A Fuzzy Integer Programming Model to Locate Temporary Medical Facilities as Part of Pre-Disaster Management

The﻿number﻿and﻿the﻿scale﻿of﻿natural﻿disasters﻿have﻿drastically﻿increased﻿over﻿the﻿last﻿decades.﻿One﻿of﻿ the﻿most﻿vital﻿stages﻿of﻿disaster﻿preparedness﻿is﻿disaster﻿response﻿planning,﻿and﻿it﻿plays﻿an﻿important﻿ role﻿in﻿limiting﻿material﻿and﻿immaterial﻿consequences,﻿such﻿as﻿those﻿caused﻿by﻿large﻿scale﻿earthquakes.﻿ In﻿order﻿to﻿minimize﻿human﻿suffering﻿and﻿death,﻿the﻿aim﻿of﻿establishing﻿a﻿well-designed﻿humanitarian﻿ relief﻿chain﻿must﻿be﻿to﻿provide﻿medicine,﻿water,﻿shelter,﻿emergency﻿food﻿and﻿supplies﻿to﻿the﻿affected﻿ areas.﻿From﻿a﻿holistic﻿perspective,﻿providing﻿timely﻿first﻿aid﻿and﻿rapid﻿transfer﻿of﻿injured﻿victims﻿to﻿a﻿ medical﻿facility﻿is﻿one﻿of﻿the﻿most﻿essential﻿component﻿of﻿such﻿chain.﻿Thus,﻿the﻿location﻿of﻿first﻿aid﻿ hospitals﻿must﻿be﻿determined﻿following﻿a﻿careful﻿thought﻿and﻿planning﻿process.﻿This﻿study﻿presents﻿a﻿ fuzzy﻿integer﻿programming﻿model﻿to﻿determine﻿the﻿best﻿location﻿of﻿the﻿temporary﻿hospitals﻿which﻿are﻿expected﻿to﻿support﻿extant﻿state﻿hospitals﻿after﻿a﻿major﻿earthquake.﻿This﻿study﻿applies﻿the﻿proposed﻿ fuzzy﻿model﻿to﻿the﻿Üsküdar﻿province﻿of﻿Istanbul﻿and﻿identifies﻿optimum﻿number﻿and﻿locations﻿of﻿field﻿hospitals﻿for﻿a﻿severe﻿earthquake﻿scenario.

Throughout the history, Istanbul has been exposed many devastating earthquakes.More precisely,32earthquakesbetweenthe4thand19thcenturieshaveaffectedIstanbul(seeFigure2).Approximately every 300 years, Istanbul has been exposed to very severe earthquakes (Istanbul MetropolitanMunicipality,2009).
The main contributions of this work are threefold: Firstly, this study takes into account the numberofheavilyinjuredvictimsasuncertainparameter.Duetounforeseeablenatureofapossible

PROBLeM DeFINITION
Afteralarge-scaledisaster,medicaltreatmentofdisaster-victimsisoneofthefirstandmost vital issue.To serve this purpose, the extant hospitals are of paramount importance, yet possiblyinsufficientdependingonthescaleoftheevent.Thus,temporaryfieldhospitals shouldbeestablished,thatofferfirstaidmaterialandmedicalassistancestartingfromthe very early hours of the incidence.Additionally, the population hit by the disaster should be effectively destined to the prepared hospitals considering their capacities and transfer times.Whilemodelingtheproblem,afuzzyenvironmentmayruleduetotheuncertainties associated with disaster intensity, strike probability, infrastructure-disruption, and the scale of the damage in a relief chain (Chakravarty, 2014b).In addition, the dominating characteristicsthatbringadditionalcomplexityanduniquechallengesincaseofadisaster areasfollows (Ivgin,2013): • Unpredictabilityofdemand,intermsoftiming,location,typeandimpact; • Suddenlyoccurringdemandandshortleadtimesforawidevarietyofsupplies;and • Highcostofunsatisfieddemand(i.e.lossoflives).

Figure 3 .
Figure 3. Membership function of N j 

Figure 4 .
Figure 4. Istanbul earthquake zones distribution map (Earthquake Zoning Map Index of Turkey, 2017)

Figure 6 .
Figure 6.Total number of hospitals needed for different α levels

Figure 7 .Figure 8 .
Figure 7. Number of people in each neighborhood assigned to each hospital for α=1