies with the importance of the unmet demand versus that of the cost: \(\lambda \textrm{Cost} + (1 - \lambda) \textrm{UDemand}\). Figure 3 shows the installed warehouse capacity per year, which demonstrates that a greater importance for unsatisfied demand corresponds to a greater installed capacity.
The distribution of this installed capacity for the Nampula province is highly dependent on its population distribution, transportation network, and rivers (see Figure 4). The district with the highest capacity is the province’s capital.
In the future, additional research should explore this strategic planning problem for the entirety of Mozambique. Our research group at the Complutense University of Madrid is also investigating other decision aid models for logistics and disaster management that will hopefully contribute to the last-mile distribution of humanitarian aid and recovery decisions.
Acknowledgments: This work was supported by Spanish government grant PID2019-108679RB-I00.
References
[1] Inter-Agency Network for Education in Emergencies. (2010). INEE minimum standards for education: Preparedness, response, recovery. Retrieved from https://inee.org/resources/inee-minimum-standards.
[2] Rodríguez, A. (2021). Stochastic modelling and scenarios generation for disaster management. Modelización estocástica y generación de escenarios para gestión de desastres. [Ph.D. Thesis, Complutense University of Madrid]. Retrieved from https://eprints.ucm.es/id/eprint/67479/1/T42827.pdf.
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Begoña Vitoriano is an associate professor in the Faculty of Mathematical Sciences and the Interdisciplinary Mathematics Institute at the Complutense University of Madrid, Spain. Her main research interest is operational research with strong focus on applications, and she leads the research group "Decision Aid Models for Logistics and Disaster Management (Humanitarian Logistics).” Vitoriano has been the President of the Spanish Society of Statistics and Operational Research since 2022. |
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Adán Rodríguez-Martínez is a member of the research group "Decision Aid Models for Logistics and Disaster Management (Humanitarian Logistics)" at the Complutense University of Madrid, Spain. His thesis investigated the treatment of uncertainty in natural disasters through scenario generation and stochastic modeling for decision-making. |
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María Teresa Ortuño is an associate professor in the Faculty of Mathematical Sciences and a member of the Interdisciplinary Mathematics Institute at the Complutense University of Madrid, Spain. Her research interests include the broad area of operational research, and her focus in recent years has been mathematical models for humanitarian logistics and green technologies. |