or models with stochastic components in disaster operations management: a literature survey

Accepted Manuscript

Survey

OR models with stochastic components in disaster operations management: A

literature survey

Maria Camila Hoyos, Ridley S. Morales, Raha Akhavan-Tabatabaei

PII: S0360-8352(14)00413-6

DOI: http://dx.doi.org/10.1016/j.cie.2014.11.025

Reference: CAIE 3878

To appear in: Computers & Industrial Engineering

Received Date: 12 December 2013

Revised Date: 24 November 2014

Accepted Date: 27 November 2014

Please cite this article as: Hoyos, M.C., Morales, R.S., Akhavan-Tabatabaei, R., OR models with stochastic

components in disaster operations management: A literature survey, Computers & Industrial Engineering (2014),

doi: http://dx.doi.org/10.1016/j.cie.2014.11.025

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers

we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and

review of the resulting proof before it is published in its final form. Please note that during the production process

errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

http://dx.doi.org/10.1016/j.cie.2014.11.025

http://dx.doi.org/http://dx.doi.org/10.1016/j.cie.2014.11.025

OR Models with Stochastic Components in Disaster Operations

Management: A Literature Survey

Maria Camila Hoyos, Ridley S. Morales, Raha Akhavan-Tabatabaei∗

Centro para la Optimizacion y Probabilidad Aplicada (COPA), Departamento de Ingenierıa Industrial,Universidad de los Andes, Cr 1E No. 19A-10, Bogota, Colombia

Abstract

The increasing number of affected people due to disasters, the complexity and unpre-dictability of these phenomena and the different problems encountered in the planning andresponse in different scenarios, establish a need to find better measures and practices inorder to reduce the human and economic loss in this kind of events. However this is not aneasy task considering the great uncertainty these phenomena present including the multiplenumber of possible scenarios in terms of location, probability of occurrence and impact, thedifficulty in estimating the demand and supply, the complexity of determining the numberand type of resources both available and needed and the intricacy to establish the exactlocation of the demand, the supply and the possible damaged infrastructure, among manyothers. Disaster Operations Management has become very popular and, considering theproperties of disasters, the use of tools and methodologies such as OR have been given a lotof attention in recent years. The present work provides a literature review on the OR mod-els with some stochastic component applied to Disaster Operations Management (DOM),along with an analysis of these stochastic components and the techniques used by differentauthors to cope with them as well as a detailed database on the consulted papers, whichdifferentiates this research from other reviews developed during the same period, in order togive an insight on the state of the art in the topic and determine possible future researchdirections.

Keywords: Disaster operations management, Operations research, Stochastic modeling

1. Introduction

The International Federation of Red Cross and Red Crescent Societies (IFRC) definesdisaster as a sudden, calamitous event that seriously disrupts the functioning of a communityor society and causes human, material, and economic or environmental losses that exceedthe community’s or society’s ability to cope with using its own resources (IFRC, 2012).

∗Corresponding author. Tel.: +57 1 3394949x3780Email address: [email protected] (Raha Akhavan-Tabatabaei)URL: http://wwwprof.uniandes.edu.co/~r.akhavan (Raha Akhavan-Tabatabaei)

Preprint submitted to Computers & Industrial Engineering December 9, 2014

Since the beginning of the millennium, almost 2.7 billion people have been affected, 1.1million killed and a damage of 1.3 trillion dollars has been reported worldwide due only tonatural disasters (United Nations Office for Disaster Risk Reduction, 2012). The IndianOcean Tsunami (2004), caused by an in-depth ocean earthquake, the Chilean earthquake(2010) and Japan’s Earthquake (2011) are listed among the 10 largest earthquakes in theworld since 1900 (USGS Earthquake Hazard Program, 2012). The Indian Ocean Tsunami(2004) is also considered as one of the deadliest disasters of the last century, leaving 280,000deaths and causing the evacuation of 1.7 million people in 12 countries (BBC News, 2005).The Japan earthquake and Tsunami (2011), considered the world’s costliest disaster since1965, accounts for an estimated economic loss of 240 billion dollars, representing 4.1% of thecountry’s GDP of that year and other disasters such as the European Heat Wave (2003) andCyclone Nargis (2008) have also accounted for over 70,000 casualties each (IFRC, 2010).

On the other hand, technological disasters, which are the result of man-made productfailures and are typically accidental, have accounted for additional thousands of affectedand dead people. These can be categorized as transport system accidents (large-scale road,air and maritime accidents), collapse of constructions, large fires, and technological andtoxic accidents (nuclear power plant accidents, leakage of hazardous substances) (Weisæthet al., 2002). Examples around the world include Japan’s Fukushima nuclear power stationfailure after Japan’s earthquake in 2011, which is still producing leakages of highly toxicwater and whose total consequences cannot yet be known, the 2013 Savar building collapsein Bangladesh which accounted for 2500 injured people and 1129 deaths and Chernobylnuclear disaster on April 26, 1986 which is considered the deadliest accidental structuralfailure in modern human history and probably the most remembered one (Weisæth andTønnessen, 1995).

In order to keep a record of these events, the Centre for Research on the Epidemology ofDisasters (CRED) has developed the International Disaster Database (EM-DAT) containinginformation on the occurrence and impact of more than 18,000 disasters since 1900. Foran event to be considered in this database ten or more people should be reported dead, ahundred or more affected and there should be a declaration of state of emergency or the callfor need of international assistance (CRED, 2012).

According to the information in the EM-DAT database, the total number of natural andtechnological disasters seems to be increasing, as well as the number of people affected bythem. This may be influenced by problems ranging from high structural and social vulner-ability, lack of emergency planning, limited resources (money, personnel, medical attentionunits, etc.), uncertainty and variability of demand, response times, structural reliability andthe delay in the arrival of aid teams. For instance, the catastrophic impact of the HaitiEarthquake (2010) to the country’s society was in great measure a consequence of inade-quate seismically resistant infrastructure, the government’s low capacity to respond to anevent of this magnitude and the late arrival of specialized teams of international aid (it be-gan 24 hours after the quake strike), due mostly to the poor transportation infrastructure(Greenberg, 2010). On the contrary, in the case of the Chilean Earthquake, the governmenthad anticipated the possibility of such an event happening and had developed plans for re-

2

2. DOM definitions and boundaries of the study

Research on DOM has been given great attention in the past decade in response to thecatastrophic impact of disasters during this period and the need for better practices in orderto tackle these events, however the span of DOM is not known by most people. Rawls andTurnquist (2012) define DOM as the sequence of operations that seek to prevent or reducethe injuries, fatalities, and damages resulting from a disaster; and to facilitate the recoveryfrom such an event. Similarly, Altay and Green III (2006) consider it as the set of activitiesthat are performed before, during, and after a disaster with the goal of preventing loss ofhuman life, reducing its impact on the economy and returning faster to a state of normalcy.As it can be seen, DOM considers all the actions taken to reduce the disaster impact, fromthe minimization of vulnerability and mitigation of risk, to the reconstruction proceduresand the implementation of programs to return to normalcy.

According to FEMA (2004), the DOM life cycle is divided into four main stages or phases:mitigation, preparedness, response and recovery. Mitigation refers to the actions taken toprevent a disaster, reduce the chance of it happening, or reduce its damaging effects. Zoningand land use plans, building codes, barrier construction and vulnerability and risk assessmentare part of the activities of this phase. Preparedness includes plans or preparations made tosave lives and to help response and rescue operations. It aims to reduce the response timeby the advance procurement and pre-positioning of needed resources. Activities such as the

3

sponding in an efficient way. There was almost no need of international assistance, and thecapacity and control of the government over the situation reduced the impact of the disasterconsiderably (Benjamin et al., 2011). This demonstrates the fact that efficient planning andresponse can drastically reduce the social, economic and environmental impact of disasters.

In this way, Disaster Operations Management (DOM) provides techniques to prepare acommunity and reduce the severity of damage caused by all types of disasters by developingcommunications system, stockpiling inventory, building adequate structures, etc. Each ofthese decisions and actions could make a community more resilient to natural disasters, ifdone properly (Guha-Sapir and Santos, 2012). Nevertheless, the decision-making process tosupport emergency response is not an easy process and differs greatly from business logistics,because it involves a high level of uncertainty in the number of people who are affected and inneed of attention (Christie and Levary, 1998; Van Wassenhove and Pedraza Martinez, 2012).Therefore, employing tools and techniques to model this stochasticity into the decision-making process is essential in preparedness and response against disasters.

This document surveys the recent body of literature that applies Operations Research(OR) techniques to improve the decision-making process in DOM and includes at least onestochastic component in their proposed model. The rest of this document is organizedas follows: Section 2 presents the most important definitions of DOM and establishes thejustification of the research and the search methodology. The survey of literature is presentedin Section 3, an analysis on the stochastic components and the methods used to approachthem is presented in Section 4 and conclusions and possible future research is suggested inSection 5. Finally, Appendix A shows the constructed database for the review.

recruitment and training of personnel, emergency planning and the acquiring of vehicles,equipment and resources are also performed in the preparedness stage.

The response activities take place immediately after the disaster and consider all themeasures taken to safely attend affected people. The emergency plans are activated, theurban search and rescue begin, affected people are evacuated and taken for medical careand emergency supplies are mobilized. Finally the recovery stage refers to the long termplans to follow in order to return to normalcy, including debris removal, reconstruction ofinfrastructure and implementation of financial assistance programs, among others.

DOM is being used by many governments around the world in order to reduce disas-ters’ impact. However the unpredictability (probability of occurrence, location, impact),magnitude (limiting response capacity), uncertainty (number of victims or affected, demandlocation, damaged infrastructure) and complexity (possibility of replicas or secondary dis-asters, communication and coordination difficulty) of these events can make it difficult todevelop efficient plans. This is due to the fact that there are many variables that should beconsidered in the different analyses which are almost impossible to predict.

In recent years, the OR community has given a lot of attention to DOM and has demon-strated its appropriateness and usefulness in the area. One of the first thorough reviewsdeveloped in the topic was conducted by Altay and Green III (2006). In their research, 109articles were consulted considering all kind of disasters and OR methodologies which werelater categorized by journal, phase of disaster, research methodology, research contribution,disaster type and problem scenario. With their work it could be seen that most of literaturein OR focused on the mitigation phase, and mathematical programming, including heuris-tics, was used as the main tool to attack the problems. According to this survey, a betterunderstanding of the inputs and characteristics of different events as well as the developmentof new solution methodologies were needed. They also pointed out that there should be moreresearch on multi-agency structures in order to facilitate the coordination and communica-tions during disasters, there should be more models using soft OR techniques and there wasstill need for the development of more methods for the recovery phase.

As a continuation to this research, Galindo and Batta (2013) conducted a bibliographicreview on OR models in DOM from 2005 to 2012, comprising 155 articles. In their study theyfollowed the same classification scheme as Altay and Green and carried out a comparisonwith their DOM research trends. They concluded that there has not been a significant changein the methodology percentages since 2006 and mathematical programming is still the mostwidely used methodology, but there has been more interest in preparedness and responsethan mitigation in recent years. One of their most valuable contributions is the researchassumption section where the appropriateness of each of the assumptions used in DOMwas analyzed considering its applicability. In their conclusion they mentioned the lack ofresearch developed in conjunction with humanitarian organizations, the lack of papers for therecovery phase and the need to better understand and analyze the inputs and assumptionsin the models.

Complementary to these studies, several important reviews are carried out on human-itarian logistics. Kovacs and Spens (2007) have consulted 98 articles up to 2005, focusing

4

on logistics and supply chain management in disasters. In their review of academic andpractitioner literature they exalt the importance of research in the different stages and theneed of solutions to affront the challenges of disasters such as the destabilized infrastructure,uncertainty in demand, supply and response time and the need of dynamic models to copewith this challenges. Overstreet et al. (2011), reviewed 51 articles and provided a good ref-erence for humanitarian logistics’ complexities and future research, including areas such asplanning policies and procedures, organization’s personnel, infrastructure, transportation,information technology or communications and inventory management. Wright et al. (2006)focuses on the applications of OR in homeland security and explores the opportunities forthe operations researchers to contribute to this field from the point of view of the US De-partment of Homeland Security which was formed after the attacks of September 11, 2001.Simpson and Hancock (2009) review the OR foundation in the emergency response phaseand discuss the existing and at times paradoxical challenges of the field, only focusing onone of the four phases of a disaster. Lettieri et al (2009) offer a systematic review of theliterature on disaster management within the period 1980-2006, with the goal of contributingto the existing knowledge on disaster management. They do not focus on a specific type ofhazard but instead attempt to define the state of the art of the discipline. Finally, Libera-tore et al. (2013), reviewed 27 articles. In each a methodology to deal with uncertainty inhumanitarian logistics was identified. The contributions of these methodologies to the topicare tremendous, however they are not usually applied by practitioners.

As it was pointed out by Altay and Green III (2006) and backed by the other surveysmentioned above, among all the OR techniques, mathematical programming has been giventhe most attention, and considering this, there have been more literature reviews in thisarea than in the others. Caunhye et al. (2012) conducted a review on optimization mod-els in emergency logistics, classifying their findings according to the operation carried out:facility location, relief distribution and casualty transportation and model types, decisions,objectives and constraints. Future research in multi-objective and dynamic models, modelsincluding the possibility of inter-facility stock transfer and casualty transportation combin-ing transportation time, injury seriousness and on-field treatment are some of the directionsproposed by the authors. de la Torre et al. (2012) conducted a review on the Vehicles Rout-ing Problem in disaster-affected regions to deliver goods and services to distribution pointsand beneficiaries, classifying their review according to the characteristics of the problem(allocation policies, needs assessment, uncertainty in demand and supply, vehicle and routescharacteristics) and their different objectives (minimization of time of delivery, minimizationof costs, minimization of unsatisfied demand etc).

The large number of papers found by each of these reviews shows the momentum thatresearch in the topic has gained. However, none of these reviews examines the existing bodyof literature of OR models in DOM from the point of view of their stochastic components,except for Liberatore et al (2013) which covers a limited number of papers. Taking intoaccount the multiple uncertainties of disasters, the use of stochastic components in themodels has acquired great popularity and so the development of a literature survey on howto model this uncertainty using OR tools and techniques seems appropriate at the time, as

5

it could highlight the best Stochastic OR practices in the field and light the way to furtherimprovements. On the other hand, the last thorough review on OR models developed byGalindo and Batta (2013) included papers up until 2010, however there have been moreadvances in the topic since then, work that has not yet been reviewed and that accounts fornearly 50 percent of the literature reviewed in the present survey.

The objectives of the present work include a bibliographic review on OR techniqueswith stochastic components in DOM, with its main contribution being an analysis of thestochastic components present in each paper and the methodologies used to solve or modelthem. Another major contribution is the creation of a database of the recent developmentsin the topic, useful for future researchers and a classification of all the consulted articlesaccording to the phase of disaster, OR technique and publication year. Finally the paperidentifies the lacking work and possible future research directions in DOM with stochasticityincluded.

For the literature review, the time period considered in the research ranges from 2006to 2012. The EBSCO, Emerald, IEEE Explore, INFORMS Journals, JSTOR, ScienceDirectand SpringerLink databases were consulted and the keywords “catastrophe”, “disaster”, “dis-aster operations management”, “disaster relief”, “disaster response”, “emergency response”,“humanitarian logistics”, “disaster decision models” and “relief operations” were used inthe search process. According to the abstract, only the articles that applied an OR tech-nique (Mathematical Programming, Simulation, Probability and Statistical Models, ExpertSystems and Artificial Intelligence, Queuing Theory and Decision Theory) were taken intoaccount. After this preliminary classification, the articles were filtered, leaving only the onesthat considered any uncertainties or stochastic components. Then, for each paper the ref-erences were reviewed and relevant papers from the references were selected with the sameprocess. After this procedure was done, a total of 101 papers were included in the review.

After the filtering process, a classification method was established and the articles wereclassified according to the phase of disaster (Mitigation, Preparedness, Response, Recovery),the OR technique used (Mathematical Programming, Simulation Models, Probability andStatistical Models, Expert Systems and Artificial Intelligence, Decision Theory and MultiAttribute Utility Theory, Queuing Theory), the publication year (2006-2012) and the jour-nal (European Journal of Operations Research, Socio Economic Planning Sciences, Trans-portation Research, Safety Science, among others). Among the OR techniques used in theclassification in Altay and Green (2006) only six were considered in this review. Stochasticand constraint programming, which were separated in Altay and Greens classification, wereincluded in mathematical programming in this research. Regarding fuzzy sets just one ar-ticle was found on the topic so this methodology was not included, as nor was the soft ORtechniques for the same reason. Based on the previous information, a statistical analysis onthe number of papers in each area was developed, a summary and analysis on the stochasticcomponents used in each paper was added and a database with the relevant information ofall the consulted papers was created.

6

3. OR Research in DOM

The reviewed articles consider work using different OR techniques that focus on multi-ple problems. The emphasis of mathematical programming is mainly on the preparednessand response operations considering facility pre-positioning, resource allocation, relief dis-tribution and casualty transportation. Simulation research focuses on the development ofmodels that help process and analyze input data for the response phase and consider mostlythe development and use of spatial decision support systems and geographical informationsystems. The consulted probability and statistical models affront problems of the mitiga-tion phase with the use of artificial neural networks and time series techniques in order tohave better forecasts for events such as floods, snow disasters and typhoons; they also workon demand prediction and risk assessment in disasters. The decision theory models mostlyapply methodologies as MAUT (Multi-Attribute Utility Theory), multi-criteria analysis andBayesian network models to determine disasters risk and attention policies. Finally, from thearticles found in queuing theory, 2 of them focus on Markovian processes used in predictionand forecasting, and the others consider network survivability.

3.1. Characterization of articles

From the 101 articles reviewed, 48 use mathematical programming, 9 apply simulationmodels, 20 probability or statistical models, 12 use expert systems or artificial intelligence, 8work with decision theory methods and 4 use queuing theory, as shown in Figure 1. Amongthem, 22 are considered part of the mitigation phase, 28 of the preparedness stage, 47 of theresponse stage and 4 recovery stage, as shown in Figure 2.

Figure 1: Classification of articles by OR methodology (2006-2012).

This distribution of articles reveals that the popular trends in DOM research focus pri-marily on mathematical programming models with stochastic features for the preparednessand response phases, with many of them having a simulation component as well. Meanwhilethe probabilistic and statistical methods were used mostly on risk and prediction analysisin the mitigation phase and decision theory covers all of the stages. Work on the recoverystage, as well as on queuing theory methodologies, has not been given much attention so far.

7

Figure 2: Classification of articles by phase of disaster.

Figure 3: Papers timeline.

In addition in Figure 3 the evolution of the number of articles for each of the OR areasis shown. As it can be seen, the number of papers in mathematical programming withstochastic components increased steadily from 2006 to 2012, presenting a peak in 2007. Asimilar behavior could be seen with the probability and statistics area, having its peak inthe year of 2010. Simulation and queuing theory papers on the other hand, did not followany particular trend but they both got to zero between 2011 and 2012. Finally for decisiontheory a constant number of articles can be seen, with an increase in the years 2007 and2011. Taking into account these trends, the application of simulation and queuing theoryresearch should be enhanced. In the next sections a more detailed analysis on the papersis carried out in order to establish the most popular research directions according to eachmethodology classification.

8

3.2. Mathematical ProgrammingFor mathematical programming research, four main classifications were used in the study

facility location, which focuses on the preparedness stage, and three response stage researchdirections, i.e., resource allocation, relief distribution and casualty transportation.

3.2.1. Facility Location and Resource AllocationFacility location problems involve the pre-positioning of warehouses and distribution of

medical centers in the most convenient and effective locations in order to be able to provideassistance during the disaster. Resource allocation models focus on the activities of locatingresources before or right after the occurrence of a disaster. Most of the consulted papers inmathematical programming consider the facility location or prepositioning, combined withresource allocation, relief distribution and sometimes casualty transportation. In the facilitylocation front, Jia et al. (2007) developed three different heuristics: a genetic algorithm, alocation-allocation heuristic and a Langrangian relaxation heuristic to determine the facilitylocation of medical supplies in case of a large-scale disaster. In their model they considereduncertainty on the demand and supply location which they tackled by giving each demandpoint a factor of likelihood to be impacted. They formulate a maximal covering problemwith the possibility of having multiple facilities with different quality levels for each demandpoint, with the objective of maximizing covered demands.

Chang et al. (2007) developed a two stage stochastic programming, scenario-based modelfor planning flood emergency logistics to give a solution to the emergency problem with uncer-tainty on demand location and quantity, considering a multi-group, multi-level, multi-echelonnetwork. In the first stage they group disaster areas and classify their level of emergency,while minimizing the expected shipping distance; the second stage contains the location-allocation model, with the objective of minimizing the costs (facility setup, transportation,demand shortage) they select the local rescue bases to open, the quantity of rescue equip-ment to send to storehouses and the routes that emergency transportation should follow.They use Geographic Information System (GIS) and sampling based approximation in theircase study of a flood in Taipei City.

Using Mixed Integer Programming (MIP), Balcik and Beamon (2008) developed a modelfor location and stock pre-positioning of distribution centers, maximizing the expected de-mand covered by them, considering stochastic components in the location of demand, amountof demand for a great variety of supplies and supply quantity and location. They tested theirprogram by modeling the global location of distribution centers based on earthquake strikehistorical data.

Rawls and Turnquist (2010) proposed a Langrangian L-shaped heuristic algorithm forsolving a two- stage stochastic scenario-based MIP in order to provide an emergency responsepre-positioning planning tool for hurricane and other disaster scenarios. In their model theobjective is to minimize the expected costs over all scenarios that result from the selectionof facility locations and sizes, commodity stocking decisions, unused material holding costsand unmet demand penalties, considering uncertainty in demand for stocked supplies andtransportation network availability. With their case study on preparedness for hurricanethreats in the South-eastern United States, they showed a reduction of approximately 30%

9

in the computational time in comparison with the results from commercial MIP software.Afterwards, they developed the multi-period version with a two-stage, dynamic and scenariobased stochastic program for the preposition and allocation of facilities and commoditydistribution after a disaster event, with the objective being the minimization of total costs.This model considered multiple periods and scenarios, as well as the possibility of includinginfrastructural damage in the network (Rawls and Turnquist, 2012).

Sheu et al. (2005) developed a model for forecasting relief demand and clustering de-mand points according to their uncertain urgency status with a fuzzy clustering techniquein order to allocate daily consuming relief commodities in disasters, with the objective ofminimizing the travelling costs from relief centers for real time analysis. Balcik et al. (2008)mixed the resource allocation and relief distribution by proposing a multi-period MIP todetermine schedules for a fixed set of vehicles and an equitable allocation of resources, bythe minimization of transportation and unsatisfied or late-satisfied demand costs and themaximization of the benefits of aid recipients, for local distribution points using a rollinghorizon to cope with the uncertainty in supply and demand. Their approach considers twophases, the first one generates all possible delivery routes, the second one determines theamount of supplies to be sent to each demand point by the vehicles in the coming periods.

As it can be seen, a lot of recent facility location and resource allocation models involveMIP and stochastic programming combined with heuristic algorithms in order to reduce thecomputational time and facilitate the problem’s convergence. Another interesting approachfound was the inclusion of multi-period analysis when solving this kind of problems.

3.2.2. Relief Distribution and Casualty Transportation

The Relief Distribution and casualty transportation models center their attention onfinding the best possible routes for the transportation of resources from distribution centersto the affected people, or people from the disaster site to hospitals or medical centers. Tzenget al. (2007) developed a fuzzy multi-objective linear programming model for designing reliefdelivery systems. The model considers three objectives: first, minimization of total costs,second, minimizing the total travel time and third, maximizing the minimal satisfactionduring the planning period using a prediction for the commodity demand at each establishedpoint and an uncertainty analysis of achievement for each objective. The Taichung, NantouCity earthquake in September 1999 was used as the case study to test the model. Other multi-objective models include the evacuation in transportation networks, proposed by Stepanovand Smith (2009) which considers an integer programming set-packing formulation for thestochastic emergency evacuation problem with uncertainty in demand.

Models considering MIP are applied frequently in this field. Yan and Shih (2009) de-veloped a multi-objective, mixed-integer, multi-commodity network flow problem for theroadway repair and relief distribution, with the objective of minimizing the length of timerequired for these activities, within a limited period of time. They created the problemin a time-space network and used the weighting method for the objective functions and aheuristic algorithm to solve the problem considering an error tolerance in order to cope withthe uncertainty or unavailability of post-disaster information. Zhang et al. (2012) proposeda local Search heuristic with MIP for the multiple-disaster multiple-response emergency al-

10

location and disaster relief problem, considering the stochastic occurrence of a secondarydisaster and having as the objective the minimization of total rescue costs of primary andsecondary disasters. Their algorithm reduced the computational time by 26.4% comparedto the optimization based method. Other models containing MIP are seen in Wohlgemuthet al. (2012) and Rottkemper et al. (2012).

Two-stage stochastic programming models are also very popular in the field. As an ex-ample, Shen et al. (2009) proposed a model divided in two stages, a planning stage and anoperational stage. For the first stage, the route planning, they developed a stochastic pro-gramming model, considering the uncertainty in the model by including chance constraintsand quantifying all the unmet demand. The second stage was developed in order to includethe uncertain parameters (once they are observed) to the model. Three different strategieswere used for this stage, Linear programming recourse strategy, a knapsack recourse strat-egy and a re-planning, for comparison. Other authors that developed models with two-stageprogramming include Maqsood and Huang (2013) model for flood management and Tricoireet al. (2012) bi-objective two-stage stochastic program with recourse, scenario-based, usingthe epsilon-constraint heuristic method with branch and bound for relief distribution.

Finally, programs including casualty transportation or evacuation are also frequent in theliterature. Chiu and Zheng (2007) developed a cell transmission based linear program modelfor the simultaneous traffic assignment and departure schedule for multi-priority groups andevacuation traffic flows for emergency response to disasters using models to estimate theuncertain demand based on demographic data and travel activity patterns. Yi and Ozdamar(2007) considered a two-stage mixed integer multi-commodity network flow model for thecapacitated Location-Routing Problem (LRP). Their objective included the minimizationof unsatisfied demand and delay in commodity and healthcare service. In the model theycategorized wounded people, considered an expansion of the hospital capacities and predictedfuture demand per period.

3.2.3. Search and Rescue

Among other activities and scenarios for mathematical programming problems, the searchand rescue activity has acquired popularity in recent years. It focuses on models that tryto optimize the search and rescue activities in order to save the lives of as many people aspossible in the first hours of the disaster. Jotshi and Batta (2008) developed a heuristicto deal with the problem of search for an immobile entity (uniformly distributed) on anundirected network. Their objective was to minimize the search time, considering thatthere is no communication between the searcher and the entity and that the location ofthe entity is not known with certainty, but a region of interest could be found from datafusion. The solution is found using the Eulerian graph conversion. Chen and Miller-Hooks(2012) proposed a scenario based, Multi-stage stochastic program with column generationfor the Urban Search and Rescue Team Deployment Problem USAR-TDP, in order to getthe optimal search and rescue team deployment. Having the maximization of the expectednumber of saved lives as their objective, they could establish the routes and deployment ofsearch teams, considering that the number of teams varies with period, the demand dependson diminishing likelihood of survival and building damage, and newly devastated sites are

11

discovered and enter the model following a Poisson process. A summary of the results areshown in Figure 4, Figure 5 and Figure 6.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Minimize Cost

Minimize Unsatisfied Demand

Maximize coverage

Maximize expected number of lives

Minimize Travel Time

Maximize costumer benefit

Minimize errors

Maximize System Flow

Minimize distance

Total of Articles 48

Figure 4: Classification of Mathematical Programming articles by objective function.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Mixed Integer problem

Two Stage Stochastic Program

Genetic Algorithms

Robust Optimization

Clustering

Entity Search Heuristics

Network Optimization

Other Heuristics

Dynamic Programming

Total of Aritcles 48

Figure 5: Classification of Mathematical Programming articles by optimization methodology.

3.3. Simulation Models

Simulation methodologies in DOM focus primarily on the use of Spatial Decision SupportSystems (SDSS) and Discrete Event Simulation (DES) models. Most of the SDSS researchhas focused on the integration of forecasting and early warning models with GIS applications.In the SDSS combining GIS area, there has been a great number of simulation papersincluding Horner and Downs (2007) research on a flexible geographic information system-based network flow model for routing, that combines a GIS and a flexible network flow

12

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Facility Prepositioning

Resource allocation

Relief Distribution

Evacuation

Optimal Search and Rescue

Other


Figure 6: Classification of Mathematical Programming articles by problem to solve.

13

model for the distribution of relief goods to populations after a hurricane occurrence. Themodel identifies locations to localize distribution centers, including multiple policies and withthe possibility of visualizing the planning scenarios. Other papers such as Ye et al. (2010)(GIS-based study of natural disaster vulnerability for Xiamen city) and Chen et al. (2010)(secondary disaster pre-warning based on GIS and subsequent risk analysis), also use thiskind of systems.

Massaguer et al. (2006) developed a multi-agent simulation system for disaster responseactivity that takes information from instrumented points in the University of California,Irvine, and combines geographic space simulation and agent behavior for a building evacua-tion simulation. They use a geographical spatial system, modeling each person as an agentand using neural networks for the agent decision making part. El-Anwar et al. (2009) devel-oped an automated system to support decision-makers in optimizing post-disaster temporaryhousing arrangements. The system consists of three phases: data collection, automated opti-mization and output analysis and visualization and considers as objectives the minimizationof negative socio-economic impacts, maximization of housing safety, minimization of negativeenvironmental impacts and the minimization of public expenditures.

Finally, four research works consider the DES approach. Yi et al. (2010) proposed ageneric simulation model to represent the operations of hospitals during an earthquake dis-aster scenario, and with the obtained results they fitted generalized regression equationsin order to obtain steady-state hospital capacities during this event. Nore˜developed a simulation model for the transfer of injured people to temporary and perma-nent hospitals after an earthquake scenario, considering triage classifications and hospitalcapacities. Lee et al. (2009) models the supply chain of relief goods, the distribution opera-tion and the dynamics of the demand after a disaster and Fonseca et al. (2009) proposed asimulation tool for hurricane evacuation planning in the I-65 major US Interstate highway,

0 1 2 3 4 5

Discrete Event Simulation

Multi-Agent Simulation

Automated decision support system

Geographic Information System

Total of Articles 9

Figure 7: Classification of Simulation articles by used methodology.

3.4. Probability and Statistical Models

The probability and statistical approach in DOM focuses on the risk management modelsthat forecast the occurrence of a determined event using time series analysis, dynamic pro-gramming models for the design of disaster relief systems, statistical modeling to analyze anddetermine natural and man-made disaster risks, the use of Bayesian Networks for the riskassessment of events and probabilistic models to describe and analyze emergency systemsand evacuation. Forecast models consider the work developed by Mishra and Desai (2006) ondrought forecasting based on time series using Auto-Regressive Integrated Moving Average(ARIMA) and Artificial Neural Networks (recursive multi-step and direct multi-step), basedon the Standardized Precipitation Index (SPI) and Moreira et al. (2008) SPI-based droughtforecasting using log-linear models, in Alentejo Region, Portugal, which demonstrated thatthe utilized method was a useful tool for short drought warning. Other works on that topicalso include Xu et al. (2010) that proposes a model on the demand forecast of commoditiesafter natural disasters applying a hybrid forecasting method integrating, Empirical ModelDecomposition (EMD) and ARIMA models, used in the prediction of agricultural productsfor the response to the 2008 Chinese winter storms.

On the other hand, statistical models are greatly used in the risk assessment stage.Guikema (2009) proposes a statistical learning methodology, considering a diverse set ofmethods designed to perform inference analysis over large, complex data sets, for risk analy-sis of the impact of natural disasters in large-scale, critical infrastructure systems and electricpower distribution systems, transportation systems, etc. Toya and Skidmore (2007) developa model to estimate the relationship between measures of economic development and theeffect of natural disasters, using linear regression analysis for deaths and damages or GDP

14

including statistical testing to identify variation in relevant traffic variables affecting the flowof vehicles. Figure 7 shows the distribution by methodology for the total of articles.

vs. different economic and social factors, while Chatterjee and Abkowitz (2011) developa linear regression model for the regional terrorism risk assessment, expressed in expectedannual monetary terms as a function of attributes such as population density and criticalinfrastructure. Other statistical models can be found in McLay et al. (2012) for the analysisof the volume and nature of emergency medical calls during severe weather events and Donget al. (2011) for predicting the failure probability of landslide dams, which are landslides thatblock water flow on rivers for some time, forming natural lakes, that finally breakdown aftersome time once they can’t contain the lake anymore. Other models using probability toolsinclude Chu and Wang (2012) that present a new approach for addressing the event proba-bility uncertainties and analyzing probability distribution, in order to construct probable firescenarios, and Jacobson et al. (2012) who study the probability distribution of aspects suchas survival time and service times of patients in order to develop a model to assign differentpriority levels to victims of disasters, based on their injuries. They modeled the problem asa priority assignment problem in a clearing system with multiple classes of impatient jobsthat are classified by lifetime, service time and reward distributions, with the objective ofmaximizing total expected rewards. Figures 8 and 9 show the classification of articles inProbability and Statistics.

0 1 2 3 4 5 6 7 8 9

LINEAR OR LOGLINEAR REGRESSION

ARIMA

SELF BALANCING CUSUM

BAYESIAN NETWORK

PROBABILITY DISTRIBUTIONS


Figure 8: Classification of articles in Probability and Statistics based on used methodology.

3.5. Artificial Intelligence and Expert SystemsArtificial Intelligence mostly uses ANN (Artificial Neural Networks) and case base rea-

soning in their models. The use of ANN can be found in Lee (2008) and Wu et al. (2008),that apply Back Propagation Artificial Neural Networks (BP-ANN) to forecast the short-term storm surge and surge deviation in Taichung harbor, Taiwan, during 2003 and developa risk evaluation method for heavy snow disasters, considering environmental possibilities ofhazard and disaster inducing factors in Xilingol, Mongolia respectively. ANN is also used byLee and Evangelista (2006), Nefeslioglu et al. (2008) and Chauhan et al. (2010) in Landslide

15

0 1 2 3 4 5 6 7

FORECASTING

DECISION SUPPORT SYSTEM

RISK EVALUATION

DEMAND PREDICTION

ALLOCATION OF RESOURCES

ROAD TRAFFICABILITY

MEDICAL CALLS ANALYSIS


Figure 9: Classification of articles in Probability and Statistics based on the objective.

methodology to create micro-zoning maps, by superimposing maps of slope, flood susceptibil-ity, soil, swelling and liquefactions potential, combining GIS with simple additive weightingand Analytical Hierarchy Process methods to provide a weight to each layer. Other papers

16

Susceptibility Mapping, employed by Mishra and Desai (2006) to develop drought forecastingbased on rain time series in the West Bengal region, India and applied in Liao et al. (2012),Mardiyono et al. (2012), Song et al. (2012), Kung et al. (2012) and Danso-Amoako et al.(2012) as a method to establish building or infrastructure damage, estimate life casualtiesafter an earthquake and prediction of debris flow disasters. Case base reasoning is used byLiu et al. (2012) for resources demand prediction to be applied to emergency logistics aftera disaster occurrence.

3.6. Decision TheoryDecision theory research has become popular due to the multi-organizational character-

istic of disaster management. This review contemplates models using Bayesian probabilis-tic networks, Analytical Hierarchy Process (AHP), multi-criteria decision making, multi-attribute evaluation and other decision theory methodologies to facilitate the decision mak-ing process and analysis of different information, while considering the possibility of havingmultiple decision makers. Models consulted using Bayesian probabilistic networks includeBayraktarli et al. (2005) that developed a model for earthquake risk management, based onexposure, vulnerability and robustness of the structures, and the probability of earthquakeoccurrence, and Frey and Butenuth (2011) that created a dynamic Bayesian network for theassessment of the functionality of infrastructural objects after a natural disaster, with a casestudy of the trafficability of roads after flooding.

In the multi-criteria front, Zhijun et al. (2009) developed a model using the AHP andthe Weighted Comprehensive Method (WCM) to determine the risk degree of grassland firein Jilin province, China, with the use of GIS tools. Ca˘

similar to Tesfamariam et al. (2010), propose multi-criteria decision techniques, includinguncertainties in the decision making process, considering multiple decision makers and fuzzyutilities, for seismic risk management.

Finally, multi-attribute models include articles like Zhai et al. (2007) that proposes amulti-attribute model for evaluation of flood management in Japan and Kailiponi (2010)that proposes a multi-attribute utility theory model for analyzing evacuation decisions. Theformer article studies the relationship between important attributes of flood prevention mea-sures (external flood reduction, internal flood reduction, early warning systems, environmen-tal protection and willingness to pay for countermeasures) and socio-economic factors andtests its model using information from Toki and Nagoya cities in Japan. The latter at-tempts to optimize conflicting objectives for evacuation decisions, considering the high levelof uncertainty during events of disaster. Results are shown in Figure 10.

0 1 2 3 4

GANP (Group Analytic Network Process)

AHP (Analitical Hyriarchic Process)

Multi criteria or MAUT

Game Theory

Decision and logic trees

Decision Support System

Total of Articles 8

Figure 10: Classification of decision theory models based on the used methodology.

4. Stochastic components

In their review on Uncertainty in Humanitarian Logistics for Disaster Management, Liber-atore et al. (2013) established five major parameters considering uncertainty in humanitarianlogistics: 1: Demand, that can comprehend the number of affected population and/or thequantity of required relief goods, 2: Demand location and 3: Affected areas, parameters thatare directly related to the demography of the location and the disaster’s impact, 4: Supply,that considers the products’ quality and availability in a post-disaster scenario, and finally5: Transportation network, where all possible damages to the infrastructure or congestionsare included. Based on this classification but dividing the ”affected areas” parameter intotwo different factors: one considering disaster hazard and occurrence uncertainty and theother one to consider the site or infrastructure damage, and including a new parameter ”Hu-man behavior”, we have conducted an analysis on stochastic components for all of the 101

17

papers reviewed in this article, in which the stochastic component is shown along with thetechnique used to model the uncertainty and the disaster stage when found. The summaryof this analysis is presented in Table 1.

Table 1: Stochastic Components

18

Stochastic Parameter StochasticComponent

Papers addressing thecomponent

Stage ofdisaster

Approach to model stochasticity

Disaster hazard andoccurrence uncertainty

Earthquake andother disasters haz-ard, exposure andvulnerability

Bayraktarli et al. (2006),Yi and Ozdamar (2007),El-Anwar et al. (2009),Guikema (2009), Tong, Z.Zhang, J. Liu. X. (2009),Kailiponi (2010), Legg etal. (2010), Barker andHaimes (2009), Hashemi etal. (2011), Lagaros etal. (2011), Qi and Al-tinakar (2011), Rottkem-per et al (2011), Velmaand Gaulker (2011), Wanget al (2012), Guanquan etal. (2012), Maqsood andHuang (2012), Song et al(2012), Van Steenbergen etal. (2012), Wang and Lin(2012)

Mitigation andResponse

Use of probability functions and hazard mapsfrom major international building codes andstudies, Monte Carlo simulation and statisticallearning to establish hazard and vulnerabilityparameters and distributions. Some also useBayesian probability networks to study the in-terdependence between the different parameters.

Ocurrence andseverity of droughts,floods, storms, snowor other disasters.

Lee and Evangelista(2006), Mishra and Desai(2006), Brito and Almeida(2007), Paulo and Pereira(2007), Xiang et al.(2007), Lee (2008), Wu etal. (2008), Nefeslioglu etal. (2008), Yilmas (2009),Chauhan et al. (2010),Han et al (2010), Pradhanand Lee (2010), Donget al (2011), Wang et al(2011), Akgun (2012),Danso Amoako (2012),Jacobson et al. (2012),Kung et al. (2012), Lianget al. (2012), Liao et al.(2012), Xu et al. (2012)

Mitigation Use of ARIMA, Logistic regression, recursivemulti-step artificial neural networks and Markovchains methods to model the behavior of the phe-nomenon, forecasting the disaster impacts or es-tablishing accident scenario probabilities.

Probability of a dis-aster occurrence

Zhai et al. (2007), Velmaand Gaulker (2011), Doyenet al. (2012), Wang et al.(2012)

Mitigation andResponse

Consider multiple scenarios, each with a givenprobability, to cope with the uncertainty of dis-aster occurrence.

Occurrence andseverity of droughts

Moreira et al. (2008) Mitigation Use of a loglinear model to develop short termprediction of drought severity classes. They alsoevaluated confidence intervals in order to un-derstand the drought evolution and to estimatedrought class transition probabilities.

Demand uncertainty

Forecasting demandof commodities aftera disaster

Xu et al. (2010) Preparednessand Response

Use of EMD-ARIMA method to forecast the de-mand of certain commodities after a disaster im-pacts a certain region.

Demand uncertainty

Lee et al. (2009), Yaoet al. (2009), Liu et al(2012), Xu et al. (2012)

Preparednessand Response

Use of Genetic algorithms or case-base reason-ing to establish demand in different points of thenetwork or robust optimization with constraintsregarding the uncertainty in demand.

Ben-Tal et al. (2011) Preparednessand Response

Use of AARC methodology to deal with the un-certainty in demand, where each demand belongsto a box uncertainty set and use joint constraintsto create an upper bound for possible values.

Blecken et al . (2010), Liand Li (2012), Rottkemperet al. (2012), Tricoire etal. (2012)

Recovery Part of the demand in known (based on time se-ries analysis and causal models) while another isvariable given certain probabilities or distribu-tions that depend on the operational risks presentin the region

Demand uncertaintyand medical supplyinsufficiency

Jia et al. (2007), Leeet al. (2009), Murali etal. (2011), Zhan andLiu (2011), Murali et al.(2012)


Each demand point is covered by multiple facil-ities, located at different distances so that theoverall coverage is achieved based on expectedvalues of demand. Muroli and Zhan and Liu alsoused chance constraints to include the probabil-ity distribution of demand at each demand point.

SpaceTable 1: (Continued) Stochastic Components

19



Stage ofdisaster


Demand location

Demand uncer-tainty, number ofpossible sites fortemporary cen-ters and resourcesavailable

Yi and Ozdamar (2007),Balcick and Beamon(2008), Beraldi and Bruni(2009), Akhavan-Tabataeiand Rios (2011), Gormezet al. (2011), Gunnecet al. (2011), Zhan andLiu (2011), Chen andMiller-Hooks (2012)


Use of different scenarios, each with a knownprobability of impact and location, to cope withuncertainties in demand and disaster location forthe model.

Demand location Chang and Hsueh (2007),Chang et al. (2007), Lei(2007), Henterick et al.(2010), Rawls, C. Turn-quist, M. (2010), Li et al.(2011), Rawls, C. Turn-quist, M. (2012)


Use of multiple disaster scenarios, with probabil-ities for each one, to establish possible demandlocations based on GIS and other analysis func-tions of disaster potential/hazard.

Uncertainty in thelocation of an entityand the probabilityof detection of theentity

Jotshi and Batta (2008) Response The entity is considered to be uniformly dis-tributed in an Eulerian graph.

Human behaviorCharacteristics andpossible decisionstaken by an agentinvolved in anevacuation

Massaguer et al. (2006),Kailiponi (2010)


Defining different agents by providing a mean anda variance for each of the agent’s profile parame-ters and evaluating their behavior using multiplescenarios or by doing a probability assessment ofthe possible behaviors.

Uncertainty in crite-ria weights

Levy and Taji (2007) Response Use of ordinal information in group decision mak-ing to establish the preferences of the criteria.

Supply Supply (resourcelevels, vehicle avail-ability) and demanduncertainty

Balcick et al. (2008) Response Use a rolling-horizon framework to capture themultiperiodicity of the problem, as well as its in-herent supply and demand uncertainties.

Site or infrastructuredamage

Probability of dam-age from an attackor disaster

Zhuang and Bier (2007),Ezell et al. (2010)

Mitigation Level of attacker effort is represented as a contin-uous variable, allowing the probability of damageto be modeled as a function of the levels of bothattacker effort/disaster magnitude, vulnerabilityand defensive investment.

Uncertainty due topossible inaccuracyin determining theconsequences (interms of emergencyresponse) of bridgecollapse.

Bana e Costa et al. (2008) Mitigation Develop a sensitivity analysis introducing in themodel an interval of uncertainty of 0.5 h aroundthe consequence estimated for each structure.

Level of damage andprobability of accu-racy in informationon road conditions

Jotshi and Batta (2009) Response Each road is given a level of damage based on in-formation given by civilians, police officers, fire-fighters etc, and a probability of accuracy of thisinformation, based on the source and previous in-formation of the point.

Level of damage ofinfrastructure

Frey and Buttenuth (2010) Response Use of a Bayesian network to model the behaviorof the system after a disaster, and establish itstrafficability.

Survival probabilityof an structure(bridges, highwaysetc.)

Peeta et al. (2010), Rawls,C. Turnquist, M. (2010),Cimellaro et al. (2010),Hassin et al. (2010)

Response The survival probability is obtained from expertsopinions or analysis taking into account the in-tensity of the event and loss estimation func-tions, with the possibility of increasing the sur-vival probability or resilience by investing moreresources on given structures.

Damage level of astructure (bridges,highways etc.)

Mardiyono et al. (2010) Response Development of a backpropagation artificial neu-ral network model to establish the level of dam-age of a structure given a certain disaster.

Trafficability oftransportation network Reliability of a route Vitoriano et al. (2010),

Nolz et al. (2011), Liber-atore et al. (2012), Yi andKumar (2007), Yushimitoand Ukkusuri (2008), Renet al. (2012)

Response Establish an attribute of reliability which in thiscase is given by the probability to cross com-pletely an arc in the route, based on damage ex-pected in each region.

SpaceTable 1: (Continued) Stochastic Components

20



Stage ofdisaster


Trafficability oftransportation network

Emergency calls andtravelling times

Beraldi and Bruni (2009),Huang and Fan (2011),Noyan et al (2012)


Uncertainty is handled by including in the tradi-tional two stage framework stochastic constraintsor their probabilistic counterparts allowing thesystem manager to evaluate different solutions byvarying reliability levels.

Occurrence of traf-fic events that maycause delay in evac-uation.

Fonseca et al. (2009) Preparednessand Response

Time of arrival, final destination exit and acci-dent proneness are assigned based on cumulativeprobability distributions based on empirical datacollected in data collection phase of the project.Other variables as accident factor and accidentdelay time are generated as user-defined proba-bility distributions given by expert officials andthe entry of entities is treated as a stochastic pro-cess with Poisson or Binomial distributions.

Probabilities ofpacket loss after theevent and routingprobabilities

Heegaard and Trivedi(2009)

Response Routing probabilities are imported from ns-2simulations before and after a failure, reroutingand repair. The routing probabilities can also beobtained from operational networks.

Congestion and timedelays on road linksand blockage proba-bilities

Heegaard and Trivedi(2009), Chen et al (2012)

Response Use of M/G/c/c state dependent queuing mod-els to cope with congestion and time delays onroad links and stochastic constraints to controlblockage probabilities.

Taking into account these results, it can be seen that most of the mitigation research isdeveloped with the objective of reducing the uncertainties in disaster hazard or occurrence,by developing models to forecast disaster’s impact or models that could explain in a betterway the behavior of the phenomena. The use of probability functions from known inter-national codes or studies, or the use of ARIMA, logistic regression and Artificial Networkmodels and Markov chains are very popular in this stage. In the preparedness and responsephases it can be stated that the demand quantity and location uncertainty is a major con-cern, given the large number of papers that take this factor into account. However it canbe seen how uncertainty factors such as infrastructure reliability and transportation com-plications are acquiring more popularity. The use of multiple scenario models, undirectedor directed graphs, stochastic programming and robust optimization analysis are among themost popular techniques to model the uncertainties in the preparedness and response stages.

A factor that is still in its early stages is the modeling of human behavior in post-disaster events, an area that may provide interesting and useful information for many DOMmodels, and so is seen as a very promising future research direction. Finally it can be saidthat as in the previous analysis the recovery stage has not been very popular, however themethodologies used in prior stages, mainly in the response stage, can be used to tackle thestochastic components of the recovery stage.

5. Conclusions and Future Research

The reviewed articles consider work using different OR techniques to solve problemsarising in DOM. The emphasis of Mathematical Programming research is mainly on the pre-paredness and response operations considering facility pre-positioning, resource allocation,relief distribution and casualty transportation. Simulation research focuses on the devel-opment of models that help to process and analyze input data for the response phase andconsider mostly the development of spatial support decision systems using geographic infor-mation systems, with a few DES models. The consulted probability and statistical models

21

affront problems of the mitigation phase with the use of logistic regression and time seriestechniques and the Artificial Intelligent and Expert Systems use ANN in order to providebetter forecasts for events such as floods, snow disasters and typhoons; they also work ondemand prediction and risk assessment in disasters. The decision theory models mostlyapply methodologies such as MAUT and multi-criteria analysis to determine disaster riskand attention policies. Finally, from the articles found in queuing theory, 2 of them focuson Markovian processes used in prediction and forecast, and the others consider networksurvivability.

A great amount of research has been done with OR methods in DOM in recent years;however there are still some topics that have not received sufficient attention in the literatureof OR in DOM. Due to the uncertainty of the occurrence and magnitude of disasters, there isa lack in the consideration of different scenarios and planning for them, as a measure to copewith the uncertainty. Many models assume various parameters or variables without previousanalysis, which can lead to important mistakes during the planning and response phases.As it was proposed by Altay and Green III (2006), a better understanding of the specificcharacteristics of the events and their impact is still needed in order to develop pertinentmodels.

There has been a greater popularity for the development of multi-disciplinary modelsthat include different methodologies in order to respond to a specific problem. The use ofprobabilistic or stochastic tools can help with the accuracy of the assumptions of optimizationmodels, as the use of queuing theory elements helps to replicate the real system behavior.The use of simulation can help visualizing data and results in comparing the performance ofthe model with the real system and the use of multi-objective and multi-criteria models fordecision making seems appropriate considering the different actors involved in the decisionprocess. This is how the combination of different methodologies in one model can facilitatethe handling of information and the decision making process.

The previous solutions respond to problems in DOM as a whole, however, a significantamount of research is also focused on the different stages of a disaster. In the preparednessand response phases one of the encountered limitations includes models for the allocationof resources that assume that resources and commodities are stocked in distribution centerswith restricted capacity, to which the demand points are assigned, but that do not considerthe possibility of inter-facility stock transfer. Each center has to attend a specific number ofdemand points, and they are charged an unmet demand fee, but the possibility to assign aspecific demand point to another distribution facility is not considered. This is also causedby the lack of contemplation of multiple periods in the models. Recently there is a trend toinclude multi-period analysis, but there still is a reduced number of models that implementit. The use of multi-period models helps the decision maker, as it is a more comprehensiveanalysis and new information can be included for the future periods, once it is known.

Another topic that has not been studied much in the response phase is the inventoryplanning in the distribution or local relief centers, mostly because of the uncertainty ofsupply and demand of commodities. During and after disasters, most of the relief items orcommodities that are donated, arrive at uncertain times and can involve a large variety of

22

items. A good distribution of these items among all the relief centers as well as the goodmanagement of these resources is important to address the shortages or scarcity. Models thatinclude allocation of resources, distribution relief and inventory planning can contribute tothe literature and help in the development of decision making models.

On the other hand, the evacuation and casualty transportation research has been limitedand so needs further study. From the modeling of search and rescue activities, consideringthe information on potential zones to find trapped victims, the availability of teams in thedisaster zone, the arrival of international teams, the magnitude of the disaster and theefficiency in the victims’ retrieval to the deployment of emergency transportation and theprovision of health care is needed in order to reduce the number of casualties due to a disasteras was also states in Galindo and Batta (2013). Models that include transportation, inter-arrival and service times, injury seriousness, medical centers capacities among other factorsform an important research direction in this front. Also, the contemplation of the possibilityof having damage in the infrastructure, as well as possible secondary disasters should be anintegral part of the models, as they are one of the most important causes of loss of efficiency inthe response phase. The effectiveness and productivity in this stage are crucial, and given itsmulti-organizational characteristic, a good coordination and cooperation between multiplerelief agencies and governments is essential. Further research in topics like communicationnetworks in disasters, information systems, as well as consideration of multi-objective ormulti-criteria models are needed for making better decisions.

Based on the stochastic component analysis, a tendency to include demand quantityand location uncertainty in the models can be observed, mainly by considering multiplescenarios, each with a specific probability of occurrence. However there are other techniquesthat have not been used commonly and can provide a major contribution to many modelssuch as the use of genetic algorithms and the consideration of covering multiple demandpoints with multiple distribution centers to ensure the demand satisfaction. The strategyof multiple scenarios is also used to quantify the impact of the disaster that is also tackledby assigning probability distributions or hazard maps given by major building codes orstudies and using forecasts made with logistic regression, ARIMA models or ANN. Anothermethodology that can be used to include uncertainty in demand, supply or disaster impactis the use of sensitivity analysis including intervals of uncertainty in demand, supply orestimated disaster consequences.

Finally, as it has been mentioned by multiple authors, more research is necessary in therecovery phase of DOM. The mitigation, attention and response phases have been given thedue attention, and there is a good amount of studies in each of these stages, however theplanning for long term scenarios and the return to normalcy is still lacking. Activities likedebris removal and facility repair should be given more importance in the DOM cycle andOR methodologies seem a good way to attack this kind of problems.

References

Akgun, A., 2012. A comparison of landslide susceptibility maps produced by logistic regres-sion, multi-criteria decision, and likelihood ratio methods: a case study at izmir, turkey.

23

Landslides 9 (1), 93–106.

Altay, N., Green III, W. G., 2006. Or/ms research in disaster operations management. Eu-ropean Journal of Operational Research 175 (1), 475–493.

Balcik, B., Beamon, B. M., 2008. Facility location in humanitarian relief. InternationalJournal of Logistics Research and Applications 11 (2), 101–121.

Balcik, B., Beamon, B. M., Smilowitz, K., 2008. Last mile distribution in humanitarianrelief. Journal of Intelligent Transportation Systems 12 (2), 51–63.

Bana e Costa, C. A., Oliveira, C. S., Vieira, V., 2008. Prioritization of bridges and tunnelsin earthquake risk mitigation using multicriteria decision analysis: Application to lisbon.Omega 36 (3), 442–450.

Barker, K., Haimes, Y. Y., 2009. Assessing uncertainty in extreme events: Applications torisk-based decision making in interdependent infrastructure sectors. Reliability Engineer-ing & System Safety 94 (4), 819–829.

Bayraktarli, Y. Y., Ulfkjaer, J., Yazgan, U., Faber, M. H., 2005. On the application ofbayesian probabilistic networks for earthquake risk management. In: 9th internationalconference on structural safety and reliability, Italy, Rome.

BBC News, January 2005. Indonesia quake toll jumps again.URL http://news.bbc.co.uk/2/hi/asia-pacific/4204385.stm

Ben-Tal, A., Chung, B. D., Mandala, S. R., Yao, T., 2011. Robust optimization for emergencylogistics planning: Risk mitigation in humanitarian relief supply chains. Transportationresearch part B: methodological 45 (8), 1177–1189.

Benjamin, E., Bassily-Marcus, A. M., Babu, E., Silver, L., Martin, M. L., 2011. Principlesand practice of disaster relief: Lessons from haiti. Mount Sinai Journal of Medicine: AJournal of Translational and Personalized Medicine 78 (3), 306–318.

Beraldi, P., Bruni, M. E., 2009. A probabilistic model applied to emergency service vehiclelocation. European Journal of Operational Research 196 (1), 323–331.

Berkoune, D., Renaud, J., Rekik, M., Ruiz, A., 2012. Transportation in disaster responseoperations. Socio-Economic Planning Sciences 46 (1), 23 – 32.

Blecken, A., Danne, C., Dangelmaier, W., Rottkemper, B., Hellingrath, B., 2010. Optimalstock relocation under uncertainty in post-disaster humanitarian operations. In: SystemSciences (HICSS), 2010 43rd Hawaii International Conference on. IEEE, pp. 1–10.

Brito, A. J., de Almeida, A. T., 2009. Multi-attribute risk assessment for risk ranking ofnatural gas pipelines. Reliability Engineering & System Safety 94 (2), 187–198.

24

Caunhye, A. M., Nie, X., Pokharel, S., 2012. Optimization models in emergency logistics: Aliterature review. Socio-Economic Planning Sciences 46 (1), 4 – 13.

Cagl Kolat, Doyuran, V., Ayday, C., Szen, M. L., 2006. Preparation of a geotechnical mi-crozonation model using geographical information systems based on multicriteria decisionanalysis. Engineering Geology 87 (34), 241 – 255.

Central Intelligence Agency, 2012. The world factbook - haiti.URL https://www.cia.gov/library/publications/the-world-factbook/geos/ha.html

Chang, M.-S., Hsueh, C.-F., 2007. Developing geographic information system for flood emer-gency logistics planning. In: Proceedings of the 2007 summer computer simulation con-ference. Society for Computer Simulation International, pp. 652–659.

Chang, M.-S., Tseng, Y.-L., Chen, J.-W., 2007. A scenario planning approach for the floodemergency logistics preparation problem under uncertainty. Transportation Research PartE: Logistics and Transportation Review 43 (6), 737–754.

Chatterjee, S., Abkowitz, M. D., 2011. A methodology for modeling regional terrorism risk.Risk Analysis 31 (7), 1133–1140.

Chauhan, S., Sharma, M., Arora, M., Gupta, N., 2010. Landslide susceptibility zonationthrough ratings derived from artificial neural network. International Journal of AppliedEarth Observation and Geoinformation 12 (5), 340–350.

Chen, L., Miller-Hooks, E., 2012. Optimal team deployment in urban search and rescue.Transportation Research Part B: Methodological 46 (8), 984 – 999.

Chen, T., Miao, L., Yuan, H., 2010. Secondary disaster prewarning based on gis and subse-quent risk analysis. In: Communication Systems, Networks and Applications (ICCSNA),2010 Second International Conference on. Vol. 2. pp. 292–295.

Chen, X., Kwan, M.-P., Li, Q., Chen, J., 2012. A model for evacuation risk assessment withconsideration of pre-and post-disaster factors. Computers, environment and urban systems36 (3), 207–217.

Chiu, Y.-C., Zheng, H., 2007. Real-time mobilization decisions for multi-priority emergencyresponse resources and evacuation groups: Model formulation and solution. TransportationResearch Part E: Logistics and Transportation Review 43 (6), 710 – 736.

Christie, P. M. J., Levary, R. R., 1998. The use of simulation in planning the transportationof patients to hospitals following a disaster. Journal of Medical Systems 22, 289–300.

Chu, G., Wang, J., 2012. Study on probability distribution of fire scenarios in risk assessmentto emergency evacuation. Reliability Engineering & System Safety 99 (0), 24 – 32.

25

Cimellaro, G. P., Reinhorn, A. M., Bruneau, M., 2010. Framework for analytical quantifica-tion of disaster resilience. Engineering Structures 32 (11), 3639–3649.

CRED, 2012. Em-dat the international disaster database.URL www.emdat.be/criteria-and-definition

Danso-Amoako, E., Scholz, M., Kalimeris, N., Yang, Q., Shao, J., 2012. Predicting damfailure risk for sustainable flood retention basins: A generic case study for the widergreater manchester area. Computers, Environment and Urban Systems 36 (5), 423–433.

de la Torre, L. E., Dolinskaya, I. S., Smilowitz, K. R., 2012. Disaster relief routing: Integrat-ing research and practice. Socio-Economic Planning Sciences 46 (1), 88 – 97.

Dessouky, M. M., Ordonez, F., Murali, P., 2009. Capacitated facility location with distance-dependent coverage under demand uncertainty.

Dong, J.-J., Tung, Y.-H., Chen, C.-C., Liao, J.-J., Pan, Y.-W., 2011. Logistic regressionmodel for predicting the failure probability of a landslide dam. Engineering Geology117 (1), 52–61.

Doyen, A., Aras, N., Barbarosoglu, G., 2012. A two-echelon stochastic facility location modelfor humanitarian relief logistics. Optimization Letters 6 (6), 1123–1145.

Duran, S., Gutierrez, M. A., Keskinocak, P., 2011. Pre-positioning of emergency items forcare international. Interfaces 41 (3), 223–237.

El-Anwar, O., El-Rayes, K., Elnashai, A., 2009. An automated system for optimizing post-disaster temporary housing allocation. Automation in Construction 18 (7), 983 – 993.

Ezell, B. C., Bennett, S. P., Von Winterfeldt, D., Sokolowski, J., Collins, A. J., 2010. Prob-abilistic risk analysis and terrorism risk. Risk Analysis 30 (4), 575–589.

FEMA, 2004. The four phases of disaster. FEMA - Emergency Management Institute.

Fetter, G., Rakes, T. R., 2011. A self-balancing cusum approach for the efficient alloca-tion of resources during post-disaster debris disposal operations. Operations ManagementResearch 4 (1-2), 51–60.

Fonseca, D. J., Moynihan, G. P., Johnston, J., Jennings, J., 2009. A simulation tool forhurricane evacuation planning. Modelling and Simulation in Engineering 2009, 10.

Frey, D., Butenuth, M., 2011. Multi-temporal damage assessment of linear infrastructuralobjects using dynamic bayesian networks. In: Analysis of Multi-temporal Remote SensingImages (Multi-Temp), 2011 6th International Workshop on the. pp. 61–64.

Galindo, G., Batta, R., 2013. Review of recent developments in or/ms research in disasteroperations management. European Journal of Operational Research 230 (2), 201 – 211.

26

Gormez, N., Koksalan, M., Salman, F., 2011. Locating disaster response facilities in istanbul.Journal of the Operational Research Society 62 (7), 1239–1252.

Greenberg, E., 2010. Profs: Infrastructure problems exacerbated haiti quake disaster.URL http://cornellsun.com/section/news/content/2010/01/26/profs-infrastructure-problems-exacerbated-haiti-quake-disaster

Guanquan, C., Jinhui, W., 2012. Study on probability distribution of fire scenarios in riskassessment to emergency evacuation. Reliability Engineering & System Safety 99, 24–32.

Guha-Sapir, D., Santos, I. (Eds.), 2012. The Economic Impacts of Natural Disasters. OxfordUniversity Press.

Guikema, S. D., 2009. Natural disaster risk analysis for critical infrastructure systems: Anapproach based on statistical learning theory. Reliability Engineering & System Safety94 (4), 855 – 860.

Gunnec, D., Salman, F. S., 2011. Assessing the reliability and the expected performance ofa network under disaster risk. OR spectrum 33 (3), 499–523.

Han, P., Wang, P. X., Zhang, S. Y., Zhu, D. H., 2010. Drought forecasting based on theremote sensing data using arima models. Mathematical and Computer Modelling 51 (11),1398–1403.

Hashemi, M., Alesheikh, A. A., 2011. A gis-based earthquake damage assessment and set-tlement methodology. Soil dynamics and earthquake engineering 31 (11), 1607–1617.

Hassin, R., Ravi, R., Salman, F. S., 2010. Facility location on a network with unreliablelinks. Tech. rep., Working paper. Retrieved May 30, 2010, from http://www. di. unipi.it/di/groups/optimize/Events/proceedings/M/B/4/MB4-4. pdf.

Heegaard, P. E., Trivedi, K. S., 2009. Network survivability modeling. Computer Networks53 (8), 1215–1234.

Horner, M. W., Downs, J. A., 2007. Testing a flexible geographic information system-basednetwork flow model for routing hurricane disaster relief goods. Transportation ResearchRecord: Journal of the Transportation Research Board 2022 (1), 47–54.

Huang, Y., Fan, Y., 2011. Modeling uncertainties in emergency service resource allocation.Journal of Infrastructure Systems 17 (1), 35–41.

IFRC, 2010. World disasters report 2010 - focus on urban risk.URL http://www.ifrc.org/Global/Publications/disasters/WDR/WDR2010-full.pdf

IFRC, 2012. What is a disaster?URL www.ifrc.org/en/what-we-do/disaster-management/about-disasters/what-is-a-disaster/

27

Iraq Body Count, 2012. Documented civilian deaths from violence.URL www.iraqbodycount.org/database/

Jacobson, E. U., Argon, N. T., Ziya, S., 2012. Priority assignment in emergency response.Operations Research 60 (4), 813–832.

Jia, H., Ordez, F., Dessouky, M. M., 2007. Solution approaches for facility location of medicalsupplies for large-scale emergencies. Computers & Industrial Engineering 52 (2), 257 – 276.

Jotshi, A., Batta, R., 2008. Search for an immobile entity on a network. European Journalof Operational Research 191 (2), 347 – 359.

Jotshi, A., Gong, Q., Batta, R., 2009. Dispatching and routing of emergency vehicles indisaster mitigation using data fusion. Socio-Economic Planning Sciences 43 (1), 1–24.

Kailiponi, P., 2010. Analyzing evacuation decisions using multi-attribute utility theory(maut). Procedia Engineering 3 (0), 163 – 174.

Kovacs, G., Spens, K. M., 2007. Humanitarian logistics in disaster relief operations. Inter-national Journal of Physical Distribution & Logistics Management 37 (2), 99–114.

Kung, H.-Y., Chen, C.-H., Ku, H.-H., 2012. Designing intelligent disaster prediction modelsand systems for debris-flow disasters in taiwan. Expert Systems with Applications 39 (5),5838–5856.

Lagaros, N. D., Karlaftis, M. G., 2011. A critical assessment of metaheuristics for schedulingemergency infrastructure inspections. Swarm and Evolutionary Computation 1 (3), 147–163.

Lee, S., Evangelista, D., 2006. Earthquake-induced landslide-susceptibility mapping usingan artificial neural network. Natural Hazards and Earth System Science 6 (5), 687–695.

Lee, T.-L., 2008. Back-propagation neural network for the prediction of the short-term stormsurge in taichung harbor, taiwan. Engineering Applications of Artificial Intelligence 21 (1),63–72.

Lee, Y. M., Ghosh, S., Ettl, M., 2009. Simulating distribution of emergency relief suppliesfor disaster response operations. In: Winter Simulation Conference. Winter SimulationConference, pp. 2797–2808.

Legg, M. R., Nozick, L. K., Davidson, R. A., 2010. Optimizing the selection of hazard-consistent probabilistic scenarios for long-term regional hurricane loss estimation. Struc-tural Safety 32 (1), 90–100.

Lei, F., 2007. Dynamic multi-objective emergency relief logistics: A decision support systemframework. In: Grey Systems and Intelligent Services, 2007. GSIS 2007. IEEE Interna-tional Conference on. IEEE, pp. 779–783.

28

Lettieri, E., Masella, C., Radaelli, G., 2009. Disaster management: findings from a systematicreview. Disaster Prevention and Management 18 (2), 117–136.

Levy, J. K., Taji, K., 2007. Group decision support for hazards planning and emergency man-agement: A group analytic network process (ganp) approach. Mathematical and ComputerModelling 46 (7), 906–917.

Li, A. C., Xu, N., Nozick, L., Davidson, R., 2011. Bilevel optimization for integrated shelterlocation analysis and transportation planning for hurricane events. Journal of Infrastruc-ture Systems 17 (4), 184–192.

Li, X., Li, Y., 2012. A model on emergency resource dispatch under random demand andunreliable transportation. Systems Engineering Procedia 5, 248–253.

Li, X., Wang, X., Shao, W., Xia, L., Zhang, G., Tian, B., Li, W., Peng, P., 2007. Forecastof flood in chaohu lake basin of china based on grey-markov theory. Chinese GeographicalScience 17 (1), 64–68.

Liang, W.-j., Zhuang, D.-f., Jiang, D., Pan, J.-j., Ren, H.-y., 2012. Assessment of debris flowhazards using a bayesian network. Geomorphology 171, 94–100.

Liao, Z., Wang, B., Xia, X., Hannam, P. M., 2012. Environmental emergency decision sup-port system based on artificial neural network. Safety Science 50 (1), 150 – 163.

Liberatore, F., Pizarro, C., Blas, C., Ortuo, M., Vitoriano, B., 2013. Uncertainty in hu-manitarian logistics for disaster management. a review. In: Vitoriano, B., Montero, J.,Ruan, D. (Eds.), Decision Aid Models for Disaster Management and Emergencies. Vol. 7of Atlantis Computational Intelligence Systems. Atlantis Press, pp. 45–74.

Lin, Y.-H., Batta, R., Rogerson, P., Blatt, A., Flanigan, M., 2009. A logistics model fordelivery of critical items in a disaster relief operation: heuristic approaches. TransportationResearch Part E.

Liu, W., Hu, G., Li, J., 2012. Emergency resources demand prediction using case-basedreasoning. Safety science 50 (3), 530–534.

Maqsood, I., Huang, G., 2013. A dual two-stage stochastic model for flood management withinexact-integer analysis under multiple uncertainties. Stochastic Environmental Researchand Risk Assessment 27 (3), 643–657.

Mardiyono, M., Suryanita, R., Adnan, A., 2012. Intelligent monitoring system on predic-tion of building damage index using artificial neural network. TELKOMNIKA IndonesianJournal of Electrical Engineering 10 (1), 155–164.

Massaguer, D., Balasubramanian, V., Mehrotra, S., Venkatasubramanian, N., 2006. Multi-agent simulation of disaster response. In: ATDM workshop in AAMAS. Vol. 2006. Citeseer.

29

McLay, L. A., Boone, E. L., Brooks, J. P., 2012. Analyzing the volume and nature of emer-gency medical calls during severe weather events using regression methodologies. Socio-Economic Planning Sciences 46 (1), 55–66.

Mishra, A., Desai, V., 2006. Drought forecasting using feed-forward recursive neural network.Ecological Modelling 198 (12), 127 – 138.

Moreira, E. E., Coelho, C. A., Paulo, A. A., Pereira, L. S., Mexia, J. T., 2008. Spi-baseddrought category prediction using loglinear models. Journal of Hydrology 354 (14), 116 –130.

Murali, P., Ordonez, F., Dessouky, M. M., 2012. Facility location under demand uncertainty:Response to a large-scale bio-terror attack. Socio-Economic Planning Sciences 46 (1), 78–87.

Nefeslioglu, H., Gokceoglu, C., Sonmez, H., 2008. An assessment on the use of logistic regres-sion and artificial neural networks with different sampling strategies for the preparationof landslide susceptibility maps. Engineering Geology 97 (3), 171–191.

Ngueveu, S. U., Prins, C., Wolfler-Calvo, R., 2008. A memetic algorithm for the cumulativecapacitated vehicle routing problem. In: EU/MEeting.

Nolz, P. C., Semet, F., Doerner, K. F., 2011. Risk approaches for delivering disaster reliefsupplies. OR spectrum 33 (3), 543–569.

Norena, D., Yamın, L., Akhavan-Tabatabaei, R., Ospina, W., 2011. Using discrete eventsimulation to evaluate the logistics of medical attention during the relief operations inan earthquake in bogota. In: Proceedings of the Winter Simulation Conference. WinterSimulation Conference, pp. 2666–2678.

Noyan, N., 2012. Risk-averse two-stage stochastic programming with an application to dis-aster management. Computers & Operations Research 39 (3), 541–559.

Overstreet, R. E., Hall, D., Hanna, J. B., Rainer Jr, R. K., 2011. Research in humanitarianlogistics. Journal of Humanitarian Logistics and Supply Chain Management 1 (2), 114–131.

Paulo, A. A., Pereira, L. S., 2007. Prediction of spi drought class transitions using markovchains. Water resources management 21 (10), 1813–1827.

Pradhan, B., Lee, S., 2010. Delineation of landslide hazard areas on penang island, malaysia,by using frequency ratio, logistic regression, and artificial neural network models. Envi-ronmental Earth Sciences 60 (5), 1037–1054.

Qi, H., Altinakar, M., 2011. A gis-based decision support system for integrated flood man-agement under uncertainty with two dimensional numerical simulations. EnvironmentalModelling & Software 26 (6), 817–821.

30

Rawls, C. G., Turnquist, M. A., 2010. Pre-positioning of emergency supplies for disasterresponse. Transportation Research Part B: Methodological 44 (4), 521 – 534.

Rawls, C. G., Turnquist, M. A., 2012. Pre-positioning and dynamic delivery planning forshort-term response following a natural disaster. Socio-Economic Planning Sciences 46 (1),46–54.

Ren, X., Zhu, J., Huang, J., 2012. Multi-period dynamic model for emergency resourcedispatching problem in uncertain traffic network. Systems Engineering Procedia 5, 37–42.

Rottkemper, B., Fischer, K., Blecken, A., 2012. A transshipment model for distributionand inventory relocation under uncertainty in humanitarian operations. Socio-EconomicPlanning Sciences 46 (1), 98 – 109.

Rottkemper, B., Fischer, K., Blecken, A., Danne, C., 2011. Inventory relocation for overlap-ping disaster settings in humanitarian operations. OR spectrum 33 (3), 721–749.

Shen, Z., Dessouky, M. M., Ordez, F., 2009. A two-stage vehicle routing model for large-scalebioterrorism emergencies. Networks 54 (4), 255–269.

Sheu, J.-B., 2010. Dynamic relief-demand management for emergency logistics operationsunder large-scale disasters. Transportation Research Part E: Logistics and TransportationReview 46 (1), 1 – 17.

Sheu, J.-B., Chen, Y.-H., Lan, L. W., et al., 2005. A novel model for quick response todisaster relief distribution. In: Proceedings of the Eastern Asia Society for TransportationStudies. Vol. 5. pp. 2454–2462.

Simpson, N., Hancock, P., 2009. Fifty years of operational research and emergency response.Journal of the Operational Research Society, S126–S139.

SONG, R., HE, S., ZHANG, L., 2009. Optimum transit operations during the emergencyevacuations. Journal of Transportation Systems Engineering and Information Technology9 (6), 154 – 160.

Song, Y., Gong, J., Gao, S., Wang, D., Cui, T., Li, Y., Wei, B., 2012. Susceptibility assess-ment of earthquake-induced landslides using bayesian network: A case study in beichuan,china. Computers & Geosciences 42, 189–199.

Stepanov, A., Smith, J. M., 2009. Multi-objective evacuation routing in transportation net-works. European Journal of Operational Research 198 (2), 435 – 446.

Tesfamariam, S., Sadiq, R., Najjaran, H., 2010. Decision making under uncertaintyan exam-ple for seismic risk management. Risk Analysis 30 (1), 78–94.

The Economist, 2011. Natural disasters. counting the cost.URL http://www.economist.com/blogs/dailychart/2011/03/natural disasters

31

Tinguaro Rodrıguez, J., Vitoriano, B., Montero, J., 2010. A natural-disaster managementdss for humanitarian non-governmental organisations. Knowledge-Based Systems 23 (1),17–22.

Toya, H., Skidmore, M., 2007. Economic development and the impacts of natural disasters.Economics Letters 94 (1), 20 – 25.

Tricoire, F., Graf, A., Gutjahr, W. J., 2012. The bi-objective stochastic covering tour prob-lem. Computers & Operations Research 39 (7), 1582 – 1592.

Tzeng, G.-H., Cheng, H.-J., Huang, T. D., 2007. Multi-objective optimal planning for design-ing relief delivery systems. Transportation Research Part E: Logistics and TransportationReview 43 (6), 673 – 686.

Ukkusuri, S. V., Yushimito, W. F., 2008. Location routing approach for the humanitarianprepositioning problem. Transportation Research Record: Journal of the TransportationResearch Board 2089 (1), 18–25.

United Nations Office for Disaster Risk Reduction, 2012. Infographic: The economic andhuman impact of disasters in the last 12 years.URL http://infographiclist.com/2013/05/08/the-economic-and-human-impact-of-disasters-in-the-last-12-years-infographic/

USGS Earthquake Hazard Program, November 2012. Largest earthquakes in the world since1900.URL http://earthquake.usgs.gov/earthquakes/world/10 largest world.php

Van Hentenryck, P., Bent, R., Coffrin, C., 2010. Strategic planning for disaster recovery withstochastic last mile distribution. In: Integration of AI and OR techniques in constraintprogramming for combinatorial optimization problems. Springer, pp. 318–333.

Van Steenbergen, N., Ronsyn, J., Willems, P., 2012. A non-parametric data-based approachfor probabilistic flood forecasting in support of uncertainty communication. EnvironmentalModelling & Software 33, 92–105.

Van Wassenhove, L. N., Pedraza Martinez, A. J., 2012. Using or to adapt supply chainmanagement best practices to humanitarian logistics. International Transactions in Oper-ational Research 19 (1-2), 307–322.

Verma, A., Gaukler, G. M., 2011. A stochastic optimization model for positioning disasterresponse facilities for large scale emergencies. In: Network Optimization. Springer, pp.547–552.

Vitoriano, B., Ortuo, M., Tirado, G., Montero, J., 2011. A multi-criteria optimization modelfor humanitarian aid distribution. Journal of Global Optimization 51 (2), 189–208.

32

Wang, J., Yang, H., Zhu, J., 2012a. A two-stage stochastic programming model for emergencyresources storage region division. Systems Engineering Procedia 5, 125–130.

Wang, J.-P., Lin, C.-W., Taheri, H., Chan, W.-S., 2012b. Impact of fault parameter un-certainties on earthquake recurrence probability examined by monte carlo simulationanexample in central taiwan. Engineering Geology 126, 67–74.

Weisæth, L., Knudsen Jr, Ø., Tønnessen, A., 2002. Technological disasters, crisis manage-ment and leadership stress. Journal of hazardous materials 93 (1), 33–45.

Weisæth, L., Tønnessen, A., 1995. Public reactions in norway to radioactive fallout. Radia-tion Protection Dosimetry 62 (1-2), 101–106.

Wen, R., Huang, Q., Luo, N., Zhao, Q., 2008. The study on spatial decision support servicesarchitecture based on grid gis in emergency response platform. In: Wireless Communica-tions, Networking and Mobile Computing, 2008. WiCOM ’08. 4th International Conferenceon. pp. 1–5.

Wohlgemuth, S., Oloruntoba, R., Clausen, U., 2012. Dynamic vehicle routing with anticipa-tion in disaster relief. Socio-Economic Planning Sciences 46 (4), 261 – 271.

Wright, P. D., Liberatore, M. J., Nydick, R. L., 2006. A survey of operations research modelsand applications in homeland security. Interfaces 36 (6), 514–529.

Wu, J.-d., Li, N., Yang, H.-j., Li, C.-h., 2008. Risk evaluation of heavy snow disasters using bpartificial neural network: the case of xilingol in inner mongolia. Stochastic EnvironmentalResearch and Risk Assessment 22 (6), 719–725.

xia Wanga, H., xin Niua, J., feng Wua, J., 2011. Ann model for the estimation of lifecasualties in earthquake engineering. Systems Engineering Procedia 1 (Complete), 55–60.

Xu, C., Xu, X., Dai, F., Saraf, A. K., 2012. Comparison of different models for susceptibilitymapping of earthquake triggered landslides related with the 2008 wenchuan earthquake inchina. Computers & Geosciences 46, 317–329.

Xu, X., Qi, Y., Hua, Z., 2010. Forecasting demand of commodities after natural disasters.Expert Systems with Applications 37 (6), 4313 – 4317.

Yan, S., Shih, Y.-L., 2009. Optimal scheduling of emergency roadway repair and subsequentrelief distribution. Computers & Operations Research 36 (6), 2049 – 2065.

Yao, T., Mandala, S. R., Do Chung, B., 2009. Evacuation transportation planning underuncertainty: a robust optimization approach. Networks and Spatial Economics 9 (2), 171–189.

Ye, J., Lin, G., Zhang, M., Lin, Z., Chen, J., 2010. Gis-based study of natural disastervulnerability for xiamen city. In: Geoinformatics, 2010 18th International Conference on.pp. 1–5.

33

Yi, P., George, S. K., Paul, J. A., Lin, L., 2010. Hospital capacity planning for disasteremergency management. Socio-Economic Planning Sciences 44 (3), 151 – 160.

Yi, W., Kumar, A., 2007. Ant colony optimization for disaster relief operations. Transporta-tion Research Part E: Logistics and Transportation Review 43 (6), 660–672.

Yi, W., Ozdamar, L., 2007. A dynamic logistics coordination model for evacuation andsupport in disaster response activities. European Journal of Operational Research 179 (3),1177 – 1193.

Zhai, G., Fukuzono, T., Ikeda, S., 2007. Multi-attribute evaluation of flood management injapan: a choice experiment approach. Water and Environment Journal 21 (4), 265–274.

Zhan, S.-l., Liu, N., 2011. A multi-objective stochastic programming model for emergency lo-gistics based on goal programming. In: Computational Sciences and Optimization (CSO),2011 Fourth International Joint Conference on. IEEE, pp. 640–644.

Zhang, J.-H., Li, J., Liu, Z.-P., 2012. Multiple-resource and multiple-depot emergency re-sponse problem considering secondary disasters. Expert Systems with Applications 39 (12),11066 – 11071.

Zhijun, T., Jiquan, Z., Xingpeng, L., 2009. Gis-based risk assessment of grassland fire disasterin western jilin province, china. Stochastic Environmental Research and Risk Assessment23 (4), 463–471.

Zhuang, J., Bier, V. M., 2007. Balancing terrorism and natural disasters-defensive strategywith endogenous attacker effort. Operations Research 55 (5), 976–991.

Appendix A. Supplementary material

This appendix provides a thorough classification of all the consulted papers in this arti-cle and divides them by their approach to model the stochasticity. Then for each approachpapers are further classified by their specific methodology and phase of disaster they ad-dress. The major approach classifications include Mathematical Programming, Simulation,Probability and Statistics, Artificial Intelligence and Expert Systems, Decision Theory andQueueing Theory.

34

Authors

Mu

ltip

erio

d

Mu

ltip

le

Sin

gle

Kn

ow

n

Un

kno

wn

Det

erm

inis

tic

Sto

chas

tic

Kn

ow

n

Un

kno

wn

Ho

mo

gen

eou

s

Het

ero

gen

eou

s

Sin

gle

Mu

ltip

le

Rawls, C.

Turnquist, M.

(2012)

X X X X X X X

Two stage stochastic program.

Dynamic and scenario based pre-

position and allocation model.

Facility pre-positioning, resource

allocation and relief distribution by

minimizing total costs.

Facility location, size and

commodity availability.

Used in modelling of demands for consumable

and non-consumable goods in shelters for

hurricane events in North Carolina. Set of

huricane scenarios.

Preparedness

Chen, L. Miller-

Hooks, E. (2012)X X X X X X X

Scenario based, Multi-stage

stochastic program with column

generation for USAR-TDP

Optimal search and rescue.

Teams traveling the

nodes selected to be

visited.

Employed on the case study of the Haitian

earthquake, with 110 destroyed sites identified,

15 USAR teams, a decision horizon of 5 days and

10 stages. Computational time decreases better

than in linear rate with each stage.

Response

Tricoire. F, Graf,

A. Gutjahr, W.

(2012)

X X X X X X X

Bi-objective two-stage stochastic

program with recourse, scenario-

based, using the epsilon-constraint

heuristic method with branch and

bound

Relief Distribution.

DCs to be opened and

routes for the fleet of

vehicles to get the

necessary supplies to

each opened DC.

Treatment of stochasticity: fixed sample of N

random scenarios from the original distribution,

and replace this distribution with a discrete one

where each scenario has a 1/N probability of

ocuring. Epsilon constraint approach used,

considering and saving all Pareto-optimal

solutions. For the created instances those with

more than 21 villages couldn't be solved in less

than 3 days. Low number of scenarios.

Response.

Zhang, J. Li, J. Liu,

Z. (2012)X X X X X X

Local Search heuristic with mixed

integer programming for the

multiple-disaster multiple-

response emergency allocation

problem.

Resource Allocation and Relief

Distribution.

Quantity of resource i to

deliver to each demand

node after the primary

and secondary disasters

occurance.

Computational time reduced in 26.4% compared

to the optimization based method.Preparedness

Yi, W. Özdamar,

L. (2007)X X X X X X X

Two-stage mixed Integer multi-

commodity network flow model or

capacitated location-routing

problem (LRP).

Relief Distribution and Evacuation.

Vehicle routes and

temporary facility

location.

Proposed model studies the transportation of

commodities from major supply centers to

distribution centers in affected areas and the

transport of wounded people from affected

areas to temporary and permanent emergency

units, the goal being to minimize delay in

providing commodity and health care service.

Response.

Chang, M. Tseng,

Y. Chen, J. (2007)X X X X X X

Two stage Stochastic programming,

scenario based models for planning

flood emergency logistics,

considering a multi-group, multi-

level, multi-echelon network.


allocation and relief distribution.

Center grouping, DC's to

open, quantities of

resources in DC's, routes

for relief distribution.

First stage groups disaster areas and classifies

their level of emergency. Second stage is the

location-allocation model, local rescue bases to

open, quantity of rescue equipment in

storehouses and the route design. Use of GIS and

sampling based approximation, example for

flood in Taipei city, for first 36 hours. Storage

capacity increase means total cost reduction.

Preparedness

and Response.

Chang, M. Hsueh,

C. (2007)X X X X X X

Multi group, multi-echelon, multi-

level two stage stochastic

programming model using GIS

information.


Distribution.

Structure of rescue

organizations, locations of

storehouses, allocations

of resources under

capacity restrictions and

their distribution.

Applied to Taipei City. Use the information of GIS

maps on flooding potential under different

rainfall situations. Rescue supply and demand

distances and routes are calculated by shortest

path analysis developing an origin-destination

matrix for the analysis.

Preparedness

and Response.

Jia, H. Ordóñez,

F. Dessouky, M.

(2007)

X X X X X

Three heuristics are consider for the

maximal covering problem with

multiple facility quantity and quality

of coverage requirements: a genetic

algorithm (GA), a locate-alocate

heuristic and a Langrangean

relaxation heuristic (LR).


Distribution.

Facility sites to open and

demand points covered

by each facility.

Implemented in an antrax emergency in Los

Angeles county for facility location of medical

supplies in a large-scale disaster. They show how

the order in which facilities are opened affect

the coverage model. Their results show that for

small size of posible locations (up to 20) the GA

gives better solutions. Also for most of the

considered instances the LR gave better

solutions that the location-allocation model. In

all cases the 3 heuristic outperform CPLEX

solution.

Response

Lei. (2007) X X X X X X XDynamic Multi-Objective Emergency

Relief Logistics


Distribution.

Facility sites that need to

respond to demand

points.

Based on a priority given to the demand points, a

facility is asked to send resources to one site or

another. This is a dynamic program that enables

the decision maker to add new information as it

happens by using multiple time periods ir order

to make on-time decisions.

Response

Yi and Kumar

(2007)X X X X X X X

Network flow models with real

valued and integer commodities

(injured people), i.e., a mixed

integer multi-commodity network

flow model


Distribution and evacuation

Distribution routes and

commodity allocation

Use the ant colony metaheuristic to solve the

vehicle routing problem, in which stochastic

vehicle paths are built by iteratively adding arcs

to partial itinerary using the transition

probabilities from one node to the next. The

probabilities an possible paths change

dynamically to reflect the ants’ past search

experience

Response

Balcick, B.

Beamonm B. M.

(2008)

X X X X X X

Mixed integer programming for the

maximal covering location model,

integrating facility location and

inventory decisions.


Distribution.

Proportion of item type k

of demand satisfied by DC

j in scenario s, units of

each item stored at each

DC and DC location.

Disaster impact and demand for each item in

each scenario was established based on world

population data and geographical records of

historical disasters. DC's possible location are

considered worldwide. Show results for

different pre and post-disaster budgets,

increasing one or the other, and with all the

possible scenarios, in terms of response time

and demand coverage.

Preparedness

and Response.

Mathematical Programming

Decision Variables StageD

istr

ibu

tio

n

Cen

ters

Sup

ply

loca

tio

n

Dem

an

d

Dem

an

d

Loca

tio

n

Flee

t

Co

mm

od

itie

s

Methodology Objective Description

35

Authors

Mu

ltip

erio

d

Mu

ltip

le

Sin

gle

Kn

ow

n

Un

kno

wn

Det

erm

inis

tic

Sto

chas

tic

Kn

ow

n

Un

kno

wn

Ho

mo

gen

eou

s

Het

ero

gen

eou

s

Sin

gle

Mu

ltip

le

Balcick, B.

Beamonm B. M.

Smilowitz, K.

(2008)

X X X X X X X

Two-phases mixed integer

programming for the last mile

distribution problem.

Relief Distribution.

Delivery schedule,

vehicle routes and

inventory allocation.

Present a five day horizon example. The model

achieves equitable aid distribution and cost-

efficient routings under different settings;

however not so efficient with large scale

models.

Response

Jotshi, A. Batta,

R. (2008)X X X

Heuristic for the process of

searching for an entity in an

undirected Network based on the

Chinese Postman Problem.

Evacuation.

Trail to follow with

objective of minimizing

the

expected search time

The problem of searching for a single,

uncommunicated uniformly distributed

immobile entity on an undirected network is

presented and solved using an Eulerian graph

and two different heuristics. They show the

heuristics working with three examples: on a

general graph, on a grid structured graph and in

case of a specified start vertex.

Response

Yushimito and

Ukkusuri (2008)X X X X X X

Integer programming for the

allocation of resources in the

preparedness stage.

Resource Allocation

Supply centers and

vehicle routes, with the

demand points to cover.

Define the problem as a directed graph with

vertices being all possible demand/supply

points. They consider the routing of vehicles and

the possible disruptions in the transportation

network, as well as the possibility that pre-

positioning facilities can also be disrupted by the

disaster, so the decision has to be made based

on the most reliable candidate location and the

most reliable routes to cover all affected areas or

demand points.

Preparedness

and Response.

Beraldi, P. Bruni,

M. (2009)X X X X X X

Heuristics to help solving a two-

stage stochastic programming

embeding probabilistic constraints.


allocation and relief distribution.

Locations to open,

number of vehicles

assigned to each and

demand points to be

served by each in each

scenario.

Show the exact branch and bound solution

method of an emergency service vehicle

location, as well as three heuristics: the first two

being constructive approaches and the third

consisting of a pool of non-dominated solutions

which are proven to be the best among all

possible ones. The exact solution seemed

efficient in almost every case.

Preparedness

Jotshi, A. Gong,

Q. Batta, R.

(2009)

X X X X X XRobust optimization with data

fusion with a hirearchical approach.Evacuation.

Emergency vehicle

dispatch.

Models the dispatch of emergency vehicles (for

casualty transportation) using clusters based on

information obtained during the disaster on

casualties, road conditions and patient priority.

Implemented in an earthquake scenario with

large number of casualties in Los Angeles.

Response

Stepanov, A.

MacGregor, J.

(2009)

X X X X X X

Integer programming set-packing

formulation for the stochastic

emergency evacuation problem.

Evacuation.

Is population assigned to

kth shortest egress route

from i to j.

Combination of optimization technique and

simulation methodology to evaluate the

performance measures. This allows decision

makers to cope effectively with massive regional

evacuation, along with the stochastic nature of

evacuees' departure process and traffic

congestion.

Response

Van Hentenryck

et al. (2010)X X X X X X

Multi-stage hybrid-optimization

using a mixed integer

programming for the stochastic

storage problem and customer

allocation, constraint programming

for repository routing.


Distribution.

Amount of commodity to

be stored at each node

and for each scenario and

vehicle and the best plan

to deliver the

commodities.

Establish the most effective routes for resource

allocation and distribution by minimizing the

amount of unsatisfied demands, the time it

takes to meet those demands and the cost of

storing the commodity. Implemented in

hurricane disaster scenarios for the supply of

potable water generated by the Los Alamos

National Laboratory.

Response

Legg, M. Nozick,

L. Davidson, R.

(2010)

Mixed-integer linear programming

for optimizing the selection of

hazard-consistent probabilistic

scenarios for long-term regional

hurricane loss estimation

Prediction of loss estimates due to

disasters.

Hurricanes scenarios to be

included in the analysis.

Develop a new strategy to estimate long term

huricane loss estimation by optimizing the

selection from a group of possible huricane

scenarios created or deverloped in a simulation

software ( HAZUS-MH probabilistic analysis ).

Mitigation

Peeta, S. Salman,

S. Gunnec, D.

Viswanath, K.

(2010)

X X X

Two stage stochastic program to

decide which highways to invest in

pre-disaster to avoid possible

failures.

Pre-disaster investment

optimization.

Links or highways to

invest in

Based on uncapacitated road conditions and

using a directed network the model intends to

help the decision maker to select the links to

invest in under a limited budget, with the

objective of maximizing the post-disaster

connectivity. Used in a case study with the

Istanbul highway system.

Mitigation

Rawls, C.

Turnquist, M.

(2010)

X X X X X X XTwo stage stochastic program,

scenario based pre-position model.


allocation and relief distribution by

minimizing total costs.

Facility location, size and

commodity availability.

The first-stage variables in the stochastic

optimization include the storage facility

locations and sizes, as well as stocking decisions

for various types of supplies. The second-stage

(recourse) decisions involve the distribution

of available supplies in response to specific

scenario events and network conditions

Preparedness

Vitoriano, B.

Ortuño, M.

Tirado, G.

Montero, J.

(2010)

X X X X X X

Multi-criteria Network flow

optimization model with goal

programming.

Relief Distribution.Vehicle routes and types

of vehicles to use.

Network flow model to determine the routes

and type of vehicles to use in the response after

a disaster considering vehicle velocity, distance

to demand points, capacity and availability of

resources and vehicles, with limited budget.

Implemented in the distribution aid in Port-au-

Prince, Haiti's capital, after the 2010 Earthquake.

Response


Decision Variables StageD

istr

ibu

tio

n

Cen

ters

Sup

ply

loca

tio

n

Dem

an

d

Dem

an

d

Loca

tio

n

Flee

t

Co

mm

od

itie

s

Methodology Objective Description

36

Authors

Mu

ltip

erio

d

Mu

ltip

le

Sin

gle

Kn

ow

n

Un

kno

wn

Det

erm

inis

tic

Sto

chas

tic

Kn

ow

n

Un

kno

wn

Ho

mo

gen

eou

s

Het

ero

gen

eou

s

Sin

gle

Mu

ltip

le

Song, R. He, S.

Zhang, L. (2009)X X X X X X

Location-routing problem (LRP)

combined with genetic algorithmsEvacuation.

Route for each vehicle

and shelters selected

Evacuation plan for transit-dependent residents

in the event of natural disaster. Use of multi-

graph street network considering prohibited

turns and intersection delays and neural

networks to solve the problem by minimizing

the total

evacuation time of all evacuees and maximizing

the reliability of

the service.

Response

Yao, T. Mandala,

S. Chung, B.

(2009)

X X X X X X

Robust optimization for evacuation

transportation planning under

uncertainty

Evacuation.Route for each vehicle

and shelters selected

Development of a robust algorithm to model the

evacuation after a disaster given uncertain

demands by minimizing evacuees exposure and

by creating constraints affected by demand

uncertainty.

Response

Blecken et al .

(2010)X X X X X X X

Inventory relocation heuristic

model for optimal stock relocation

under uncertainty in risk-prone post-

disaster scenarios based on

unsatisfied demand

Resource allocation

Stock of good to store in a

depot or to transport to

other ones

Development of an inventory model considering

uncertainty in the post-disaster demand and

with objective of minimizing transportation and

inventory costs and unsatisfied demand,

considering a central distribution center and

multiple regional or local depots, and

considering multiple peak demand scenarios.

Recovery

Hassin et al .

(2010)X X X X X X X

Vulnerability-based stochastic

dependency model for facility

Location on a Network with

Unreliable Links


allocation and relief distribution Facilities to open

Development of a model to locate emergency

response facilities on a network whose links are

subject to random failure after a potential

disaster event using a directer graph.

Response

Mete and

Zabinsky (2010)X X X X X X

Two-stage stochastic optimization

of medical supply location and

distribution


allocation and relief distribution

Storage locations to open

and required inventory

levels in first stage,

transportation routes in

the second

Development of a two stage model to determine

the locations to open and amount of medical

supplies needed to cope with a earthquake

disaster scenario.

Response

Ben-Tal et al.

(2011)X X X X X X X

Robust optimization of the Cell

Transmission Model (CTM) based

system optimum dynamic traffic

assignment model

Resource allocation and relief

distribution

Storage locations to open

and required inventory

levels in first stage,

transportation routes in

the second

Development of CTM model with time

dependent demand uncertainty.Response

Gormez et al.

(2011)X X X X X X X

Two stage integer programming

model


allocation Facility location

Development of a model for the prepositioning

of temporary and permanent facilities for

disasters. First stage: temporary facilities and

find number of refugees served from each TF

and in the

second stage, TFs are taken as the demand

points and location of Permanent facilities is

established. They consider multiple scenarios to

cope with uncertainty in demand and damage

caused in a case study in Istambul, with use of

GIS for possible locations

Preparedness

Huang and Fan

(2011)X X X X X X

Stochastic programming and robust

optimizationResource allocation

Trucks allocation in

different stations

Allocating multiple emergency service resources

(limited number of fire engines, fire trucks, and

ambulances to a set of predefined candidate fire

stations to

maximize the coverage) to protect critical

transportation infrastructures including service

availability chance constraints, that account for

service congestion and random accessibility

(transportation costs)

Preparedness

Li et al. (2011) X X X X X X

Scenario-based shelter location

stochastic bilevel optimization

model

Facility prepositioning and resource

allocation

Location of shelters to

open and assignation of

evacuees

The upper-level problem is to determine

where to locate shelters before observing a

hurricane scenario and, after observing a

hurricane scenario, which shelters to

open and how to assign the evacuees to these

shelters by creating O-D models in each stage

Preparedness

Lagaros et al.

(2011)X X X X X X

Deterministic and probabilistic

districting and routing problems for

scheduling infrastructure inspection

crews following a natural disaster

Resource allocation

Inspection groups to

which each built-up block

has been assigned

Develop and compare 5 different metaheuristic

approaches to establish the crews assigned for

each district and the prioritization of this groups.

Response

Muroli and

Dessouki (2011)X X X X X

Locate-allocate heurisitc for

capacitated Facility Location with

Distance-Dependent

Coverage


allocation

Location of shelters and

medicines assign to each

one

Allocation of medical centers and resources to

maximize coverage or minimize unmet demand

considering chance contraints to cope with

uncertainty in demand and a loss function that

defines how the effect of demand from a

demand point i on an open facility j decays with

an increase in distance between them.

Response

Nolz et al. (2011) X X X X X

Multi-objective optimization

problem, with three objective

functions : measure of risk,

coverage provided by the logistic

system and total travel time.

Resource allocationRoutes or tours for each

vehicle and vehicle load

two-phase Multi-objective optimization problem

considering five approaches for measuring the

risk of the distribution

tours to become impassable, in cases such as

aftershocks or secondary disaster.

Response

Rottkemper et al.

(2011)X X X X X X X

A rolling horizon approach for

solving the model of medical supply

delivery after a disaster


allocation

Quantity of commodities

in each supply center and

demand point served by

each DC.

Supply of relief items to affected areas after the

occurrence of a sudden change in demand or

supply, based on penalty costs for non-satisfied

demand and taking into account the possibility

of future disruptions that can help to balance

inventories and to reduce total non-served

demand.

Preparedness

and Response

Verma and

Gaulker (2011)X X X X X X

Two Stage Stochastic Optimization

Model for Positioning Disaster

Response Facilities for Large Scale

Emergencies


allocation

Location of facilities and

amounts to be routed

from the opened facilities

to the demand points

Optimization model that considers a correlation

of functionality of a facility given a particular

disaster scenario and given that the functioning

of a facility is directly affected by its distance

from the disaster epicente

Response

Zhan and Liu

(2011)X X X X X X

Two Stage Stochastic Optimization

Model for Emergency Logistics

Based

on Goal Programming


allocation

Location of facilities and

demand points served by

each

Optimization model with objectives of

minimizing the expected travel time and the

proportion of unmet demands, using different

scenarios to establish unknown demands.

Response

Description


Decision Variables Stage

Dis

trib

uti

on

Cen

ters

Sup

ply

loca

tio

n

Dem

an

d

Dem

an

d

Loca

tio

n

Flee

t

Co

mm

od

itie

s

Methodology Objective

37

Massaguer, D.

Balasubramanian, S.

Venkatasubramanian,

N. (2006)

Present the architecture of

DrillSim, a simulation

software to test IT solutions

for disaster response.

Multi-agent simulation for disaster

response activity software.

The model considers geographic space

simulation and agent behaviour (based

on state, observed world, role, etc) to

test various IT solutions. Case study:

building evacuation simulation.

Response

Fonseca, D. Moynihan,

G. Johntson, J.

Jennings, J. (2009)

Simulation tool for huricane

evacuation planning

Arena simulation model with

explanation on the inputs of the

model.

Constructed a hurricane evacuation

simulation for mass departure of

inhabitants of the vicinity of City of

Mobile, Alabama, considering traffic

events that may affect the evacuation.

Preparedness

El-Anwar, O. El-Rayes,

K. Elnashai, A. (2009)

Optimization of post-

disaster temporary housing

location.

Automated system to support

decision-makers.

The model is connected to a disaster

impact software and optimizes

objectives such as minimizing negative

socioeconomic impacts, maximizing

housing safety, minimizing

environmental impacts and public

expenditures.

Response

Hashemi, M. Alesheikh,

A. (2011)

Earthquake damage

assessment and settlement

methodology

GIS based earthquake damage

assessment methodology

GIS tool that incorporates all

vulnerability factors to develop a risk

or damage assessment tool.

Mitigation

Noreña, D. Akhavan, R.

Yamin, L. Ospina, W.

(2011)

Medical logistics in an

Earthquake scenario.

Discrete event simulation of

humanitarian logistics after a

disaster.

Simulation model of the transfer of

injured people to temporary and

permanent hospitals, considering their

triage classifications and hospital

capacities.

Preparedness

Lee, Y. Ghosh, S. Ettl, M.

(2009)

Development of a

simulation framework for

disaster response

Discrete event simulation of

humanitarian logistics after a

disaster.

Includes modeling of supply chain of

relief supplies, distribution operations

at distribution points, dynamics of

demand and progression of the

disaster

Preparedness and

Response

Gunnec et al. (2011)

Simulation to assess

reliability and the expected

performance

of a network under disaster

risk

Undirected graph and Monte Carlo

simulation algorithm

Evaluation of several probabilistic

measures of connectivity and

expected travel time/distance

between critical origin– destination

pairs to assess the functionality of a

given network. The input data include

themost likely disaster scenarios as

well as the probability that each

link of the network fails under each

scenario

Preparedness and

Response

Qi and Altinakar (2011)

Decision support system for

integrated flood

management using ArcGIS

based on realistic two

dimensional flood

simulations

GIS and Monte Carlo simulation

Flood hazard assessment using GIS and

remote sensing technology with the

result being hazard maps showing

spatial distribution of loss of life and

flood damage and trying to include

discharge-exceedance probability

functions and flood frequency

probability functions into the spatial

risk and uncertainty analysis.

Preparedness and

Response

Simulation

Authors Objective Methodology Description Stage of disaster

38

Bayraktarli, Y. Ulfkjaer, J.P.

Yazgan, U. Faber, M.

(2006)

Structural Earthquake Risk

Management.Bayesian probabilistic networks.

Based on exposure, vulnerability and robustness of

the structures, and the probability of earthquake

occurrance, the model determines the risk of a

certain structure and the need or not to retrofit it.

Mitigation

Mishra, A.K. Desai, V.R.

(2006)

Drought forcasting based on rain

time series

Use of ARIMA and artificial neural network

models (recursive multi-step and direct multi-

step).

Analysis and comparison of different methods for

drought forcasting, based on the SPI (standarized

precipitation index) in Purulia district of West Bengal,

India.

Mitigation

Wu, J. Ning, L. Yang, H.

(2008)

Risk evaluation for heavy snow

disasters.

Use of Back Propagation Artificial Neural

Network (BP-ANN) for heavy snow risk

analysis.

Proposed an indicator system considering

environmental possibilities of hazard, disaster

inducing factors and disaster bearing bodies to

analyze risk of heavy snow disaster in Xilingol,

Mongolia.

Mitigation

Moreira, E. Coelho, C.

Paulo, A. Pereira, L. Mexia,

J. (2008)

SPI (Standardized Precipitation

Index ) based drought category

prediction

Loglinear model for fitting observed

frequencies of SPI based drought and predict

future ones.

Three-dimensional loglinear model for fitting

observed frequencies of transition between droughts

classes (non drought, near normal, moderate and

severe) and model expected frequencies.

Mitigation

Yilmaz, I. (2009) Landslide susceptibility mapping.Logistic regression, artificial neural networks,

frequency ratio.

Comparison of the three methodologies in the

development of susceptibility maps of landslide.Mitigation

Nefeslioglu et al. (2008) Landslide susceptibility mapping.Logistic regression and artificial neural

networks.


development of susceptibility maps of landslide. They

were able to establish that susceptibility maps

developed with ANN were very optimistic and the

one based on logistic regression were too pessimitic.

Mitigation

Guikema, S. (2009)Natural disaster risk analysis for

critical infrastructure sytems

Supervised Statistical learning theory: linear or

parametric regressions.

Theory that deals with learning with the data, where

the outcomes of the measures are paired together

with their associated explanatory measures. The

difference between this and probabilistic risk analysis

is the estimation of the relationship between the

previous mentioned measures, in the first this comes

from the same data, while in the second comes from

expert opinion.

Mitigation

Xu et al. (2010)

Forecasting demand of

commodities after natural

disasters

Empirical model descompositions and ARIMA

models.

Empirical model decomposition allows to analyse the

time series assuming that the data may have

different coexisting modes of oscilations. Once this

can be modelled, the ARIMA analysis can be joined in

order to get a better forecast.

Mitigation

Fetter, G. Rakes, T. (2011)Efficient allocation of resources for

debris removal

Self balancing CUSUM approach (Cumulative

sum control charts)

Division of area in smaller regions where resources

are allocated considering the expected debris

material to remove.

Recovery

Dong, J. et al. (2011)Prediction of the failure probability

of a landslide damLogistic regression

Logistic regression is useful when the dependent

variable is categorical and the explanatory variables

are categorical, numerical or both. The factors

considered were peak flow, dam height, width and

length.

Mitigation

Chu, G. Wang, J (2012)

Probability distribution of fire

scenarios in risk assessment to

emergency evacuation

Markov chains

Use Markov Chain to obtain probability distribution of

probable fire scenario combined with ETA (Event tree

analysis).

Mitigation

Zhai, G. Fukuzono, T.

Ikeda, S. (2007)

Evaluate flood risk management in

Japan.Choice experiment for decision making.

Development of a choice experiment decision model

in order to establish the relationship between socio-

economic factors and the choice of public

preferences of flood prevention measures based on

surveys conducted in the Shonai-Toki river basin,

Japan.

Mitigation

Probability and Statistics


39

Barker and Haimes

(2009)

Sensitivity analysis on

probability distributions of

disasters

Extreme event uncertainty sensitivity

impact method (EE-USIM)

Measuring the sensitivity of extreme event

consequences to uncertainties in the

parameters of the underlying probability

distribution, for a number of economic sectors.

They use a two sided power distribution to

model the uncertainty in the parameters and a

partitioned multi objective risk method for

model the cost of risk management

implementation versus the consequences

Mitigation

Cimellaro et al. (2010)

Analytical quantification of

disaster resilience and

economic loss

Probability functions and non-stationary

stochastic process to model resilience

Develop a methodology to establish the

resilience, where resilience is taken as a non-

stationary stochastic process, of a community or

structure to a disaster and calculates de

economic loss based on parameters as disaster

intensity, time for recovery and loss functions.

Response and Recovery

Han et al. (2010) Drought forecasting Use of ARIMA models for drought forecast

VTCI index based on remote sensing data is

applied to the drought forecasting in the

Guanzhong Plain. The AR(1) model are chosen

to be the best model used and the forecast is

done with 1 and 2 steps.

Mitigation

Pradhan and Lee (2010) Delineation of landslide hazardLogistic regression, artificial neural

networks, frequency ratio.


development of susceptibility maps of

landslide.

Mitigation

Frey and Buttenuth

(2010)

Multi-temporal damage

assessment of linear

infrastructural objects

Dynamic Bayesinan Networks

Establish the functionality after natural

disasters of infrastructural objects using a

bayesian Network designed as a causal network

for every pixel, with links respresenting causal

relations between the nodes which

corresponds to random variables.

Preparedness

Akgun (2011)Prediction of the failure

probability of a landslide damLogistic regression

Logistic regression is useful when the

dependent variable is categorical and the

explanatory variables are categorical, numerical

or both. The factors considered were peak flow,

dam height, width and length.

Mitigation

Song et al. (2012)Susceptibility assessment of

earthquake-induced landslidesBayesian probabilistic networks.

Bayesian probabilistic networks used in the

suceptibility assessment of landslides caused

due to earthquakes.

Mitigation

Probability and Statistics


40

Lee and Evangelista

(2006)

Earthquake-induced landslide-

susceptibility mappingArtificial Neural Networks

Landslide-susceptibility indices were calculated

using the back-propagation weights, and

susceptibility maps were constructed from GIS

data. The susceptibility map was compared with

known landslide locations demonstrating a

prediction accuracy of 93%.

Mitigation

Mishra, A.K. Desai, V.R.

(2006)

Drought forcasting based on

rain time series

Use of ARIMA and artificial neural

network models (recursive multi-step and

direct multi-step).

Analysis and comparison of different methods

for drought forcasting, based on the SPI

(standarized precipitation index) in Purulia

district of West Bengal, India.

Mitigation

Lee et al. (2008)Storm surge forecast from real-

time observations.

Use of Artificial Neural Network, more

specific the Back-propagation neural

network to forecast the short-term storm

surge and surge deviation.

An analysis of the time series over the hourly

tidal data collected at Taichung harbor, Taiwan,

during 2003 were used to determine the

accuracy of the model, using the root mean

squared error and the correlation coeficient.

Mitigation

Nefeslioglu et al. (2008)Landslide susceptibility

mapping.

Logistic regression and artificial neural

networks.


development of susceptibility maps of

landslide. They were able to establish that

susceptibility maps developed with ANN were

very optimistic and the one based on logistic

regression were too pessimitic.

Mitigation

Wu, J. Ning, L. Yang, H.

(2008)

Risk evaluation for heavy snow

disasters.

Use of Back Propagation Artificial Neural

Network (BP-ANN) for heavy snow risk

analysis.

Proposed an indicator system considering

environmental possibilities of hazard, disaster

inducing factors and disaster bearing bodies to

analyze risk of heavy snow disaster in Xilingol,

Mongolia.

Mitigation

Chauhan et al. (2010)Landslide Susceptibility

ZonationArtificial Neural Networks

Artificial Neural Network (ANN) has been

implemented to derive ratings of categories

of causative factors, which are then integrated

to produce a landslide susceptibility zonation

map in an objective manner.

Mitigation

Mardiyono et al. (2010)

Prediction of Building

Damage Index using Neural-

Network

Artificial Neural Networks

Development of an intelligent monitoring

system utilizing artificial neural networks to

predict the building damage index which an

also provide an alert system and notification to

inform the status of the damage. Data learning

is trained on ANN utilizing feed forward and

back propagation algorithm.

Mitigation

Wang et al. (2011)Estimation of life casualties

after an earthquakeArtificial Neural Networks

Back propagation Artificial Neural Network

(ANN) considering earthquake magnitude,

depth of hypocenter, intensity of epicenter,

level of preparedness, earthquake acceleration,

population density and disaster forecasting as

the key factors and employing 37 severe

earthquake disasters as samples for the

training of the network

Mitigation

Danso Amoako (2012)

Multi-temporal damage

assessment of linear

infrastructural objects

Artificial Neural Networks

Establish the functionality after natural

disasters of infrastructural objects using a

bayesian Network designed as a causal network

for every pixel, with links respresenting causal

relations between the nodes which

corresponds to random variables.

Preparedness

Kung, H. Chen, C. Ku,H.

(2012)

Forecasting model for debris-

flow disasters

Regression Models and Artificial Neural

Networks.

Proposes three effective debris-flow prediction

models and to predict and decide the debris-

flow occurrence in Taiwan. The proposed

prediction models are based on linear

regression, multivariate analysis, and back-

propagation networks.

Recovery

Liu, W. Hu, G. Li, J.

(2012)Decision support system Case based reassoning

Presents a method for emergency resource

demand prediction using case-based reasoning

(CBR), which is also a method based on risk

analysis.

Mitigation

Liao, Z. Wang, B. Xia, X.

Hannam, M. (2012)Decision support system Artificial Neural Networks

Present a methodology for developing

environmental emergency decision support

systems (EEDSS) based on an Artificial Neural

Network (ANN) and introduces the network

architecture of the proposed ANN.

Mitigation

Artificial Intelligence and Expert systems

Stage of disasterAuthors Objective Methodology Description

41

Zhuang, J. Bier, V. (2007)

Decision Theory Technique for

the defender's allocating of

investments to reduce probability

of damage from an attack.

Game theory and Nash Equilibrium.

Model probability of damage from an attack

(Natural or terrorist) as a function of attacker

effort and defensive investment, Evaluations of

potencial targets, utilities to the damage caused

and the costs of attackers effort and defender's

investment.

Mitigation

Rodriguez, J. Vitotiano, B.

and Montero, J. (2010)

Natural-disaster management

DSS for Humanitarian NGO's

Decisión Support System using

Inductive data-based reasoning

method

The DSS enables NGO´s decision makers to

establish if the should or should not take part of

a relief opperation given the characterstics of

the disaster, its own capabilities and available

resources and past experiences in similar

disasters.

Response

Ezell et al (2010)Probabilistic Risk Analysis and

Terrorism Risk

Probability Risk Assessment

and event trees.

Develop a study on the applicability of different

probabilistic risk strategies or methodologies in

modelling terrorist attacks, based on

vulnerability and effectiveness of the attack

Mitigation

Kailiponi (2010)

Analyzing evacuation decisions

based on risk and available

information.

Multi-attribute utility theory (MAUT).

Model to determine most appropriate

evacuation decisions by minimizing loss of life,

economic disruption and organizational costs.

Considers uncertainty in the disaster hazard

profile and the behaviour of the people when

evacuating, and states the importance of

information from authorities.

Response

Brito, A. Almeida, A.

(2007)

Decision model for risk

assessment of different sections

of natural gas pipelines.

Multi-attribute utility theory (MAUT).

Use of MAUT theory considering losses of

human lives, affection to the environment and

company's financial costs. A identification of

decision makers, segmentation of the pipeline,

identification of hazard scenarios, calculation of

damage-scenario and consequence probability

and an exposure analysis were conducted.

Mitigation

Tong, Z. Zhang, J. Liu. X.

(2009)

Risk assessment of grassland fire

disaster

Analytic Hierarchy Process (AHP) and

Weighted Comprenhensive Method

(WCM)

Using GIS information of the region and the

natural disaster risk index method, where risk is

a function of hazard, exposure, vulnerability,

emergency response and recovery capability.

Mitigation

Bana e Costa, C.

Olivieira,C. Vieira, V.

(2008)

Prioritization of bridges and

tunnels according to their

vulnerability and strategic

importance for implementing

protection policies.

Multicriteria value model.

Development of a multicriteria model. It

considers vulnerability of structure (which

depends on its characteristics and the expected

hazard) and strategic importance (considering

public safety, emergency response and local

economic impacts).

Mitigation

Levy, J. Taji, K. (2007)

Improve the group decision

planning and emergency

management using incomplete

information.

GANP (Group Analytic Network

Process).

Development of a GANP considering multiple

decision makers, alternatives and criterions. Use

of a quadratic programming problem for the

assignement of group weight for the

alternatives.

Preparedness and

Response

Decision Theory


42

Paulo, A. Pereira, L.

(2007)

Drought prediction using the

SPI (Standarized Precipitation

Index), with the purpose of

developing early warning tools

and risk management plans.

Use of Non-homogeneus and

homogeneus Markov chains to

estimate the severity of drought at

some point, and the transition to other

severity drought classes considering

the actual state.

Probability of different droughts

severity classes (4), expected time in

each class of severity, recurrence time

of a drought class and the inter-state

transition probabilities are calculated.

Mitigation

Xiang et al. (2007)Flood Forecast of the Chaohu

Lake basin.Grey-Markov forecast theory. GM (1,1).

Use of a Grey-Markov model to develop

long term prediction using a time series,

which helps consider vast amount of

data and gives forecast precision of the

stochastically undulatory data.

Mitigation

Heegaard, P. Trivedi, K.

(2009)Network Survivability Modeling

Markov Chains and Phase type

distributions.

Network surivability is modeled through

Markov-Chains (M/M/1, M/M/n) and

using phase type distributions. Then

they are compared with simulation and

stochastic reward net (SRN) models

assuming exponentially distributed

inter-event times and time-

independent but phase-dependent

routing probabilities having as

performance measures the loss

probability and average number of

packets in the system at different times

Preparedness

Jacobson, E. Tanik, N.

Ziya, S. (2012)

Priority assignment in

Emergency responseMarkov Chains

Show distribution of triage classification

and service.Response

Queuing Theory


43

We survey the applicability of OR/MS techniques in disaster operations management.

We classify recent literature based on stochastic features in their models.

We show future research directions in disaster operations management literature.

We identify the recent disaster operations management contributions to society.

Highlights

or models with stochastic components in disaster operations management: a literature survey

Documents