Optimizing the Network of the Emergency Medical Service in Hanoi

Optimizing the Network of the Emergency Medical Service in Hanoi Rui Guilherme Machado Soares Master’s Dissertation Supervisor: Prof. Carlos Bragança Mestrado Integrado em Engenharia Mecânica 2016-07-04 Optimizing the Network of the Emergency Medical Service in Hanoi ii iii Otimizar a rede do Serviço de Emergência Médica em Hanói Resumo Nesta dissertação pretendeu-se analisar e melhorar a rede do Serviço de Emergência Médica em Hanói. Isto implica a alocação de ambulâncias a estações base, a fim de melhorar o nível de serviço. Este é um problema com que a área da Investigação Operacional lida. A primeira tarefa foi compreender as operações típicas que o SEM envolve e como este está organizado em Hanói. Constatou-se que dispõe de 23 veículos e são operadas 5 estações próprias. Uma estratégia envolvendo duas técnicas de IO, modelação matemática e simulação computacional, foi utilizada na procura pela melhor configuração para servir a população. No entanto, a prioridade constava em definir os pontos da rede que seriam utilizados como dados de entrada dos modelos, estes representam os postos de socorro e a distribuição da procura. A fim de aumentar a cobertura, um plano de cooperação foi explorado, e 34 instalações médicas na província foram selecionadas para serem consideradas como possíveis locais base de ambulâncias. Devido à falta de dados relativos ao histórico de chamadas de emergência, a procura foi modelada com base nos dados demográficos da região. Isto introduziu fontes de erro, o que, aliado à aleatoriedade intrínseca do SEM, levou à decisão de optar pela formulação de vários modelos matemáticos simples que serviram como pontos de partida para as várias iterações simuladas. O modelo de simulação foi construído no software AnyLogic e foi implementada uma interface de GIS para visualizar as operações e fazer os veículos seguir rotas precisas. A distribuição geográfica e taxa de chamadas de emergência foi baseada em mapas de população obtidos na plataforma ArcGIS e informações fornecidas pelo SEM de Hanói. O principal parâmetro de desempenho registado para cada iteração foi o Tempo de Resposta – período desde o pedido de emergência até que se alcance a vítima – uma vez que é o mais fortemente correlacionado com a sobrevivência da mesma. Além disso, as taxas de utilização das estações foram analisadas de forma a orientar as realocações de veículos para as novas iterações. A melhor configuração obtida dispondo apenas dos recursos originais mostrou uma redução em metade do tempo médio de espera da vítima – de 20 para 10 minutos. Várias iterações foram realizadas com a adição de ambulâncias em zonas rurais, até um máximo de 5, a fim de reduzir os longos TRs experienciados. Com 28 veículos, 90% da população foi servida em menos de 16 minutos em casos de emergência, 20% menos tempo do que era possível com os recursos originais, para a mesma porção. Ambas as configurações se mostraram robustas com o aumento da procura visto os seus desempenhos não caírem mais que 30% em qualquer indicador avaliado, mesmo tendo o número de chamadas duplicado. iv Abstract This dissertation meant to analyse and improve the network of the Emergency Medical Service in Hanoi. This entails allocating ambulances to the possible deployment stations in order to better serve the demand, often designated Facility Location Problem. The first task was to understand the typical operations that EMS involve and how it is organized in Hanoi. It was gathered that they have 23 vehicles and operating in 5 stations. A two-folded strategy implementing mathematical modelling and computer simulation was used in the pursuance of a better supply layout. However, setting the network nodes to serve as input of the models was necessary first, these represented the ambulance stations and demand distribution. In order to increase the coverage, a cooperation plan was explored, and 34 medical facilities in the province were selected to be added as possible deployment sites. As there was lack of data concerning the historic of calls, the demand was modelled based on the demographics of the region. This introduced sources of error, which, allied with the EMS intrinsic stochasticity, led to the decision of opting for the formulation of several simple mathematical models that served as starting points for the iterations with the computer simulation tool. The simulation model was built in software AnyLogic implementing GIS tools to visualize the operations and follow accurate travel paths. The distribution and rate of emergency calls was based on population maps from the ArcGIS and information provided by the Hanoi EMS. The main performance metric stored for each iteration was the Response Time, duration reaching the person in need, since it is the one most correlated with survival. Moreover, the utilization rates of the stations were analysed as a mean to guide relocations of vehicles for new iterations. The best performer design maintaining the original resources proved to reduce the average victim’s waiting time in half – from 20 to 10 minutes. Experiments were conducted with the addition of up to 5 ambulances in rural areas in order to reduce the long RTs experienced there. With 28 vehicles, 90% of the population could be served in under 16 minutes in case of emergency, 20% less than it was possible with the original resources. Both designs proved robust with increasing demand by underperforming by less than 30% in all metrics, when the rate of calls doubled. v Acknowledgements I am very grateful to the persons in Hanoi that allowed for this opportunity and helped me along the way. I would like to express my gratitude to my family and girlfriend, Catarina, for all the support given through these past months. Finally, I thank to all my friends that shared some hard work moments with me. Optimizing the Network of the Emergency Medical Service in Hanoi 1 Contents 1 Introduction ............................................................................................................................. 5 1.1 Emergency medical services .................................................................................................. 5 1.2 Purpose .................................................................................................................................. 5 1.3 Objectives .............................................................................................................................. 5 1.4 Research strategy .................................................................................................................. 6 1.5 Thesis overview ..................................................................................................................... 6 2 Literature review ..................................................................................................................... 7 2.1 Mathematical models ............................................................................................................. 7 2.2 Computer simulation .............................................................................................................. 9 3 EMS operations overview .................................................................................................... 11 3.1 Typical system ..................................................................................................................... 11 3.2 Hanoi EMS ........................................................................................................................... 12 3.3 Improvement opportunities ................................................................................................... 13 4 Mathematical modelling........................................................................................................ 14 4.1 Network nodes ..................................................................................................................... 14 4.2 Costs .................................................................................................................................... 18 4.3 Models.................................................................................................................................. 19 5 Computer simulation ............................................................................................................ 24 5.1 Description of the model....................................................................................................... 24 5.2 Performance metrics ............................................................................................................ 31 5.3 Simulation run length ........................................................................................................... 33 5.4 First results ........................................................................................................................... 33 5.5 Iterations maintaining the number of resources ................................................................... 37 5.6 Iterations increasing fleet ..................................................................................................... 40 5.7 Demand scenarios ............................................................................................................... 42 5.8 Discussion of results ............................................................................................................ 42 6 Conclusions and recommendations ..................................................................................... 44 References ................................................................................................................................ 45 Appendix A: Network nodes ................................................................................................. 48 Appendix B: Python script .................................................................................................... 50 Appendix C: Mathematical modelling results ....................................................................... 51 Optimizing the Network of the Emergency Medical Service in Hanoi 2 Acronyms ALS Advanced Life Support BLS Basic Life Support EMS Emergency Medical Services FLP Facility Location Problem OR Operations Research RT Response Time RTT Round-trip Time Optimizing the Network of the Emergency Medical Service in Hanoi 3 List of figures Figure 3.1 - Task sequence of typical EMS in Aboueljinane et al (2013) ............................................................... 11 Figure 3.2 - Currently operated deployment stations ............................................................................................. 13 Figure 4.1 - Map of possible deployment stations .................................................................................................. 15 Figure 4.2 - Map of demand nodes ........................................................................................................................ 17 Figure 4.3 - Distribution of shortest RTs with 39 stations (minutes) ....................................................................... 18 Figure 4.4 - Distribution of shortest RTs with 5 stations (minutes) ......................................................................... 18 Figure 4.5 - Inputs and outputs of the mathematical models ................................................................................. 20 Figure 5.1 - Population map of Hanoi from Esri (2015) .......................................................................................... 25 Figure 5.2 - Demand zones, with 50%, 30% and 20% of the province's population, from the inside to the outside ............................................................................................................................................................................... 27 Figure 5.3 - Block diagram of Main agent .............................................................................................................. 28 Figure 5.4 - State chart of agent Victim .................................................................................................................. 29 Figure 5.5 – Block diagram of the agent Station .................................................................................................... 29 Figure 5.6 - State chart of the agent Ambulance.................................................................................................... 30 Figure 5.7 - Control panel for the simulation .......................................................................................................... 31 Figure 5.8 - Summary of the simulation model main tasks .................................................................................... 32 Figure 5.9 – Display panel when running a simulation, showing the KPIs in real time ........................................... 33 Figure 5.10 - Distribution of RT with current design (minutes) ............................................................................... 35 Figure 5.11 - Distribution of RT with p-median5 design (minutes) ......................................................................... 36 Figure 5.12 - Distribution of RT with MCLP design (minutes) ................................................................................ 36 Figure 5.13 - Evolution of the different metrics with increasing fleet ...................................................................... 41 Figure 5.14 - Stations used in the p-median5 design (in red) ................................................................................ 42 Figure 5.15 - P-median5 design with the added 5 stations (in orange) .................................................................. 43 Optimizing the Network of the Emergency Medical Service in Hanoi 4 List of tables Table 5.1 – Parameters and variables of each agent present in the model ........................................................... 24 Table 5.2 - Population in each of the three demand zones .................................................................................... 26 Table 5.3 - Simulation results for RTT (minutes).................................................................................................... 34 Table 5.4 - Simulation results for RT (minutes) ...................................................................................................... 34 Table 5.5 - Models ordered from best performance (on top) to worst in each metric for RT .................................. 34 Table 5.6 - MCLP and p-median5 results compared with current design's (model/current) ................................... 35 Table 5.7 - Number of rescues each station made and number of times it was busy to respond (ordered by value) ............................................................................................................................................................................... 37 Table 5.8 - Number of times each station not in use was the closest to victim ...................................................... 38 Table 5.9 - Results for RT with MCLP design with ambulance relocation to station 37 ......................................... 38 Table 5.10 - Comparison with original MCLP (new/original) .................................................................................. 38 Table 5.11 - Number of rescues each station made and number of times it was busy to respond (ordered) ......... 39 Table 5.12 - Number of times each station not in use was the closest to victim .................................................... 40 Table 5.13 - Results for RT with p-median5 designs with ambulance relocation to station 13 or 22...................... 40 Table 5.14 - Comparison with original p-median5 (new/original) ........................................................................... 40 Table 5.15 - Results for RT with increasing fleet.................................................................................................... 41 Table 5.16 - Results for RT with p-median5 design the fleet increase design with double demand ...................... 42 Table 6.1 - Possible deployment stations and their coordinates ............................................................................ 48 Table 6.2 - Number of nodes used per district and their demand .......................................................................... 49 Optimizing the Network of the Emergency Medical Service in Hanoi 11 3 EMS operations overview This section is intended to explain clearer how the Emergency Medical Services work and how their performance is measured, both in general cases and in the specific situation of Hanoi, and take a critical remark on the current state of the organization in study. 3.1 Typical system As mentioned previously, EMS have the mission of attending unpredictable medical issues with the goal of reducing mortality in the population, by assisting victims and transporting them, thus increasing the recovering chances. For that, they must have a very coordinated plan in place to act fast and flawlessly at each occurrence, it usually involves two types of operations: central and external. Detailed tasks are presented in Figure 3.1. The former kind occur in a fixed facility and are responsible for receiving incoming calls, evaluating the severity of the victim’s condition and deciding the best resources to dispatch, if necessary. The external operations begin once a vehicle starts to the patient, its team is entitled to aid the person on spot and assure transportation to a medical facility when needed. The choice of this last destination is usually decided centrally though. A final step required is that the vehicle and team return to a station if there are no more emergencies to take care of. The time between receiving a call and arriving to the victim’s location is referred as Response Time, while the period including this plus reaching the hospital is known as Round-trip time. Every single situation EMS faces is unique which means that in some cases the sequence of tasks does not include all the ones mentioned, for the patient may be fully recovered on the spot, or an ambulance dispatching may not be necessary. Many systems have different vehicles to deal with varying degrees of illness. For land vehicles there are commonly three types: simple ambulances that transport patients only (predominant in developing countries), Basic Life Support vehicles which are able to stabilize minor conditions and Advanced Life Support ones, equipped with better technology to attend more severe health needs. Helicopters are sometimes part of the organization’s fleet, or at least of a cooperating entity’s, and are held for remote rescues or very urgent situations. Figure 3.1 - Task sequence of typical EMS in Aboueljinane et al (2013) Some private hospitals or other entities may operate their own EMS, however, governments maintain a public organization to ensure the availability of this so crucial service. In order to increase efficiency, cooperation between medical bodies and fire departments is common to extend the network and increase coverage and resources. In developed countries, fire stations’ vehicles are often the first to arrive. Optimizing the Network of the Emergency Medical Service in Hanoi 12 To ensure the quality of the system, many performance indicators are monitored such as the few presented below:  Response time (RT): measured from the moment the call was received until the first aid vehicle arrives on scene;  Round-trip time (RTT): response time plus the period until the victim is delivered at the hospital;  Dispatching time: moment between receiving call and the team leaving the station;  Waiting time: duration in queue until a resource is available to answer emergency request;  Loss ratio: failure to answer demand due to exceeding waiting time limit;  Survival rate: patients who lived through the reported incident;  Cost-effectiveness: amount of capital invested for increased performance. Although the survival rate is the most accurate translation of the EMS goal – save lives – it is difficult to incorporate in theoretical models used for planning. Hence it is often replaced with metrics such as RT and RTT which are very correlated. To further add complexity to the decision making process in this area, the demand it serves is vast and unpredictable – any individual may need urgent care in any place at any time. Other sources of stochasticity are the operations steps themselves – preparation time, delays in traffic and duration of the medical assistance. 3.2 Hanoi EMS This research had the contribution of the Emergency Medical Services of Hanoi and the data about their organization and operations was gathered from two interviews with the Vice Director Thanh Khan and from their public website. In Vietnam, the public EMS is split into provinces, each operating independently from each other. The province of Hanoi is populated by 7,587,000 persons and ranges over an area of 3,329 km2. For this demand, they rely on 5 deployment stations (owned and operated by them) and 23 BLS vehicles, distributed as follows:  Hoan Kiem (HK) – 8;  Tu Liem (TL) – 5;  Thanh Tri (TT) – 4;  Gia Lam (GL) – 3;  Ha Dong (HD) – 3. The Hoan Kiem building is the central one and includes the department which receives the calls and makes deployment decisions. Figure 3.2 - Currently operated deployment stations provides a better idea of the area in study and the current distribution of facilities. These are all the resources available to perform EMS for there’s no cooperation with hospitals or other entities. Optimizing the Network of the Emergency Medical Service in Hanoi 13 Figure 3.2 - Currently operated deployment stations The average number of calls each day is 300, from which only one third (100) are real emergencies. Around 90% of these are made from homes in the city and there’s not known frequency changes over the different periods of the day. The little demand may be explained by the lack resources and poor efficiency. Moreover, Vietnamese population often turn to selfmedication. Roughly, their average response time is 15 minutes, despite including almost exclusively urban rescues. Although they do keep data on received calls, these are not stored digitally, which prevented extensive data analysis from demand history. The ultimate objective of this study was to improve the service level of this organization just described by exploring with the layout of deployment stations. This improvement was decoded in shortening the RT and RTT for the entire province population. On the other hand, there were budget constraints, which were not specified but should stay reasonable. A solution utilizing the available resources was priority and further research on the impact of adding new fleet was a secondary goal. The approach should be robust in terms of demand variation and operations uncertainty. 3.3 Improvement opportunities An early remark on this information took a special note on the spatial distribution of facilities. These are concentrated towards the province centre leaving suburban and rural areas poorly covered. Moreover, the resources available seemed too few for the demand, both the number of stations and vehicles. The former could be tackled by cooperating with other entities, such as medical buildings. Optimizing the Network of the Emergency Medical Service in Hanoi 14 4 Mathematical modelling This chapter is dedicated to explain the first part of the actual solution developed – the mathematical modelling of the problem and its optimization. As mentioned earlier in this document, the operations of EMS have many sources of randomness. Although, models have been developed that tackle this issue by using probabilities, it’s still not the most accurate way to proceed. Furthermore, to estimate them, extensive data on demand and its accurate forecast is necessary, which isn’t available. Instead, in this research, very simple models were solved in order to get different designs that served as starting points for simulations. This tool is able to mimic the stochastic reality better and was, therefore, used as the tool to ultimately find the best solution for the problem. Before describing the actual models, the steps to gather the inputs they require are overviewed in the following sub-sections. The actual solving of the problems was accomplished with the tool IBM ILOG Cplex, the full results are presented in Appendix C. 4.1 Network nodes In order to solve a FLP, a set of supply and demand locations is necessary. In this context, these are the deployment stations and aggregated population nodes and the first step is to study the province of Hanoi to choose them. 4.1.1 Deployment stations On the supply side of the network there are the locations where ambulances wait idle. They may be any site with room for the vehicles, though the Hanoi EMS advised locations equipped with medical material. This allows ambulances to return to the same spot rather than having to resupply in other station. In line with the plan of a lower-cost and shorter-term solution, it wasn’t suggested building new facilities. Thus, it left choosing the set of supply nodes from existing ones. A clear possibility was to implement cooperation with other entities and use their network. It was decided, at this stage, to screen the existing medical facilities (hospitals and smaller practices) for candidates. After some research in Vietnam’s government and universities websites, it was compiled a list with the names of 663 public medical facilities in the province of Hanoi alone. However, many of these are very small practices with no room for vehicles, and some are different specialities in the same building, thus it wouldn’t make sense to consider more than one network node for those. The task was, therefore, to reduce the list to a set of independent locations which were able to serve as a station for ambulances. In order to accomplish it, the kinds of existing medical facilities had to be understood to create filters to the list, these would have to be in Vietnamese since it was the language the names were in.  Benh vien (BV) – “hospital”, is a large medical facility, usually specialized in a given field of medicine and containing emergency department  Benh vien da khoa (BVDK) – “general hospital”, is a large medical facility with multiple services and areas, most have emergency department  Phong kham (PK) – “clinic”, is a smaller office, often specialized in a field and with no big facilities to keep vehicles  Phong kham da khoa (PKDK) – “polyclinic”, is a clinic slightly bigger and with services across more areas of medicine, though usually too small to have ambulances stationed in  Phong kham da khoa khu vuc (PKDKKV) – “regional polyclinic”, is a polyclinic serving a region in rural areas, mostly smaller than the others Optimizing the Network of the Emergency Medical Service in Hanoi 15  Tam y te (TYT) or Trung tam y te (TTYT) – “health centre” or “medical centre”, are the smallest medical practices listed, these are too small to be stations After overviewing the characteristics of each kind of medical facility, it was decided that only the hospitals (general or not) are suitable candidates for emergency deployment stations. The selected keywords to find these were “benh vien” and “bv” since they include both desired types of hospital. From the original 663 names, a list of 27 possible stations emerged. These, however, do not include private and special kinds of hospitals. The privates were found in a listing from the UK embassy healthcare advice for expats living in Hanoi and with an interview with the Director of the Customer Service Department of the Hanoi French Hospital – Sau Nguyen. Finally, international, state and military hospitals were researched in the website of Vietnam’s department of health. Adding the 5 owned and operated emergency stations, it was left a list with 42 names of medical facilities. The goal was, though, to find their geographical coordinates. In order to do that, a map was created in Google Maps MyMaps inputting an Excel spreadsheet with the list of names as the search field. At that point, the problem of shared facilities between hospitals was solved by examining the obtained map – the private Hanoi French Hospital shares buildings with the state hospital Bach Mai and two previously existing deployment stations belong to the facilities of general hospitals. These were merged and the final set of possible deployment stations counted with 39 locations, 5 of which were the existing ones and 34 were new cooperation. The list went through the personnel of the Hanoi EMS to be approved, furthermore, all these entities are included in a cooperation deal that is in place, though not being used. Having the locations in the map, it was left to extract the geo-coordinates of each. It was done by exporting it to a KML file, which was processed in a spreadsheet to achieve a table with the names and respective coordinates in the format “Latitude, Longitude”, as presented in Appendix A. The Figure 4.1 presents the selected possible deployment stations in the map of Hanoi. Figure 4.1 - Map of possible deployment stations Optimizing the Network of the Emergency Medical Service in Hanoi 16 It’s possible to state how much more coverage this scenario provides compared with the original scenario, especially in the rural areas. 4.1.2 Demand points While the supply side is more straightforward, the demand adds a lot of complexity to the research due to its vastness and stochasticity. For instance, the need for emergency assistance may arise from every individual, thus the whole population are possible clients. Furthermore, unlike businesses where marketing or other factors influence customers’ desires, health incidents are more unpredictable and require quick action, which in turn implies ever ready rescue operations. Despite these difficulties, demand isn’t completely random and there are methods to forecast it. Common practice in the field is to study patterns in the history of stored calls. However, this wasn’t an option since, as mentioned, this data was not available digitally and it would be impractical to draw from paper the amount of records necessary to have statistical meaning. Another reason to deviate from this method in the research had to do with this information being biased. As laid out in previous sections, the EMS of Hanoi is inefficient, especially providing for the outer areas. It turns out that demand is, to a certain extent, elastic to supply, which means people underserved by the system turned away from it and most of the population in Hanoi (and Vietnam in general) are used to self-help. Forecasting the people’s needs from this faulty data seemed unwise then. As an alternative, the demand nodes were set based on demographic data. However, this information isn’t available, or up to date, at the ward level (smallest political division) and the population of each district was used instead. As these areas are very large and variate (from 5.29 km2, the smallest, to 428.00 km2, the largest), they had to be split into several points that represented the locations’ inhabitants. A trade-off necessary at this stage had to do with the amount of demand aggregation. On one hand, the more nodes used, the more accurate the model would be, however, this accuracy grows at the expense of increased complexity which, at some stage, hinders or even prevents finding a solution. At the very limit, a point could be drawn on the map for each individual, this was impractical though. It was decided that one node would represent an area small enough so that the difference of the travel time of an ambulance to the centre of it and to an extreme of it would be unimportant. It was used a region of 25 km2 for the purpose. In this case, and considering a circular shape for the area, the radius could be covered in 3 minutes travelling at 50 km per hour, 2.5 at 68 or 2 at 85 (approximating as a straight line). This served as a lower limit to the accuracy of the data since each district’s area was divided by 25 and that number, rounded up, was the number of demand nodes representing its population. An approximation was made here by splitting the number of people evenly through the nodes, which, in turn, were distributed through a map created in Google Maps MyMaps. In total, 151 points belong to the demand set, as presented in Appendix A. The set of coordinates of the nodes was reached in the same way as in the deployment stations’ case. Even though sources of error were introduced in this procedure, it has been proven in past research that demand aggregation inaccuracies are overweighed by the choice of appropriate models (Brotcorne et al, 2003). Moreover, the simulation part of this research was responsible for mirroring the people’s needs in a more realistic manner. The demand points were distributed as displayed in Figure 4.2. Optimizing the Network of the Emergency Medical Service in Hanoi 17 Figure 4.2 - Map of demand nodes 4.1.3 Time matrix A final piece of the network was left – the time, or distance, between every station and every demand node, this is key input to de model. In order to get that, it was used the Google Maps API Distance Matrix running with the Python IDE Spyder. This tool takes a set of origins and destinations and outputs two matrixes: one with the travel distance between each two points by the recommended road, and the other containing the time a car would spend on the same path. The sets of origins and destinations coordinates were translated into text files to serve as inputs for the program. The time matrix was targeted since it was thought to be more accurate than considering distances. This is especially important in Hanoi due to the poor condition of many roads and to the heavy traffic in some areas, and Google Maps directions times have these into account. Also, the final unit wanted was time, since the main performance metrics of EMS are RT and RTT, thus, if using distances, these would have to be converted into time and, for that, uniform speed would be considered, resulting in less authentic values. The programming script written to accomplish the task is presented in Appendix B. The resulting matrix is not included in the document since it is too big (39*151). 4.1.4 Network overview In order to have a better idea of how distant the demand nodes are from stations, the travel time to each demand point from its nearest facility (RT) was gathered from the matrix and a histogram was built with this data. As a comparison, the same method was applied using only the 5 original stations. Optimizing the Network of the Emergency Medical Service in Hanoi 18 Figure 4.3 - Distribution of shortest RTs with 39 stations (minutes) Figure 4.4 - Distribution of shortest RTs with 5 stations (minutes) At first glance, there was a major shortening in the overall and maximum estimated RTs by adding the new facilities. With 39 stations, the longest one was 61 minutes while previously it was 97, also the average time dropped from 40 to 15 minutes. 4.2 Costs Information regarding the costs of the EMS of Hanoi were not provided by the organization. However, the approach taken does not incur in high investment, therefore costs weren’t as relevant as if the creation of new facilities was intended. These topic is discussed in a more qualitative perspective then, in this section. Optimizing the Network of the Emergency Medical Service in Hanoi 19 In their owned facilities, it was assumed they have a fixed cost (F) and a cost to operate each rescue team (x). F includes the central service of receiving calls and dispatching, and also the bills of owning the 5 stations. The cost x is completely dependent on the number of teams working there, for the 23 vehicles it would be 23x then. If one team was dismissed, the variable cost would be reduced to 22x. The cost of operating the same team stationed in a hospital, for instance, would be greater than x, it was designated y. Besides the logistical complexity this case adds, it requires preparing the new facilities, such as storing supplies and communication equipment, which explain the increased cost of y. On the other hand, if a team is allocated from one of the original stations to a hospital where another team is settled already, its marginal cost is less than the first one’s since most logistical aspects are taken care of. Thus it’s assumed that x is the expense of operating a team anywhere and y is a fixed cost of starting operations in a new facility. The fixed cost F remains constant in any discussed scenario. As the first stage’s goal is to make use of the current resources, the 23 vehicles, the operating cost is fixed and only y matters, being the added cost of a solution the number of new stations chosen times y. Although it’s harder to quantify, a solution’s cost may be surpassed by its operational savings by requiring less travelling to reach victims, saving fuel and time. 4.3 Models As discussed previously, the models utilized were simple mainly because there was a lack of accurate input data and for the availability of a simulation tool which was expected to fill the weaknesses of the mathematical optimization. The major developments overviewed in FLP applied to EMS fall into reassuring multiple coverage and accounting for stochasticity in demand or operations. Both of these were tackled rather with the computer simulation model, by monitoring the utilization of stations in the first case, and including random inputs in the later. The mathematical optimization results were then mainly utilized as a starting points for iterations in the built computer environment. 4.3.1 Inputs and outputs In Figure 4.5 it is presented the data entering and leaving the models solved. The ultimate output of the models is the allocation of ambulances to the deployment stations, however, a secondary result is the facility that serves each node, in the “p" formulations, and the covered demand points, for the coverage problems. The input data changes from model to model, though the time matrix, the demand of each point and the number of vehicles are common to all. The time standards are inputs required only by the covering models (*) and percentage value is part of the DSM model only (**). Optimizing the Network of the Emergency Medical Service in Hanoi 20 Figure 4.5 - Inputs and outputs of the mathematical models 4.3.2 Variables 𝑉 Set of demand nodes 𝑊 Set of possible ambulance stations 𝑊𝑖 Set of possible ambulance stations within coverage time standard of demand node i 𝑊𝑖1 Set of possible ambulance stations within the shortest coverage time standard of demand node i 𝑊𝑖2 Set of possible ambulance stations within the longest coverage time standard of demand node i 𝑡𝑖𝑗 Travel time from station j to demand point i 𝑑𝑖 Demand of node i 𝑦𝑖 Equal to 1 if node i is covered, 0 otherwise 𝑦𝑖𝑗 Equal to 1 if node i is supplied by station j, 0 otherwise 𝑦𝑖1 Equal to 1 if node i is covered within the shortest time range by 1 vehicle, 0 otherwise 𝑦𝑖2 Equal to 1 if node i is covered within the shortest time range by 2 vehicles, 0 otherwise 𝑥𝑗 Number of ambulances placed at station j 𝑄 Longest travel time between any demand node and its closest station 4.3.3 P-median model Objective function: 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑∑𝑑𝑖𝑡𝑖𝑗𝑦𝑖𝑗 𝑖∈𝑉𝑗∈𝑊 (4.1) Optimizing the Network of the Emergency Medical Service in Hanoi 27 Figure 5.2 - Demand zones, with 50%, 30% and 20% of the province's population, from the inside to the outside 5.1.3 Model logic The actions in the model were programed in Java which is the language of the utilized software – AnyLogic. The necessary connections between agents were made in order to be possible to move flowchart agents and messages between them, thus coordinating the system. Main agent The action in the main agent happens through logic blocks, starting in the mentioned three sources in parallel, as it is shown in Figure 5.3. Before continuing down the chain, a command implemented in this block’s exit searches for the nearest facility to the newly created victim, by real road distance from the GIS map, and attributes its parameter “parGoToHospital” the selected station. To set the parameter “parNearestStation”, a code finds the set of sites with the variable “varAvailableAmbulances” greater than zero, which are the ones with immediate availability, and selects the nearest one by GIS path. In case of every existing resource being busy, it is chosen the nearest facility from the set of those with capacity different from zero, meaning it has vehicles in its fleet. Still in the same block, a command checks if the chosen station for the rescue is the nearest one, from the ones in use. If not, the variable “varBusyTimes” of this later facility is added one unit since it didn’t have vehicles available when needed. A last command adds one unit also to the variable “varGoToHospital” of the station chosen as the destination to take the victim to, meaning it was the nearest site (either in use or not). It was decided this way, instead of nearest vehicle, since ambulances are required to return to a station for resupplying after each rescue, as it was imposed by the Hanoi organization. Optimizing the Network of the Emergency Medical Service in Hanoi 28 The next block is called “timeStart” and it initiates the clock on the agent Victim that went through it. Afterwards, there is a time delay, corresponding to the time the person is waiting for an ambulance. It’s exit is only triggered by calling the function “stopDelay()” and it is invoked when the a vehicle reaches the victim. The time up to this point, the RT, is stored by placing in the chain a time measure block. The next delay represents the time of patient’s stabilization on-spot and the transportation to the hospital, being interrupted only by a stop function. The RTT is marked at this stage by a time measure block and, lastly, the agent victim sinks (leaves the simulation). Figure 5.3 - Block diagram of Main agent Victim agent When appearing in the map, besides the chosen person icon, it was added a text label to the victim which was programmed to show the parameter “parNearestStation” so that the user was able to visually follow which facility was rescuing it. The behaviour of the victims is controlled by a state chart as in Figure 5.4. After being created and its parameters set as explained previously, the first state is calling for help. An entry action was programed to create a new agent of the type Help and set its only parameter, which indicates its requester, to be itself, the victim. Still in the same sequence, the Help agent is sent to the station indicated as the nearest available, in order to be used in its block chain. The transition to the next state, called “stMovingToHospital” is triggered by receiving a message in form of the string “helped”, which comes from the agent Ambulance. At entering this state, the person icon is commanded to disappear, visually simulating the rescue team assistance and pick-up, and the function to stop the waiting for ambulance delay in the Main agent is called. Similarly, the transition to the final state occurs when the message “arrived” is received and an action follows calling the function to end the delay block “MovingToHospital” in the Main agent. Optimizing the Network of the Emergency Medical Service in Hanoi 29 Figure 5.4 - State chart of agent Victim Station agent After receiving the Request agent sent by a victim, this enters a logic blocks chain (Figure 5.5) within the agent Station. The first element is of the type “Seize” and is used to select a vehicle of the pool of resources. Here the variable indicating the available ambulances is updated (reduced by one) and the parameter “parHelp” of the seized vehicle is set to be the agent Help going through the block diagram, indicating the help request it is attending. Afterwards, a delay was placed, which ends only when a stop function is called (when the ambulance is back at base), and it follows a block to release the resource, making it available and updating the variable of available vehicles. Lastly, the variable of rescues made by the station is added one unit. Figure 5.5 – Block diagram of the agent Station Ambulance agent The vehicles’ behaviour is imposed by state charts (Figure 5.6), being the starting one named “atStation”, which represents it being idle. It transitions to the state “Preparing” when it is attributed a help request by the station. Its exit is triggered by a timeout with a triangular distribution ranging from 0.5 to 4 minutes, with mode of 2. This translates the time, in real operations, that it takes for the team to leave the station after the emergency call is received. After that, the ambulance is programed to move to the victim, selected from the parameter “parVictim” of the Help agent, by the fastest path using real roads in the map and this travel can be followed in the GIS display during the simulation. Optimizing the Network of the Emergency Medical Service in Hanoi 30 The travel speed of the vehicles is given by a triangular distribution with vertexes in 35, 60 and 90 km/h. Another transition occurs when the person is reached, at which point the string “helped” is sent to that victim as a message. The state “helping” is left when a timeout (triangular distribution with 2, 5 and 10 minutes) happens, simulating the duration of assisting the injured on-site. The next action is to move the vehicle to the destination hospital, that is retrieved from the victim’s parameter “parGoToHospital”. When it has arrived, another timeout (with a duration distributed triangularly with values 0.1, 0.5 and 1) mimics the duration of unloading the patient and the message “arrived” is sent to the agent Victim. Then, if that hospital is the vehicle’s home station, it returns to the starting idle state, otherwise it returns to its original facility, and waits for the next emergency. In either case, when the ambulance finishes the cycle, a function is called to stop the delay “rescuing” in the home station’s flowchart. Figure 5.6 - State chart of the agent Ambulance The reason to consider all time delays distributions lies on their random nature, it doesn’t last the same to assist a victim every time, or to travel a certain distance due to traffic conditions. Although triangular distributions aren’t the most accurate, they were used for there was a lack of great amounts of data to shape curves from and for their simplicity. All minimum, maximum and median values were estimated by the Hanoi EMS personnel based on their experience. They also validated the logic and sequence of tasks of the model. 5.1.4 Control panel In the pursuance of providing the EMS of Hanoi a simple and easy to work with tool, yet still complete and insightful, the simulation was needed to be made available and capable of testing different designs in varying scenarios of demand and time delays, without requiring the proprietary software AnyLogic or any difficult programming. Optimizing the Network of the Emergency Medical Service in Hanoi 31 A control panel, presented in Figure 5.7, was developed for this effect and the model was exported as a Java Applet. The main desired function was that of controlling the capacity (number of ambulances) of the stations. Thus “edit boxes” were added to the main simulation panel, one for each station, which allowed to do so. For testing different demand scenarios, it was made possible to tune the rates of each zone, either maintaining the current ratio or not. It isn’t achievable, however, for a user of the applet to change the shapes of the population areas without working in the building software. Finally, the average speed and time delays were also changeable so that they could be updated to real data shifts or to witness the gains for the overall system by improving the performance in those tasks. The times referred include the deployment, the victims’ stabilizing and the hospital drop-off. Figure 5.7 - Control panel for the simulation 5.2 Performance metrics The key indicators to evaluate a design on are the Response and Round-trip times, for these are the most strongly correlated with the victims’ survival. During the simulation, it is presented in real time the distribution of both metrics as well as their average and maximum values, as displayed in Figure 5.9. Other aspect to monitor is the utilization of each facility: number of rescues made and number of requests denied due to the unavailability of resources. This was a path to try relocations in the designs. By reviewing which stations lacked vehicles when needed and which were very scarcely utilized, ambulances were moved to where they seemed more necessary in the pursuance of reaching a better allocation plan than the original layouts. The number of instances that each station (utilized or not) was the nearest to a victim was also captured with the intent of determining which sites not in use should be allocated vehicles. Optimizing the Network of the Emergency Medical Service in Hanoi 32 The whole data is exported to a spreadsheet in the end of each run, in which further analysis can be completed. Besides building histograms and collecting maximum and average values on the performance times, the values on the percentiles 25%, 50%, 75%, 90%, 95% and 99% were exposed, for each iteration done, to have a better view of the population coverage. The summary of the described functioning of the simulation model is presented in Figure 5.8. Figure 5.8 - Summary of the simulation model main tasks Optimizing the Network of the Emergency Medical Service in Hanoi 33 Figure 5.9 – Display panel when running a simulation, showing the KPIs in real time 5.3 Simulation run length The length that a simulation run should have in order to be statistically precise is a very difficult parameter to estimate. Mahajan and Ingalls (2004) argue that it is preferable to have a longer run than several shorter replications in order to have less deviation from the expected mean results. When data is available it is a good practice to adapt the length to the range of the sample used. However, this is not the case of this research and, as to allow for several iterations in practical time, it was decided that each run would be of one virtual month, originating around 3000 calls. 5.4 First results The first layout to test in the simulation was the currently used (with the 5 original stations) in order to validate the model and have a starting point for comparisons. The 8 scenarios obtained with the mathematical modelling followed and the performance of all is summed in Table 5.3 for the RTT and in Table 5.4 for the RT, in the different metrics discussed. In terms of notation, it was adopted to call each model by their designation and add a “5” to it when referring to the formulation with the added restriction of utilizing the five original deployment stations. The model “current” specifies the current design of the Hanoi EMS. The RT will be the main focus and the best judge of a design’s values since it is the most strongly linked with survival and RTT is dependent on it. It is also the only parameter observed in most literature cases. Where the metric (RT or RTT) is not explicit, the results that are being talked about are the RTs. Optimizing the Network of the Emergency Medical Service in Hanoi 34 Table 5.3 - Simulation results for RTT (minutes) Percentile Model avg max 0.25 0.50 0.75 0.90 0.95 0.99 current 32 105 17 26 44 61 70 95 p-median 25 124 15 20 32 45 54 76 p-median5 23 161 15 19 25 39 53 76 p-centre 28 110 17 23 36 53 62 90 p-centre5 26 145 15 21 33 48 56 80 MCLP 24 126 14 20 29 40 52 92 MCLP5 29 160 16 22 33 55 82 106 DSM 26 90 18 23 31 46 55 73 DSM5 26 106 15 20 30 45 63 101 Table 5.4 - Simulation results for RT (minutes) Model avg max 0.25 0.50 0.75 0.90 0.95 0.99 current 20 82 8 14 29 43 49 65 p-median 12 62 6 9 14 25 32 39 p-median5 10 87 6 8 12 20 27 41 p-centre 15 66 7 11 22 34 37 52 p-centre5 14 85 6 9 18 30 35 55 MCLP 11 70 6 8 15 20 27 46 MCLP5 14 90 7 10 16 27 41 52 DSM 13 58 7 10 15 27 35 43 DSM5 12 58 6 9 14 30 34 49 As to easily rank the overall best designs, these were ordered from best performance (shortest time) to worst, top to bottom, in Table 5.5. Table 5.5 - Models ordered from best performance (on top) to worst in each metric for RT avg max 0.25 0.50 0.75 0.90 0.95 0.99 pmedian5 dsm pmedian5 pmedian5 pmedian5 mclp pmedian5 pmedian mclp dsm5 mclp mclp dsm5 pmedian5 mclp pmedian5 pmedian pmedian dsm5 dsm5 pmedian pmedian pmedian dsm dsm5 pcentre pmedian pmedian mclp dsm dsm5 mclp Dsm mclp pcentre5 pcentre5 dsm mclp5 dsm dsm5 pcentre5 current mclp5 mclp5 mclp5 dsm5 pcentre5 mclp5 mclp5 pcentre5 pcentre dsm pcentre5 pcentre5 pcentre pcentre pcentre pmedian5 dsm pcentre pcentre pcentre mclp5 pcentre5 current mclp5 current current current current current current It is straightforward to choose the p-median5 as the best candidate and the MCLP following it by observing the rankings. The field “maximum RT” isn’t very indicative of one’s performance because there’s randomness in the system and, as such, it is prone to outliers appearing in the extreme range of values. These also pushes the percentile 0.99 up, which is a good explanation Optimizing the Network of the Emergency Medical Service in Hanoi 35 for the weaker performance of both designs in this metric, even though ranking best in the others. In order to have a perspective of the improvements these two selected layouts mean facing the original scenario, Table 5.6 presents the fraction of time metrics obtained with those, compared to the later. Moreover, a histogram was built for each set of results, with identical axis and scales, to allow a visual comparison. Table 5.6 - MCLP and p-median5 results compared with current design's (model/current) Model avg max 0.25 0.50 0.75 0.90 0.95 0.99 MCLP 56.60 % 85.22% 74.61% 59.06% 50.44% 45.56% 54.62% 71.74% p-median5 52.62% 106.24% 72.58% 55.20% 40.28% 46.61% 53.97% 63.64% Figure 5.10 - Distribution of RT with current design (minutes) Optimizing the Network of the Emergency Medical Service in Hanoi 36 Figure 5.11 - Distribution of RT with p-median5 design (minutes) Figure 5.12 - Distribution of RT with MCLP design (minutes) From the analysis of the histograms presented, it’s possible to notice their resemblance with a Poisson distribution. It makes sense considering that the events (emergency calls) appear independently in space and occur at a given average rate, while the ambulances attempt to uniformly cover that area. The flat section of the MCLP distribution between the 10 and 19 minutes explains why this layout underperformed in covering 75% of the population. Up to this point, the p-median5 and the MCLP designs were outpointed as the strongest ones, thus, further improvements were based on them, by analysing more simulation data. Optimizing the Network of the Emergency Medical Service in Hanoi 43 Due to the iterative process utilized, and the sources of stochasticity and error, this solution isn’t known to be the optimal. It is, however, a feasible one which proved significantly better than the starting point scenario. As an experiment to witness the value added by the acquisition of new vehicles, it was tested the introduction of up to 5 ambulances. These were intended to tackle demand in rural areas, where help is usually further away than in cities, and proved their worth by shrinking the times distribution. Meaning that they reduced the higher RTs and provided that a greater portion of the population is within a shorter reach of emergency teams. Figure 5.15 - P-median5 design with the added 5 stations (in orange) Optimizing the Network of the Emergency Medical Service in Hanoi 44 6 Conclusions and recommendations The objective of finding a better allocation for the 23 ambulances in the province of Hanoi in order to improve the service level of the EMS organization was reached. The advantages of expanding the network, in the sense of increasing the number of deployment stations, were proven, and in a short-term and low-capital manner. It was demonstrated that, by adopting a design as the p-median5, rather than being restricted to the five EMS stations, the average time that the population would wait for an emergency response is 10 minutes instead of 20, and 90% of the people would be served in under 20 minutes, rather than 43, which is less than half. As to the acquisition of new fleet, the added ambulances in more remote locations proved valuable in providing quicker rescues to the whole population. As in the case of adding five vehicles, 90% of the population became covered in less than 16 minutes, an improvement of 20%. These scenarios were also exposed to an increase of 100% in demand, in the computer simulation, and proved robust still, though more studies must be conducted if a higher rate of calls is to be expected in the future. It is urged that the EMS of Hanoi starts storing and analysing demand data, in order to model it and forecast future trends. This was a missing piece of this research and the more accurate the input data, the most valuable and applicable the outcome is. Thus it is of utmost importance that the organization in study improves their understanding about the population needs and builds a better service from there. The cooperation with other existing facilities is highlighted as a very important and inexpensive step towards improving the current network. 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Optimizing the Network of the Emergency Medical Service in Hanoi 48 Appendix A: Network nodes Table 6.1 - Possible deployment stations and their coordinates Code Station / facility name Coordinates 1 Trung Tâm Cấp cứu 115 21.0222965, 105.8567074 2 Bệnh viện Thanh Trì 20.9486239, 105.8464602 3 Trung tâm Y tế Quận Long Biên 21.06865, 105.9104165 4 Trung Tâm Y Tế Hà Đông 20.9679609, 105.779196599999 5 Bệnh viện Đa khoa Y học cổ truyền 21.0342569, 105.779242999999 6 Bệnh viện đa khoa huyện Mỹ Đức 20.678369, 105.7547394 7 Bệnh viện Vân Đình 20.7253476, 105.7739645 8 Bệnh viện huyện Phú Xuyên 20.730711, 105.9147299 9 Bệnh viện huyện Thanh Oai 20.8621361999999, 105.757306999999 10 Bệnh viện Đa khoa Thường Tín 20.8680150999999, 105.8589256 11 Bệnh viện Da Khoa Nông Nghiệp 20.9211639, 105.8534329 12 Bệnh Viện Đa Khoa Huyện Quốc Oai 20.9910523, 105.6441396 13 bệnh viện đa khoa ba vì 21.2154603, 105.409355199999 14 Bệnh viện Sơn Tây 21.1527429, 105.5055714 15 Phuc Tho District Hospital 21.1036791, 105.5570161 16 Bệnh viện đa khoa Thạch Thất 21.0509625, 105.5701972 17 Bệnh viện Đa khoa Đan Phượng 21.0871188, 105.6709467 18 Bệnh viện huyện Hoài Đức 21.0564757, 105.701929 19 Bệnh viện Đa khoa Sóc Sơn 21.2499075, 105.847194199999 20 Bệnh viện Đa Khoa khu vực Mê Linh 21.1996982, 105.706879299999 21 Bệnh viện Đông Anh 21.1392295, 105.8530659 22 Bệnh viện Đa khoa Đức Giang 21.0611986, 105.8983943 23 Bệnh viện Đa khoa Gia Lâm 21.0095778, 105.9441008 24 Bệnh viện đa khoa Medlatec 21.0485391, 105.8461052 25 BỆNH VIỆN ĐA KHOA HỒNG NGỌC 21.0424817, 105.8441528 26 Saint Paul Municipal Hospital 21.0311944, 105.8350844 27 Bệnh viện Phụ sản Hà Nội 21.026959, 105.8071981 28 Bệnh viện Đa khoa Quốc tế Thu Cúc 21.0450336, 105.814457299999 29 Bệnh viện Thanh Nhàn 21.0036379, 105.8591429 30 Vinmec International Hospital 20.9961247, 105.8668284 31 National Hospital of Traditional Medicine 21.015892, 105.848636599999 32 Vietnam Cuba Hospital 21.0246076, 105.8507093 33 Bệnh viện huyện Chương Mỹ 20.9209337, 105.6982622 34 Bệnh viện Đống Đa 21.0156617, 105.827011599999 35 Bach Mai Hospital 20.999138, 105.841168899999 36 Family Medical Practice Hanoi 21.031104, 105.818295 37 International SOS Medical and Dental Clinic 21.0637718, 105.8273497 38 Military Hospital 108 21.0186139, 105.859758899999 39 E Hospital 21.0504128, 105.7892809 Optimizing the Network of the Emergency Medical Service in Hanoi 49 Table 6.2 - Number of nodes used per district and their demand District Area (km2) Population Density (pop/ km2) Nodes Demand/node Hoàn Kiếm 5.29 147334 27851 1 147334 Thanh Xuân 9.11 223694 24555 1 223694 Ba Đình 9.22 225910 24502 1 225910 Hai Bà Trưng 9.60 370726 38617 1 370726 Đống Đa 9.96 410117 41176 1 410117 Cầu Giấy 12.04 260643 21648 1 260643 Tây Hồ 24.00 130639 5443 1 130639 Nam Từ Liêm 32.27 232894 7217 2 116447 Hoàng Mai 41.04 380509 9272 2 190255 Bắc Từ Liêm 43.35 320414 7391 2 160207 Hà Đông 47.91 260136 5430 2 130068 Long Biên 60.38 271913 4503 3 90638 Thanh Trì 68.22 198706 2913 3 66235 Đan Phượng 76.80 142480 1855 4 35620 Hoài Đức 95.30 191106 2005 4 47777 Phúc Thọ 113.20 159484 1409 5 31897 Sơn Tây 113.47 125749 1108 5 25150 Gia Lâm 114.00 251735 2208 5 50347 Thường Tín 127.70 219248 1717 6 36541 Thanh Oai 129.60 167250 1291 6 27875 Mê Linh 141.26 191490 1356 6 31915 Quốc Oai 147.00 160190 1090 6 26698 Phú Xuyên 171.10 181388 1060 7 25913 Đông Anh 182.30 333337 1829 8 41667 Ứng Hòa 183.72 182008 991 8 22751 Thạch Thất 202.50 177545 877 9 19727 Mỹ Đức 230.00 169999 739 10 17000 Chương Mỹ 232.90 286359 1230 10 28636 Sóc Sơn 306.74 282536 921 13 21734 Ba Vì 428.00 246120 575 18 13673 Optimizing the Network of the Emergency Medical Service in Hanoi 50 Appendix B: Python script The following script, written in Python, was used to create the duration matrix with the Google API Distance Matrix. The coordinates of both origins and destinations were imported from two separate text files. import googlemaps with open('C:/Users/Rui/Desktop/origins.txt') as f: lista_origens = f.read().splitlines() with open('C:/Users/Rui/Desktop/destinations.txt') as f: lista_destinos = f.read().splitlines() gmaps = googlemaps.Client(key='AIzaSyBqOeR_O-thK65ATyli9fd_OCaGGm-GmzE') vector = [] for i in range(0, 151): vector = [] for origem in lista_origens: vector.append(gmaps.distance_matrix(origem,lista_destinos[i])['rows'][0]['elements'][ 0]['duration']['value']) print(vector) Optimizing the Network of the Emergency Medical Service in Hanoi 51 Appendix C: Mathematical modelling results Table 1 - Ambulance allocation results for each model station code pmedian pmedian5 p-centre pcentre5 MCLP MCLP5 DSM DSM5 1 0 1 0 1 0 1 0 1 2 1 1 0 1 0 1 0 1 3 0 1 0 1 1 1 1 1 4 1 1 0 1 1 1 1 1 5 1 1 0 1 1 1 2 1 6 0 0 0 1 0 0 0 0 7 1 1 0 0 1 1 1 1 8 1 1 0 0 1 1 1 1 9 1 1 1 0 1 1 1 1 10 1 1 0 0 1 1 1 1 11 0 0 1 1 1 0 1 0 12 1 1 1 1 1 1 1 1 13 1 1 0 1 1 1 1 1 14 0 0 0 0 0 0 0 0 15 1 1 1 0 1 1 1 1 16 0 0 1 0 1 1 0 0 17 1 1 1 0 1 1 1 1 18 1 1 0 0 1 1 1 1 19 1 1 0 1 1 1 1 1 20 1 1 0 0 1 1 1 1 21 1 1 0 1 1 1 1 1 22 1 0 0 1 0 0 0 0 23 1 1 1 1 1 1 1 1 24 0 0 1 1 0 0 0 0 25 0 0 1 1 0 0 0 0 26 0 0 1 1 0 0 0 0 27 0 0 1 1 0 0 0 0 28 0 0 1 0 1 1 1 1 29 1 1 1 1 1 1 1 1 30 0 0 1 1 0 0 0 0 31 0 0 1 1 0 0 1 0 32 1 0 1 1 0 0 0 0 33 1 1 1 0 1 1 1 1 34 1 1 1 1 0 0 0 0 35 1 1 1 0 0 0 0 1 36 1 1 1 0 0 0 0 0 37 0 0 1 0 0 0 0 0 38 0 0 1 0 1 0 0 0 39 0 0 1 1 1 1 1 1 Optimizing the Network of the Emergency Medical Service in Hanoi 52 Table 2 - Objective function result for each model p-median p-median5 p-centre p-centre5 MCLP MCLP5 DSM DSM5 11.5* 11.5* 61.5 61.5 5224357 5224357 2372515 2242002 *The values presented for the p-median problems are the objective function (sum of all distances) divided by the demand in order to show the average distance. The units of time are minutes while the covering models’ functions represent population.