ISTANBUL TECHNICAL UNIVERSITY GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY
Ph.D. THESIS
AUGUST 2020
EMERGENCY MEDICAL SYSTEM DESIGN FOR DISASTER RESPONSE
Mehmet Kürşat ÖKSÜZ
Department of Industrial Engineering Industrial Engineering Programme
Department of Industrial Engineering Industrial Engineering Programme
AUGUST 2020
ISTANBUL TECHNICAL UNIVERSITY GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY
EMERGENCY MEDICAL SYSTEM DESIGN FOR DISASTER RESPONSE
Ph.D. THESIS Mehmet Kürşat ÖKSÜZ
(507142120)
Endüstri Mühendisliği Anabilim Dalı Endüstri Mühendisliği Programı
AĞUSTOS 2020
ISTANBUL TEKNİK ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ
AFETE MÜDAHALE İÇİN ACİL TIP SİSTEMİ TASARIMI
DOKTORA TEZİ Mehmet Kürşat ÖKSÜZ
(507142120)
Prof. Dr. Emre ÇEVİKCAN ... Istanbul Technical University
Prof. Dr. Selçuk ÇEBİ ... Yıldız Technical University
Thesis Advisor : Prof. Dr. Şule Itır SATOĞLU ... Istanbul Technical University
Jury Members : Dr. Şeyda SERDAR ASAN ... Istanbul Technical University
Prof. Dr. F. Sibel SALMAN ... Koç University
Mehmet Kürşat Öksüz, a Ph.D. student of ITU Graduate School of Science Engineering and Technology student ID 507142120, successfully defended the dissertation entitled “EMERGENCY MEDICAL SYSTEM DESIGN FOR DISASTER RESPONSE”, which he prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below.
FOREWORD
In this thesis, an emergency medical center system design has been considered, including the location planning of medical centers, allocation of casualties, and assignment of medical staff for the post-disaster medical response. Firstly, a two-stage stochastic model was developed for the location-allocation problem. Then, a multi-objective dynamic stochastic model was developed for both location-allocation and medical staff assignment problem. Real case studies were conducted for the Kartal district of Istanbul by considering possible earthquake scenarios, and results were analyzed. We hope that this study will give a new perspective about the emergency medical system design and contribute to the Humanitarian Logistics literature. Besides, it is aimed to reveal the importance of this subject and create awareness. Many people have contributed to this thesis from a different point of view. Firstly, I would like to express my sincere appreciation and thanks to my advisor Prof. Dr. Şule Itır SATOĞLU, for supporting me and providing guidance throughout this study. It was a great pleasure to have the opportunity to work with her during my graduate education. I also would like to thank my thesis jury members Prof. Dr. F. Sibel SALMAN and Dr. Şeyda SERDAR ASAN, for their valuable and insightful comments and suggestions.
I would like to thank my colleagues E. Nisa KAPUKAYA and Nadide ÇAĞLAYAN, and Gözde Merve DEMİRCİ, for their contribution to data collection. I would also like to thank Dr. Furkan KAPUKAYA and Ali DOĞAN (CEO of Doctors Worldwide Turkey) to share their knowledge on medical issues. In addition, I would like to acknowledge the financial support from the Istanbul Technical University Scientific Research Projects Unit (BAP), with grant number MGA-2019-42242.
Finally, I would like to specially thank to my dear wife Elif ÖKSÜZ and my son Ahmet Yiğit ÖKSÜZ for their moral support in this challenging period and for allowing me to write this thesis.
August 2020 Mehmet Kürşat ÖKSÜZ
TABLE OF CONTENTS Page FOREWORD ... ix TABLE OF CONTENTS ... xi ABBREVIATIONS ... xiii LIST OF TABLES ... xv
LIST OF FIGURES ... xvii
SUMMARY ...xix
ÖZET ...xxi
INTRODUCTION ...1
Humanitarian Logistics / Disaster Management ... 5
Motivation ... 6
Purpose of the Thesis ... 7
Unique Aspects of the Study ... 7
LITERATURE REVIEW ...9
Facility Location Studies in HL ...10
Joint Decision Making for Facility Location, Inventory Management or Network Flow Problems ...14
Casualty Transportation/Allocation Studies in HL ...15
Medical Staff Assignment Studies in HL ...16
METHODOLOGY... 19
Stochastic Programming ...19
3.1.1 Two-stage stochastic models ... 19
3.1.2 Chance-constrained stochastic models ... 20
Discrete-time Markov Chain ...21
Multi-Objective Mathematical Programming ...22
PROPOSED STOCHASTIC MODELS AND APPLICATIONS ... 25
A Two-stage Stochastic Model for Location Planning of TMCs ...25
4.1.1 Problem definition ... 26
4.1.2 Two-stage stochastic model ... 27
4.1.3 Two-stage stochastic model without the triage ... 33
4.1.4 Case study ... 35
4.1.5 Results for the base case ... 38
4.1.6 Results for the case without triage category ... 42
4.1.7 Sensitivity analysis ... 44
4.1.7.1 Distance limit ...44
4.1.7.2 Reliability level (α) ...45
A Multi-objective Dynamic Stochastic Model for Casualty Allocation and Medical Staff Assignment Problem ...46
4.2.1 Problem definition ... 46
4.2.4 Solution methodology ... 58 4.2.5 Results ... 59 CONCLUSIONS ... 63 REFERENCES ... 69 APPENDICES ... 77 APPENDIX A ... 78 CURRICULUM VITAE... 79
ABBREVIATIONS
ELER : Earthquake Loss Estimation Routine EMC : Emergency Medical Center
EM-DAT : Emergency Events Database EMS : Emergency Medical System HL : Humanitarian Logistics
IDMC : Internal Displacement Monitoring Centre MCE : Mass Casualty Events
MOIP : Multi-Objective Integer Programming MOMP : Multi-Objective Mathematical Programming START : Simple Triage And Rapid Treatment
LIST OF TABLES
Page Table 1.1 : A classification framework for humanitarian logistics. ...5 Facility location studies for Humanitarian Logistics... 12 Table 4.1 : The key parameters used in the case study. ... 37 Table 4.2 : The population, the total expected numbers of casualties, and unassigned
casualties at each demand point. ... 40 Table 4.3 : The estimated number of casualties according to a possible earthquake
scenario (Mw=7.5). ... 56 Table 4.4 : Payoff table. ... 59 Table A.1 : Pareto optimal solutions obtained by using AUGMECON2. ... 78
LIST OF FIGURES
Page Figure 1.1 : Graphical abstract of the proposed models for Emergency Medical
Response. ...4 The number of articles according to the published year. ... 10 The distribution of studies according to the problem type. ... 10 Figure 4.1 : Design of Emergency Medical Center Response System for
post-disaster. ... 26 Figure 4.2 : The map of sub-districts (demand points), hospitals, and recommended
TMC locations in Kartal. ... 36 Figure 4.3 : Fault line for Model A and Model C... 37 Figure 4.4 : The expected percentages of unassigned casualties according to each
scenario. ... 39 Figure 4.5 : The expected percentages of unassigned casualties at each demand point over all scenarios. ... 41 Figure 4.6 : The expected percentages of unassigned casualties of each type in
scenarios S1 to S10. ... 42 Figure 4.7 : The expected percentages of unassigned casualties at each demand point over all scenarios for two cases. ... 43 Figure 4.8 : The unused capacity ratios of hospitals for the different distance limits
(km). ... 44 Figure 4.9 : The required capacity increase ratios for the different α-reliability
levels. ... 45 Figure 4.10 : The Markov Chain indicating the transitions of the health condition of
served casualties (D: Dead, DC: Discharged). ... 47 Figure 4.11 : The Markov Chain indicating the transitions of the health condition of
unserved casualties. ... 48 Figure 4.12 : The Markov Chain indicating the transition probabilities of the health
condition of served casualties. ... 58 Figure 4.13 : The Markov Chain indicating the transition probabilities of the health
condition of unserved casualties. ... 58 Figure 4.14 : The comparison of obj-2 (distance) and obj-3 (medical staff). ... 60 Figure 4.15 : The number of TMCs that must be set up after the disaster according to each scenario. ... 61 Figure 4.16 : The expected number of doctors needed in medical centers according
to each scenario. ... 61 Figure 4.17 : The expected number of nurses needed in medical centers according to
each scenario. ... 62 Figure 4.18 : The number of assigned casualties to the EMCs according to each
EMERGENCY MEDICAL SYSTEM DESIGN FOR DISASTER RESPONSE SUMMARY
Disasters are large-scale events that affect human life, both materially and spiritually. There are many precautions to be taken to mitigate the devastating effect of disasters. One of them is effectively planning of post-disaster emergency medical response system. Since the most important factor is saving human life, proper planning of medical centers, and transportation of casualties to these centers is crucial during the disaster response phase. Therefore, it is necessary to design the Emergency Medical System (EMS) before disasters. EMS consists of many components such as disaster areas, hospitals, Temporary Medical Centers (TMC), casualties, medical staff, ambulances, etc. The proper planning and design of EMS are crucial to respond casualties and serve them effectively. Therefore, location planning of TMCs or field hospitals, classification of injuries (triage), assignment and transportation of casualties, determining the needs of medical staff in the medical centers play a significant role in mitigating the devastating effect of mass casualty events like disasters or incidents.
Humanitarian Logistics or Disaster Management activities consist of preparation, supply, transportation, location, allocation, network design, tracking, and storage. Humanitarian Logistics is a challenging process, and this process contains many uncertainties. The main uncertainties in are the time, location, severity of a disaster, and size of demand. The uncertainties and variability in the complex nature of disaster management require formulating problems as a stochastic programming model in general.
Humanitarian Logistics (HL) can be divided into three main topics, which are facility location, inventory management, and network flows/design problems. In the HL literature, facility location studies are commonly divided into three categories. These are emergency medical center, relief supplies warehouse, and shelter site or collection point location problems. In large-scale emergency events such as earthquake, hurricane, flood, and tsunami, the capacity of hospitals is not enough for the treatment of the casualties. Therefore, TMCs are located at the suitable sites by considering existing hospitals to serve casualties for medical response.
In the first part of this study, it is aimed to determine the location and number of TMCs in case of an earthquake by considering different factors. In the objective function, we considered the setup cost of TMCs and the transportation cost of casualties. In addition, locations and bed capacities of the existing hospitals, possibilities of damage to the hospitals and roads are taken into account. At the same time, a widely used triage system is applied to classify casualties according to their injured level. The distances between disaster areas and EMCs also considered to minimize response time. For this problem, a two-stage stochastic programming model was developed. The proposed model finds an optimal TMC location solution while minimizing the total setup cost
model was reformulated by considering a single-type of casualty to show the effect of triage on the solution of the problem. Based on the different earthquake scenarios in JICA Report (2002), a real case study was conducted for the Kartal district of Istanbul. The results were presented, and a sensitivity analysis was performed for critical parameters.
The medical staff planning of medical centers is vital as wells as the location planning of medical centers to provide services to all casualties assigned to these centers. Therefore, the medical staff capacity should be considered in addition to the patient's capacity when assigning casualties to the medical centers. Besides, assuming that all of the expected casualties occur immediately after the disaster causes ineffective and unrealistic usage of resources. There is also another fact that a casualty might not stay in the same health condition as time passes. For these reasons, a multi-objective dynamic stochastic model was proposed for the medical staff assignment, casualty allocation, and TMC location planning simultaneously. In the proposed model, it is aimed to minimize the expected values of the total number of unserved casualties, the distance between disaster areas and emergency medical centers, and the number of medical staff needed. The first 72 hours after the disaster was considered and divided into four periods to reflect the dynamic behaviour of such events. Thus, with the dynamic model, it is aimed to use the capacities of emergency medical centers more efficiently and realistically. The stochastic nature of casualties’ health condition was also included the model as a Discrete-time Markov Chain. For the case study, Kartal district data used in the model-1 has been updated according to the recently published report of the Istanbul Metropolitan Municipality (IBB-KRDAE, 2020). AUGMECON2 method was applied to solve the multi-objective model, and the results were analysed.
According to the results for the case study in the first model, the total patient capacity of existing hospitals and all recommended TMCs are not enough for the most probable earhtquake scenarios defined in JICA Report (2002). However, for the most optimistic scenario, setting up 53 out of 74 candidate TMCs after the disaster is suffcient to assign all casualties to the medical centers. Besides, the percentage of unassigned casualties is 14.9% for the most probable scenario and the average percentage of unassigned casualties over all scenarios is about 10%. In the second case study, where the injured estimates are taken from the most recent study (IBB-KRDAE, 2020), there is enough capacity to assign all casualties to the EMCs over all scenarios. The number of TMC that must be set up is 50 for the worst-case scenario and 21 for the base-scenario. The results and analysis for both models offers some managerial insights associated with the number of temporary medical centers needed, their locations, additional capacity requirements, required number of medical staff, and allocation of casualties. We hope that this study will give a new perspective about the pre- and post-disaster emergency medical system design and contribute to the Humanitarian Logistics literature.
AFETE MÜDAHALE İÇİN ACİL TIP SİSTEMİ TASARIMI ÖZET
Belli bir yerleşim bölgesindeki topluluğun yaşantısını bozan ve kendi kaynakları ile normal hale dönemeyeceği derecede ciddi insani, çevresel ve ekonomik zararlar meydana getiren olaylara afet denir (IFRC, 2017). Geçmişten günümüze kadar, deprem, fırtına, tsunami, gibi doğal afetlerin yanında terörist saldırılar gibi insanların neden olduğu afetler de meydana gelmektedir. Bunun yanında afetler, oluş hızına göre aniden meydana gelen veya yavaş meydana gelen afetler olarak da ikiye ayrılmıştır (Van Wassenhove, 2006). Deprem, sel ve tsunami aniden gerçekleşen türdeki afetlere; kuraklık, kıtlık ve savaş nedeniyle meydana gelen toplu göçler ise yavaş gelişen türden afetlere örnek olarak verilebilir.
Doğal afetler her yıl çok sayıda insanı etkilemektedir. Acil olaylar veri-tabanına (EM-DAT: Emergency Events Database) göre 1997-2017 yılları arasında dünyada, 8223 doğal afet meydana gelmiş ve milyonlarca insan bunlardan etkilenmiştir (Url-1). Geçmiş verilere göre, her yıl ortalama 500 doğal afet meydana gelmekte ve yaklaşık 70.000 kişinin ölümüne ve 200 milyon kişinin ise olumsuz etkilenmesine neden olmaktadır (Duran ve diğ, 2011). 17 Ağustos 1999’da meydana gelen Richter ölçeğine göre 7.6 büyüklüğündeki Marmara Depremi’nde yaklaşık 18.000 insanımız hayatını kaybetmiş, 50.000 kişi yaralanmış, 500.000 vatandaşımız evsiz kalmıştır (Kilci ve diğ, 2015). Bu deprem, yaklaşık 1.4 milyon kişiyi olumsuz etkilemiş ve neredeyse 20 milyar dolar maddi zarar oluşmuştur (Kasapoğlu ve Ecevit, 2003). Bu bilgiler, doğal afetlerin insan hayatını ve yaşadıkları çevreyi ne kadar olumsuz etkilediğini göstermektedir.
Afet, terör saldırısı veya savaş gibi kitlesel yaralı olayların sonrasında, büyük miktarda kaynak ihtiyacı doğurmakta (yiyecek, içecek, ilaç, çadır vs.) ve bu ihtiyaçların dağıtımını gerektirmektedir. Bu ihtiyaçların afetten etkilenen insanlara zamanında ulaştırılmasının sağlanması; bu sürecin doğru bir şekilde planlanması, yönetimi ve kontrolü büyük önem taşımaktadır. Bu nedenle, İnsani Yardım Lojistiği (Afet Yönetimi) faaliyetlerinin etkin ve sistematik bir şekilde gerçekleştirilmesi, afet öncesi veya sonrası meydana gelen zararların en aza indirilmesinde önemli bir rol oynamaktadır. İnsani yardım lojistiği, afetten etkilenmiş insanların ihtiyaçlarını karşılamak amacıyla gerekli malzemelerin ve bilgilerin kaynak noktasından tüketim noktasına maliyet bakımından etkin ve verimli akışı ile depolanmasının planlanması, uygulanması ve kontrol edilmesi süreci olarak tanımlanmaktadır (Thomas ve Mizushima, 2005). Bu süreç; hazırlık, planlama, tedarik, ulaşım, yerleşim, dağıtım, izleme ve depolama gibi farklı faaliyetlerden oluşmaktadır. 2004 yılında Hint Okyanusu’nda ve 2010 yılında Haiti’de meydana gelen depremler insani yardım lojistiğinin ne kadar karmaşık ve güç olduğunu göstermiştir. 12 Ocak 2010’da Haiti’de meydana gelen 7.0 büyüklüğündeki depremde 500,000’den fazla insan ölmüş veya yaralanmış, en az 2 milyon insan ise evsiz kalmıştır. (IDMC, 2011). Yardım malzemeleri ancak depremden iki gün sonra bölgeye ulaştırılabilmiştir (Url-2). Daha
sonra, birçok insani yardım organizasyonu afet bölgesine intikal etmesine rağmen, bilgi ve koordinasyon eksikliği nedeniyle acil müdahalenin etkili bir şekilde gerçekleştirildiğini söylemek mümkün değildir (Altay ve Labonte, 2014). Bu ve benzeri afetlerin ve küresel krizlerin insanlar üzerindeki yıkıcı etkisi, afet öncesi, sırası ve sonrası lojistik faaliyetlerin iyileştirilmesi ve geliştirilmesi ile ilgili çalışmaların önemini gün geçtikçe arttırmaktadır. Son yıllarda insani yardım lojistiğinin önemi daha iyi anlaşılmış, bu konudaki çalışmalar artmıştır.
Tüm yardım faaliyetlerinin temel amacı, ihtiyaç sahiplerine yardımı zamanında ve ihtiyaç miktarı kadar ulaştırmaktır. Geleneksel Tedarik Zinciri’nde olduğu gibi İnsanı Yardım Tedarik Zinciri de; nihai müşteriye (afetzede) doğru ürünü, doğru kalitede, doğru zamanda ve doğru yerde ulaştırmayı sağlayacak şekilde tasarlanmalıdır. Tedarik, depolama, envanter yönetimi, ulaştırma ve dağıtım fonksiyonlarını içeren İnsani Yardım Lojistiği, afet yönetiminin en önemli unsurlarından biridir.
İnsani yardım lojistiği son derece zor bir süreçtir ve bu süreç birçok belirsizlik içermektedir. Temel belirsizlikler afetin şiddeti, gerçekleşeceği zaman, yer ve talebin büyüklüğüdür. Afet yönetimindeki belirsizlikler ve değişkenlik, problemlerin genel olarak stokastik bir programlama modeli olarak formüle edilmesini gerektirmektedir. İnsani yardım lojistiği ilgili akademik literatür üç ana başlık altında toplanmaktadır. Bunlar; tesis yerleşimi, envanter yönetimi ve ağ tasarım/akışlarıdır. Tesis yerleşimi ile ilgili çalışmalar, operasyonların konumsal yönlerine odaklanır ve tesis yerinin, insani yardım lojistiği kapsamındaki maliyet, hizmet ve müdahale süresi gibi unsurlar üzerindeki etkilerini araştırır. Literatürdeki afet lojistiği ile ilgili tesis yerleşimi çalışmaları üç kategoriye ayrılabilir. Bunlar; yardım malzemeleri depo yerleşimi, acil tıp merkezi yerleşimi ve sığınak bölgesi yerleşimi problemleridir. Bu üç tesis türünün farklı kullanımları olmasına rağmen, bu problemlerin ulaşılan toplam kişi sayısını maksimize etmek, tesisler ile afetten etkilenenler arasındaki mesafeyi minimize etmek ve en uygun tesis yerinin seçilmesini sağlamak gibi benzer amaçları vardır.
Bu tez çalışmasının ilk bölümünde, mevcut hastanelerin yerleri ve kapasitesi, yaralıların önceliklendirilmesi (triyaj) ile yolların ve hastanelerin zarar görme olasılıkları göz önünde bulundurularak afet sonrasında kurulacak olan geçici tıp merkezlerinin yerinin ve sayısının belirlenmesi amaçlanmıştır. Ayrıca, tıp merkezlerine yaralılar atanırken tıbbi müdahale süresinin en aza indirmek için afet bölgeleri ile tıp merkezleri arasındaki mesafeler dikkate alınmıştır. Bu problem için iki-aşamalı stokastik bir programlama modeli geliştirilmiştir. Önerilen modelde, geçici tıp merkezlerinin toplam kurulum maliyetinin beklenen toplam taşıma maliyetinin en aza indirilmesi amaçlanmıştır. Modelde, atanamayan yaralı sayısı kriteri için α-güvenilirlik kısıtlamaları da kullanılmıştır. Ayrıca, yaralıları sınıflandırmanın problemin çözümü üzerindeki etkisini anlamak için önerilen model triyaj olmadığı durum için (tek tip yaralı) yeniden formüle edilmiştir. İstanbul’da gerçekleşmesi beklenen farklı deprem senaryolarına göre Kartal ilçesi için gerçek bir vaka çalışması yapılmış, sonuçları sunulmuş ve önemli parametreler için duyarlılık analizi yapılmıştır.
Tıp merkezlerinin yerleşim planlamasının yanı sıra tıp merkezlerinin sağlık personeli planlaması da bu merkezlere atanan yaralılara hizmet vermeyi garantilemek için hayati öneme sahiptir. Bu nedenle, yaralı ataması yapılırken tıp merkezlerinin kapasitesine ek olarak sağlık personeli kapasitesi de dikkate alınmalıdır. Ayrıca, tüm yaralıların afetten hemen sonra meydana geldiği varsayımı, kaynakların etkisiz ve gerçekçi olmayan kullanımına neden olmaktadır. Yaralıların zaman geçtikçe aynı sağlık
durumunda kalmayabileceği de başka bir gerçektir. Bu sebeplerden dolayı, sağlık personeli görevlendirmesi, yaralı ataması ve geçici tıp merkezlerinin yerleşim planlamasını birlikte ele alan çok-amaçlı dinamik bir stokastik model önerilmiştir. Önerilen modelde, hizmet verilemeyen toplam yaralı sayısı, afet bölgeleri ve acil tıp merkezleri arasındaki mesafe ve ihtiyaç duyulan sağlık personeli sayısının beklenen değerinin minimizasyonu amaçlanmıştır. Afetten sonraki ilk 72 saat dikkate alınmış ve bu tür olayların dinamik davranışını yansıtmak için bu zaman dilimi dört periyoda ayrılmıştır. Böylece, dinamik model ile acil tıp merkezlerinin kapasitelerinin daha verimli ve gerçekçi bir şekilde kullanılması amaçlanmıştır. Yaralıların sağlık durumundaki değişim, kesikli-zamanlı Markov Zinciri olarak tasarlanmış ve modele dahil edilmiştir. Vaka çalışması için ilk bölümde kullanılan Kartal ilçesi verileri yakın zamanda yayınlanan İstanbul Büyükşehir Belediyesi’nin raporuna (IBB-KRDAE, 2020) göre güncellenmiştir. Çok-amaçlı modelin çözümü için AUGMECON2 (Augmented Epsilon Constraint Method 2) yöntemi uygulanmış ve sonuçlar analiz edilmiştir.
İlk modeldeki vaka çalışmasının sonuçlarına göre, JICA Raporunda (2002) tanımlanan en olası deprem senaryoları için mevcut hastanelerin ve önerilen tüm geçici tıp merkezlerinin hasta kapasitesi yeterli değildir. Ancak, en iyimser senaryoda tüm yaralıları tıp merkezlerine atayabilmek için 74 aday geçici tıp merkezinden 53'ünün kurulması yeterli olmaktadır. Ayrıca, en olası senaryo için atanamayan yaralı oranı %14,9 iken, tüm senaryolar dikkate alındığında bu oranın ortalaması %10'dur. Yaralı tahminlerinin en güncel çalışmadan (IBB-KRDAE, 2020) alındığı ikinci modeldeki vaka çalışmasında, tüm senaryolarda yaralıların tıp merkezlerine atanması için yeterli kapasite vardır. Depremden sonra kurulması gereken geçici tıp merkezi sayısı, en kötümser senaryo için 50 iken temel senaryo için 21'dir. Her iki modelin sonuçları ve analizler, ihtiyaç duyulan geçici tıp merkezlerinin sayısı, konumları, ek kapasite gereksinimi, gerekli tıbbi personel sayısı ve yaralıların ataması ile ilgili bazı yönetimsel bilgiler sunar. Bu çalışmanın afet öncesi ve sonrası acil tıbbi sistem tasarımına yeni bir bakış açısı kazandıracağını ve İnsani Yardım Lojistiği literatürüne katkı sağlayacağını umuyoruz.
INTRODUCTION
Natural disasters affect a large number of people every year. Based on the historical data, each year, about 500 natural disasters causing the death of nearly 70.000 people and influence more than 200 million people worldwide (Duran et al., 2011). EM-DAT (Emergency Events Database) reported that about 8000 natural disasters occurred in the last decade in the world, and these disasters affected millions of people (Url-1). The Marmara earthquake occurred on 17 August 1999 (Mw=7.6) has caused the death of nearly 17,000 people in Turkey. In this earthquake, about 50,000 people were injured, and approximately 500,000 people became homeless (Kilci et al., 2015). Besides, about 1.4 million people influenced by the earthquake and 20 billion dollars loss incurred (Kasapoğlu and Ecevit, 2003). In addition, on 12 January 2010, an earthquake (Mw=7.0) occurred in Haiti, affecting the capital of Port-au-Prince and nearby municipalities, caused killing or injuring more than 500,000 people and displacing at least two million people (IDMC, 2011). Relief supplies could be reached to Haiti two days after the earthquake (Url-2). Later, although many humanitarian organizations reached the region, it is not possible to say that an effective emergency response was carried out due to the lack of information and coordination (Altay and Labonte, 2014). These devastating events show that natural disasters significantly affect both human life and habitat. It also demonstrated that humanitarian logistics planning is critical in the pre- and post-disaster stages.
After Mass Casualty Events (MCE) such as disaster, terrorist attack or war, a large number of resources (food, water, beverages, medicine, tents, etc.) and allocation of these needs are required. The efficiently and systematically planning and management of these needs are required to provide services to affected people on time to mitigate damages of the disaster.
Humanitarian logistics consists of different activities, such as facility location, relief supplies, transportation or allocation of casualties, distribution of resources, warehouse management, etc. In the humanitarian logistics literature, facility location
studies are divided into three categories in general, which are the emergency medical center, relief supplies warehouse, and shelter site/collection point location problems. Emergency Medical Centers, including the hospitals and Temporary Medical Centers (TMCs) have an essential role in the treatment of injured and preventing the loss of human lives in the post-disaster stage. The existing hospitals are the main element of post-disaster medical response. Besides, it is a fact that the capacity of hospitals is not enough in mass casualty events. For this reason, TMCs must be set up in suitable areas immediately after the disaster to provide treatment of a large number of casualties. Therefore, the location planning of TMCs is critical to respond to injuries on time. Thus, it is provided to efficient use of the resources and reaching as many injured as possible.
The question investigated in this study is where temporary medical centers could be located to respond casualties on time by taking into various factors such as distances between disaster areas and medical centers, the possibility of damage to the hospitals and roads, and different casualty classes.
In the first part of this thesis, it is aimed to determine the location and number of TMCs in case of an earthquake by considering different factors. In the objective function, we considered the setup cost of TMCs and the transportation cost of casualties. In addition, locations and bed capacities of the existing hospitals, possibilities of damage to the hospitals and roads are taken into account. At the same time, a widely used triage system is applied to classify casualties according to their injured level. The distances between disaster areas and EMCs also considered to minimize response time. For this problem, a two-stage stochastic programming model was developed. In the model, it is aimed to minimize the total setup cost of the TMCs and the total expected transportation cost of the casualties. Also, it is aimed to show the effect of casualty classification (triage) on the results. For this purpose, a straightforward model was presented by taking into account a single-type of casualty.
A real case study was conducted to test the proposed model for the district of Kartal in Istanbul, which is considered as one of the most affected districts in a possible Istanbul earthquake. Istanbul Metropolitan Municipality and the Japan Cooperation Agency have presented a comprehensive report for the possible earthquake in Istanbul (JICA, 2002). In this report, four earthquakes scenarios have been introduced with the
expected number of buildings to be damaged, the estimated proportion of injured and dead for each district. The data used in the case study have taken from JICA (2002), and twenty scenarios have derived from the four scenarios.
In natural disasters, the medical staff planning of medical centers is crucial as wells as the location planning of medical centers to ensure providing services to all casualties assigned to these centers. In large-scale disasters, significant support is received from national and international organizations as well as the local government. Therefore, effectively directing this support to disaster-affected areas to provide service to the casualties is vital. In past events, it is a fact that there were cases where there was more medical staff in a disaster area than needed, and there was not enough medical staff in another disaster area. The way to overcome this situation is to effectively assignment of medical staff according to the available sources and data to direct them to the disaster areas.
In the second part of this thesis, we proposed a multi-objective stochastic model for the dynamic casualty allocation and medical staff assignment problem. In the model, there are three objective functions that are:
The minimization of the total expected number of unserved casualties.
The minimization of the total expected demand weighted distance between disaster areas and EMCs.
The minimization of the total expected number of medical staff (doctors and nurses) needed in the hospitals.
We conducted a case study for the revised Kartal data by considering the most recent study. The AUGMECON2 method (Mavrotas and Florios, 2013) was used to solve the multi-objective model for the Kartal case, and results were analyzed.
There are many differences between the proposed models although there are some similarities. In the second model, the main difference is consideration of multi-period planning by taken into first 72h after disaster and updating EMC capacities according to the dynamic casualty assignment. Another one is considering the medical staff assignment problem in addition to the location planning of TMCs and transportation of casualties. Besides, Markov Chain transition probabilities for the health condition of casualties are applied in the second model.
Developing a two-stage stochastic model
Possibility of damage to roads Distances between
disaster areas and EMCs
Possibility of damage to
hospitals
Solving proposed model by using CPLEX for
Kartal data (JICA, 2002) Location and capacity of existing EMCs Expected number of casualties for different scenarios Transportation cost and capacity
of ambulances Number of available Medical Staffs at hospitals Developing a multi-objective dynamic stochastic model
Solving proposed model by using AUGMECON2 and CPLEX for new
Kartal data (IBB-KRDAE, 2020) Emergency Medical Response
Model-1 Location Planning and
Casualty Allocation
Model-2 Medical Staff Assignment
and Casulty Allocation
Results of Case Study and Sensitivity
Analysis
Analysis of Results
Conclusions and Suggestions
Figure 1.1 : Graphical abstract of the proposed models for Emergency Medical Response.
The graphical abstract of the proposed models for Emergency Medical Response is presented in Figure 1.1. In the next sub-sections, humanitarian logistics/disaster management is introduced, then the motivation, purposes, and unique aspects of the study are explained. In Chapter 2, the literature related to this study is reviewed, and similar and different aspects of the studies are presented. In Chapter 3, the methodologies used in this study are explained. Then, the proposed two models and applications are presented in Chapter 4. Finally, conclusions, suggestions, and some future research directions explained in Chapter 5.
Humanitarian Logistics / Disaster Management
Disaster is an event that disrupts society's life in a particular place and causes serious human, environmental and economic damages that cannot be normalized with their resources (IFRC, 2017). In addition to natural disasters such as earthquakes, hurricanes, and tsunamis, some disasters caused by people such as terrorist attacks. Disasters are divided into two as sudden-onset or slow-onset according to the speed of occurrence (Van Wassenhove, 2006). Earthquake, flood, and tsunami are sudden-onset disasters; mass migrations due to drought, famine, and war are examples of slow-onset disasters (Leiras et al., 2014).
Fritz Institute has defined the term of Humanitarian Logistics as:
“The process of planning, implementing and controlling the efficient, cost-effective flow of and storage of goods and materials as well as related information, from the point of origin to the point of consumption to alleviate the suffering of vulnerable people.” (Thomas and Mizushima 2005). Similarly, Humanitarian Logistics can be defined as; implementation and control of the necessary food, materials, information, and services from the source point to the consumption point efficiently and cost-effectively to mitigate the damage and meet the needs of the people affected by disasters. This process consists of preparation, planning, procurement, transportation, location, distribution, tracking, and storage activities. The destructive effects of disasters and the global crisis on people increase the importance of logistics activities before, during, and after the disasters. All these activities are also mentioned as Disaster Management in some studies. On the other hand, facility location, network design, inventory management, transportation, and distribution functions are called Humanitarian Logistics as an element of Disaster Management.
Table 1.1 : A classification framework for humanitarian logistics (adapted from Leiras et al., 2014).
Disaster type Disaster lifecycle stage Problem type Optimization type Decision level Stakeholders
Natural Mitigation Facility
Location Deterministic Strategic
Local and international organizations
Man-made Preparedness Inventory
Management Stochastic Tactical
Nongovernmental organizations (NGO)
Slow-onset Response Network
Flows/Design Operational
Government, Military
A classification framework for humanitarian logistics is presented in Table 1.1, which was adapted from Leiras et al. (2014). The main problem types are Facility Location, Inventory Management, and Network Flows/Design. The problems are generally modeled stochastically because of many uncertainties in humanitarian logistics. There are many stakeholders for disaster management, such as government, local and international organizations, NGOs, and industry. The decision level may be strategic, tactical, or operational according to the planning type and horizon. The determination of locations of TMCs, relief supplies warehouses, or shelter sites include strategic decisions since they can be decided before disasters and don’t change in short periods. On the other hand, the transportation, allocation or distribution problems related to operational and tactical decisions since they can change depending on the time and according to many factors.
Motivation
After the Marmara earthquake in 1999, some doctors reported that the biggest problem encountered in emergency departments was that the casualties were not classified according to the triage system in the disaster area (Keskin and Kalemoğlu, 2002; Bulut et al., 2005). It was also stated that the number of casualties who came to hospitals was above the capacity of some hospitals. Therefore these patients were transferred to other suitable hospitals. These problems prevented the timely response to the patients and caused the excessive density in the patient records. This and similar problems were also expressed in several studies for large-scale natural disasters (Abolghasemi et al., 2006; Mulvey et al., 2008; Xiang et al., 2009). In addition, Gautschi et al. (2008) and Haojun et al. (2011) stated the importance of triage and field hospitals/TMCs to use the limited medical resources effectively and to mobilize these resources for saving more patients. Besides, in past disasters, it is a fact that there were cases where there was more medical staff in a disaster area than needed, and there were not enough medical staff in another disaster area.
The motivation behind this study comes from the above facts experienced in past disasters. Despite the local and national governments and NGOs have put efforts for timely response to disasters and effective use of resources, several studies report relatively low levels of disaster preparedness even in disaster-prone areas (Kohn et al., 2012). The Operations Research (OR) and Management Science (MS) studies about
disaster operations provide different insights for both governments and organizations to mitigate the devastating impacts of disasters.
Purpose of the Thesis
Firstly, we aimed to decide the location of TMCs and the allocation of casualties to the EMCs by considering many factors that affect the planning of emergency response. We also aimed to show the effect of the triage system on the results by comparing the single-type of casualty. In the two-stage stochastic model, the minimization of the total setup cost of TMCs and total expected transportation cost of casualties was aimed. Thus, some decisions can be made according to different scenarios, such as:
Number and locations of TMCs that should be set up after the disaster.
The casualties that should be assigned to the EMCs according to their types and disaster areas.
We evaluated that there are still important factors when planning the emergency medical response system. One of the most important factors is the time-dependent change in demand (number of casualties). In other words, not all casualties come into just after the disaster, like in earthquakes. For this reason, multi-period decision making was considered in the second model. There is also another fact that a casualty might not stay in the same health condition during the planning horizon. Therefore, Markov chain transition probabilities of the health condition of casualties were included in the model. By the way, two transition matrix was created for served and unserved casualties since the health condition differs according to the situation of them.
Mainly, it is aimed to emphasize the importance of post-disaster emergency medical system design and give managerial insights to decision-makers. The primary purpose of such studies is minimizing response time and thus saving more people's lives.
Unique Aspects of the Study
In the first part of this study, a two-stage stochastic model was proposed for the location planning of TMCs and casualty allocation to EMCs for post-disaster emergency response. This is the first study, which proposes a stochastic model to
disaster while considering the existing hospitals, different types of casualties, setup cost of TMCs, and transportation cost of casualties. There are also important factors considered in the model, such as:
Possibility of damage to roads and hospitals.
α-reliability constraints for the number of casualties to provide a predetermined reliability level (α) in the solutions.
Distance limit constraints to the immediate casualties to prevent them from being assigned to hospitals in long distance.
Sensitivity analysis for different α-levels and distance limits to see the effect of these parameters on solutions.
In the second part of this study, a multi-objective dynamic stochastic model was proposed for the medical staff assignment and casualty allocation problem after disasters. To the best of our knowledge, there is no study in the literature that considers the multi-period assignment of casualties and medical staff under uncertainty. Possibility of damage to roads and hospitals and distance limit constraints were used in the same manner in the model-1. There are also unique aspects of this study, such as:
Minimization of the expected number of unserved casualties, distances, and the number of medical staff needed by multi-objective optimization.
Markov chain transition probabilities for the health condition of served and unserved casualties, separately.
Updating the capacity of EMCs dynamically according to the assigned casualties for each period.
LITERATURE REVIEW
The number of academic studies on Humanitarian Logistics and Disaster Management increased rapidly in the last decades, as shown in Figure 2.1. In the literature, the problems generally divided into three main categories that are facility location, inventory management, and network flow/design (Leiras et al., 2014). The distribution of studies on Humanitarian Logistics according to the problem type was presented in Figure 2.2. On the other hand, there are also significant problems such as casualty transportation, evacuation planning, debris management, emergency vehicle routing, etc. in the literature.
The articles have been compiled and examined by using some keywords in Web of Science and Google Scholar databases. The keywords used are:
Humanitarian Logistics, Disaster Management, Disaster Logistics, Emergency Logistics, Facility Location, Casualty Allocation,
Medical Staff Assignment/Planning.
In addition to this review, references in some studies were also examined. The studies that could not be obtained from databases and considered important were added to the literature review. Then, the studies dealing with the Facility Location, Casualty Allocation, and Medical Staff Assignment problems focused on in this study were determined. The studies for each type of problem are discussed together with their familiar and different aspects. The objective functions, constraints, and assumptions used in the problems are stated. The articles are classified and analyzed according to the method used, the type of disaster discussed, and the factors such as uncertainty (stochastic/deterministic).
The number of articles according to the published year.
The distribution of studies according to the problem type.
Disasters cause random impacts and require demand-based, cost-effective solutions that make Operation Research (OR) or Management Science (MS) techniques suitable for them (Altay and Green, 2006). Galindo and Batta (2013a) discovered new gaps, challenges, and future research directions for humanitarian logistics after the literature study of Altay and Green (2006). Recently, Farahani et al. (2020) conducted a comprehensive literature review study for OR/MS research in humanitarian operations. According to this review, there is still a need for practical and realistic studies focusing on different aspects of disaster management.
Facility Location Studies in HL
The studies on facility location focus on the spatial aspects of the operations and explore the impact of the facility on factors such as cost, service, and response time.
0 50 100 150 200 250 300 350 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 N ube r o f A rt ic le Year 49% 21% 21% 9% Facility Location Network Flow Inventory Management Other
In the HL literature, facility location studies divided into three categories in general. These are; the emergency medical center, relief supplies warehouse, and shelter site/collection point location problems. These three types of facilities have different functions, but they have similar objectives, such as maximizing the total number of people reached, minimizing distances between facilities and affected areas, and determining the most suitable locations (Kilci et al., 2015).
In terms of the level of decision, facility location studies are related to strategic; inventory management studies include tactic; network design studies concern operational level decisions. Facility location studies generally consider the response time to demand, the distance between disaster areas and relief/medical centers, transportation costs, and the satisfied demand rate when determining the locations. In the literature, the problem of facility location has been studied more extensively than other problems. Some of the studies that focus on facility location for Humanitarian Logistics were presented in Table 2.1. In case of a disaster, there are many uncertainties, such as the effect of the disaster, demand for relief supplies, response time to the casualties, the probability of damage to the buildings and roads, and the expected number of casualties in disaster areas. Because of these uncertainties, the stochastic programming models are generally used to formulate the problems. In the models, various objectives are considered such as maximization of the expected value of the coverage (Balcik and Beamon, 2008; Lu et al., 2009; Salman and Yücel, 2015), minimization of expected total transportation distance or cost (Chang et al., 2007; Galindo and Batta, 2013b), and minimization of average response time (Duran et al., 2011, Toro-Díaz et al., 2013).
The deterministic models have also proposed by assuming exact data and parameters. Besides, simulation techniques such as agent-based and discrete-event simulations were used in some studies to evaluate different approaches for disaster response (Wang et al., 2012; Beamon & Kotleba, 2006). In the deterministic studies, the number and location of the facilities were decided by solving the p-median, p-center, cluster coverage or mixed-integer programming models (Jia et al., 2007; Ablanedo-Rosas et al., 2009; Lu et al., 2009; Görmez et al., 2011; Salman and Gül, 2014; Kilci et al., 2015). Also, minimization of transportation, total facility setup, and storage costs was aimed at some deterministic studies (Barbarosoğlu and Arda, 2004, Campbell and
Facility location studies for Humanitarian Logistics.
Authors Year Method Disaster type Randomness
Günneç & Salman 2007
Two-stage Stochastic Programming, Goal Programming
Earthquake Stochastic
Jia et al. 2007 Set covering, P-median and
P-center model Terrorist attack Deterministic Chang et al. 2007 Two-stage Stochastic Programming, Sample Average App. Flood Stochastic
Balcik & Beamon 2008 Mixed Integer Programming Earthquake Stochastic
Ablanedo-Rosas et al. 2009 Set covering model Earthquake Deterministic
Lu et al. 2009 Maximal covering model,
Ant Colony Optimization Global Deterministic
Huang et al. 2010 P-center, Heuristic
Algorithm Global Stochastic
Mete & Zabinsky 2010 Two-stage Stochastic
Programming Earthquake Stochastic
Salmerón & Apte 2010 Two-stage Stochastic
Programming Hurricane Stochastic
Duran et al. 2011 Stochastic Programming,
Simulation Global Stochastic
Görmez et al. 2011 Integer Programming Earthquake Deterministic
Döyen et al. 2012
Two-stage Stochastic Programming, Lagrange relaxation
Earthquake Stochastic
Galindo & Batta 2013 Stochastic Programming,
Aggregate heuristic Hurricane Stochastic
Toro-Díaz et al. 2013 Non-linear mixed-integer programming, Genetic Algorithm Global Stochastic Lu 2013 P-center, Simulated
Annealing Earthquake Stochastic
Salman & Gül 2014 Multi-period Mathematical
Model Earthquake Deterministic
Kilci et al. 2015
Mixed-integer
Programming, Sensitivity Analysis
Earthquake Deterministic
Salman & Yücel 2015 Stochastic Programming,
Tabu Search Earthquake Stochastic
Aydin 2016 Two-stage Stochastic
Programming Earthquake Stochastic
Fereiduni & Shahanaghi 2017 Robust Model, Monte Carlo
Simulation Earthquake Stochastic
Manopiniwes & Irohara 2017 Stochastic Programming Flood Stochastic
Tavana et al. 2018
Mixed Integer Programming, Meta-heuristics
Earthquake Deterministic
Liu et al. 2019 Bi-objective model, ε–
constraint method Earthquake Deterministic
Adarang et al. 2020 Bi-objective Mixed Integer
Programming Earthquake Deterministic
In some studies, equity/fairness was considered for delivering emergency aid to all demand points fairly. In other words, objective functions such as the minimization of the maximum distance between demand points and facilities (Jia et al., 2007; Huang
et al., 2010), and the minimization of the maximum response time to any demand point (Lu, 2013) have been used to ensure fairness.
In the literature, the location problem of the relief supplies’ warehouses, shelters or casualty collection points have been often studied. In a relatively small number of past studies, the location problem of temporary medical centers was considered. Ahmadi-Javid et al. (2017) stated that there were very few stochastic programming models and robust optimization studies for the location problem of medical centers. Jia et al. (2007) proposed a stochastic p-median model to determine the location of medical centers by considering the uncertainty of the demand, the probability of damage to the facilities, and the capacity fluctuations. The proposed model was tested for different disaster types expected to occur in Seattle city.
Mete and Zabinsky (2010) proposed a two-stage stochastic programming model for medical warehouse location and supply distribution problem. In the first stage, the location of the warehouses and requirements for each type of medical supply is decided. In the second stage, the distribution of the medical supplies to the hospitals is aimed at the model. Similarly, Salmerón and Apte (2010) proposed a two-stage stochastic programming model for facility location and distribution problems. In the facility location problem, they considered different facilities that are warehouses, medical centers, ramp areas, and shelters. The authors also considered the distribution problem of materials and transportation of casualties in the model.
Aydin (2016) proposed a stochastic p-median model for determining the locations of the field hospitals (TMCs) to be set up in case of a possible earthquake for Zeytinburnu districts of Istanbul. The failure of the existing hospital was considered in the proposed model. Liu et al. (2019) integrated the temporary medical center location and casualty allocation problems to maximize the expected survivals and minimize total operational cost. A bi-objective deterministic model and an iteration method based on the ε– constraint method were developed to solve the model. Recently, Adarang et al. (2020) proposed a bi-objective mixed-integer programming model for the location-routing problem that includes hospitals, TMCs, and emergency vehicles (ambulances and helicopters). Two types of casualties (immediate and minimal) were considered in the model. It is aimed to minimize the relief time in the first objective function, and total location cost of TMCs and transfer points and routing cost of vehicles in the second
In the literature, many factors have been considered in the studies. Damage to the facilities (Paul and MacDonald, 2016) or disruption of the stocks (Rawls and Turnquist, 2010) were considered in the models. Some specific constraints were also defined in the literature. For example, chance-constraints were used in several studies (Garrido et al., 2015; Hong et al., 2015; Rawls and Turnquist, 2011; Renkli and Duran, 2015). In addition, Noyan (2012) used a risk-averse approach in contrast to the previous studies to demonstrate the effect of a risk measure for the solutions.
Joint Decision Making for Facility Location, Inventory Management or Network Flow Problems
In the literature, a limited number of studies considered the allocation of relief supplies and network flow problems together with the location decisions (Balcik and Beamon, 2008; Duran et al., 2011, Salman and Yücel, 2015). Besides, there is a limited number of past studies that deal with both facility location, inventory management, and network flow problems (Fereiduni and Shahanaghi, 2017; Manopiniwes and Irohara 2017; Tavana et al., 2018). Fereiduni and Shahanaghi (2017) proposed a single-objective mathematical model for a network design problem in which the location of TMCs, distribution of relief supplies, and evacuation problems are taken into account simultaneously. In the proposed model, it aimed to minimize the total transportation, inventory holding, and fixed facility setup costs. The authors stated that only a solution for small problem sizes could be obtained by using the model.
Manopiniwes and Irohara (2017) proposed a multi-objective stochastic integer-programming model that integrates three different problems of facility and warehouse locations, evacuation planning, and relief distribution for pre- and post-disaster stages. In addition to the cost, the factor of equity in relief distribution is considered, and tradeoffs between these two are discussed. The minimization of the maximum response time between facilities and demand points was included in the objective function to maximize equity. Tavana et al. (2018) considered the central warehouse location, perishable inventory planning, and vehicle routing problems for pre- and post-disaster stages in two phases. The authors developed a mixed-integer programming model and proposed two meta-heuristics to solve the problem.
Casualty Transportation/Allocation Studies in HL
In the literature, casualty transportation or allocation problem has already considered in the emergency medical center location studies. On the other hand, some studies focused the casualty transportation by emergency vehicles such as ambulances and helicopters.
Casualty transportation involving the evacuation and transportation of the injured from the affected areas to the emergency medical centers is one of the most critical actions of emergency logistics (Safeer et al., 2014). In the casualty transportation studies, the distance and transportation times are minimized (Horner & Widener, 2011; Wilson et al., 2013; Yi & Kumar, 2007) or the service level and the number of served casualties are maximized in the objective functions (Feng and Wang, 2003; Yi and Özdamar, 2007). In addition, Barbarosoğlu et al. (2002) considered casualty transportation by helicopters and aimed to minimize the number of helicopter tours.
In some EMC system design studies, hospital (facility) placement and casualty transportation, facilities with medical equipment and medical equipment, water, etc. distribution have been optimized simultaneously. Salman and Gül (2014) proposed a multi-period mathematical model for determining the locations of the new emergency medical centers to be established, determining the capacities of the centers at the beginning of each period, and moving the casualties to these centers. The purpose of the model is to minimize the total transportation and waiting times of the casualties and the total setup cost of the new facility. Özdamar and Demir (2012) proposed a hierarchical clustering and network design model for the problem of transporting the casualties from the disaster area to the emergency medical centers and distributing aid materials to the casualties. In the model, it is aimed to minimize the estimated total transportation time to ensure the efficient use of the vehicles. The proposed deterministic model has been tested for 15 hypothetical problems consisting of 100 to 500 demand points and a scenario of clean water distribution after a possible earthquake in Istanbul. In addition, Toro-Díaz et al. (2013) proposed a nonlinear mixed-integer stochastic programming model for the location and ambulance distribution problem together. A Genetic Algorithm has been proposed for the solution of the mathematical model. The measure of equity (fairness) was taken into account for the variance of individual response times to the casualties. In the proposed model,
the minimization of response time or maximum covering was aimed. The authors stated that a better result was obtained when minimizing response time in the objective function.
Repoussis et al. (2016) proposed a mixed integer programming model for the ambulance dispatching, casualty allocation, and treatment order problem. It is aimed to minimize the overall response time and the total flow time required for the treatment of all casualties. A hypothetical case for a terror attack was considered for testing the proposed model. An exact and a MIP-based heuristic were proposed to solve the problem. Gu et al. (2018) developed a mixed-integer programming model for location TMCs, allocation of casualties to these centers, and distribution of medical supplies under a limited budget. The casualties are classified as emergency and non-emergency, and the maximization of the number of served casualties was aimed. In addition to the proposed model, a greedy algorithm was proposed to solve large-scale problems.
Medical Staff Assignment Studies in HL
Medical staff assignment problem for emergency response has been studied less than the other problems in the literature. It is also crucial in casualty transportation to provide medical service in the EMCs. In the literature, this problem has been considered in different ways. Lodree et al. (2014) proposed a queueing network for the allocation of medical staff (doctors and nurses) to the different casualty classes to cope with the sudden increase in demand for medical response. The queueing network was modeled as a stochastic dynamic programming problem with a discrete-time finite horizon, and three heuristic policies were developed. Heterogeneous team collaboration (doctor+nurse) was also considered for the immediate casualties. Caunhye and Nie (2017) looked at the casualty allocation problem from a different perspective by considering the movements of self-evacuees. The authors proposed a three-stage stochastic model for the location of alternative medical centers and the allocation of casualties. For the solution of the problem, a Benders decomposition-based algorithm was developed, and for a large number of scenarios, a two-stage approximation model was proposed.
In recent studies, Niessner et al. (2018) proposed three simulation-optimization models for the dynamic allocation of medical staff (physicians and medics) at field hospitals
to minimize rescue time and the number of deceased patients. The proposed models were tested for a gas explosion scenario at a small town’s farmers’market by applying different policies. Pouraliakbarimamaghani et al. (2018) proposed a multi-objective integer programming model for the location planning of temporary medical centers near the hospitals and allocation of casualties by considering the medical staff and bed capacity of the hospitals. The authors proposed a non-dominated sorting genetic algorithm (NSGA-II) and a non-dominated ranking genetic algorithm (NRGA) to solve the problem for 15 hypothetical cases. Shavarani et al. (2019) developed a bi-objective mixed-integer nonlinear model for the assignment of medical staff (surgeons and anesthetists) to the operating rooms of hospitals in case of mass casualty events. It is aimed to minimize the expected number of functioning operating rooms and to minimize the expected value of the distance between seriously injured people and a suitable operating room. A simulated annealing algorithm (SA), genetic algorithm (GA), and particle swarm optimization (PSO) were proposed to solve the model by weighting the objective functions for a possible worst-case earthquake scenario in Tehran.
Based on this review, it can be concluded that the problems of location planning of emergency medical centers, transportation of the casualties, and assignment of medical staff under uncertainty have been studied limitedly in the literature. However, these problems are significant for emergency medical response planning after a disaster. In this regard, the proposed models will complete an important gap in humanitarian logistics literature.
METHODOLOGY
Stochastic Programming
In real-life problems, there are many uncertain parameters, such as demand, cost, capacity, time, resources, etc. Stochastic Programming is a common approach to include uncertain parameters in optimization problems and increasingly used in applied sciences and engineering (Birge and Louveaux, 2011). There are several fields such as logistics, transportation, energy, finance, telecommunication, manufacturing, medicine, etc. that used stochastic programming models to solving and analyzing various problems in these fields.
In the Humanitarian Logistics/Disaster Management problems, there are many uncertainties such as the effect of the disaster, demand for relief supplies, response time to the casualties, the probability of damage to the facilities, and the expected number of casualties, etc. Because of these uncertainties, stochastic programming is generally used in this field. In Disaster Management studies, estimating the parameters to define uncertain data is confusing, imprecise, or even impossible. Therefore, the stochastic nature of uncertainty can be represented by using a set of forecasted discrete scenarios, each with an occurrence probability.
Stochastic problems can be modeled as single-stage or multi-stages. Single-stage problems try to find an expected value for the single optimal decision for given scenarios. Multi-stage problems consider the decisions made before the next stages. It tries to find an optimal sequence of decisions.
3.1.1 Two-stage stochastic models
Generally, stochastic models consist of two-stages, where we have a set of decisions to be taken without full information on some random events in the first-stage. Then, full information is received on the realization of some random vector 𝜉 in the second-stage. Hence, recourse (corrective) actions are taken.
The general formulation of a two-stage stochastic programming model is as follows (Birge and Louveaux, 2011):
𝑀𝑖𝑛 𝑐𝑇𝑥 + 𝐸
𝜉𝒬(𝑥, 𝜉) (3.1)
𝑠. 𝑡. 𝐴𝑥 = 𝑏 , (3.2)
𝑥 ≥ 0 , (3.3)
where, 𝑐𝑇𝑥 denotes the optimal value of the first-stage decision, 𝐸
𝜉 denotes the
mathematical expectation with respect to random vector 𝜉 and, 𝒬(𝑥, 𝜉) is the optimal value of the second-stage problem, which is defined as follows:
𝑀𝑖𝑛 𝑞𝑇𝑦 (3.4)
𝑠. 𝑡. 𝑊𝑦 = ℎ − 𝑇𝑥 , (3.5)
𝑥, 𝑦 ≥ 0 , (3.6)
The second-stage problem depends on the data ξ(ω) ≡ (q(ω), h(ω), T(ω)), elements of which can be random, while the matrix W is assumed to be known beforehand. The matrices T(ω) and W are called the technology and recourse matrices, respectively (Kleywegt and Shapiro, 2001).
3.1.2 Chance-constrained stochastic models
In some cases, decision-makers want to ensure the solution quality of a problem by a predefined reliability level. In such problems, we use stochastic programming models that involve chance (or probabilistic) constraints. Charnes and Cooper (1959) first introduced the chance-constrained model as a tool to solve optimization problems under uncertainty. They approached the problem by developing a method that ensured that the decision made by a model led to a certain probability of complying with constraints. In other words, chance-constraints are defined to provide a predetermined reliability level (α) in the solutions and can be described as P(g(x, ξ) ≥ 0) ≥ α. The concept of reliability ensures that the solution met all demands in scenarios comprising at least 100α percentage of all outcomes.
Chance-constrained models were studied extensively in the stochastic programming literature. Daskin et al., (1997), introduced the idea of this confidence level for a facility location problem called α-reliable location model. In the model, the user defines a set of scenarios, each with a probability of occurrence. Then, the model endogenously selects a subset of the scenarios (called reliability set) whose total probability of occurrence is at least α and optimizes a measure of performance over that selected subset of scenarios.
Rawls and Turnquist (2012) adopted the concept of reliability level in a different way for the pre-positioning and dynamic delivery planning of emergency supplies under uncertainty. They defined a binary decision variable denoted by γs that indicates if a scenario s is included in the reliable set. Similarly, we adapted this idea to the proposed models and defined δs that takes 1, if a scenario s is included in the reliable set, 0 otherwise. Then, we added chance-constraints in the models to define the condition of a reliable set. The use of chance-constraints in the proposed models was also described in the mathematical model definitions.
Discrete-time Markov Chain
A discrete-time stochastic process is called a Markov chain, in which the next state depends only on the present state (Ross et al., 1996). For a discrete-time system, if 𝑋𝑛 is the state of the system at time n, then {𝑋𝑛 : 𝑛 ≥ 0} is a Markov chain if:
𝑃𝑟[𝑋𝑛 = 𝑗 | 𝑋𝑛−1 = 𝑖𝑛−1, 𝑋𝑛−2 = 𝑖𝑛−2, … … … , 𝑋0 = 𝑖0]
= 𝑃𝑟[𝑋𝑛 = 𝑗 | 𝑋𝑛−1 = 𝑖𝑛−1] = 𝑃𝑖𝑗 (3.7) The state of the system at time n depends only on the state of the system at time n-1 and does not depend on any other state before time n-1. Therefore, the Markov Chain has a one-step memory.
𝑃𝑖𝑗, denotes the probability that the chain, whenever in state i, moves next (one unit of time later) into state j, and is referred to as a one-step transition probability. The square matrix 𝑃 = 𝑃𝑖𝑗 (i, j ∈ S) is called the one-step transition matrix, and since when leaving state i, the chain must move to one of the states j ∈ S, each row sums to one that forms a probability distribution. For each i ∈ S; ∑𝑗∈𝑆𝑃𝑖𝑗 = 1.
