International Journal of Health System and Disaster Management

: 2013  |  Volume : 1  |  Issue : 2  |  Page : 85--91

Urban trauma centers locating using coverage supply-demand model

Nasser Pourmoallem1, Seyed Ehsan Jafari Nasab1, Amir Reza Barshan2,  
1 Department of Transportation and Traffic Engineering, University of Isfahan, Iran
2 Department of Civil Engineering, Imam Khomeini International University, Qazvin, Iran

Correspondence Address:
Seyed Ehsan Jafari Nasab
Faculty of Transportation, University of Isfahan


Introduction: Nowadays the factors of the considerable number of the human death are traffic accident, wars, and work incidents. The researches show that most of these deaths happen among the youth in their most productive period of life and result in many disability adjusted life years. Methodology: One of the ways of reducing these injuries is producing a medical system which increases the probability of the saving of severely injured persons. According to available scientific clues, trauma system can be a good solution to control the injuries. This system is an organized and coordinated effort which provides the injured persons with complete medical care in a given geographical region. It is also integrated with local medical systems. This system can decrease the measure of preventable deaths to 50% and the measure of all incidental death to 15-20%. One of the important matters in providing medical emergency services is the location of these facilities in cities so that more people can access them in standard time. Trauma center is an equipped hospital which is known as the heart of trauma system. The aim of this research is the selection of optimum location of some trauma centers with different levels as emergency medical services (EMS) facilities, out of some candidate location in Kerman city. In this paper, maximal covering location problem (MCLP) model from the available EMS location models, was used. Findings and Conclusion: The results of using trauma system and trauma center locating in Kerman city was not comparable with the present situation in which there is just one emergency services center in a hospital with low equipment and limited coverage. If a level-I trauma center is established in Kerman, 87% of demands of EMS will be covered, and if two level-II trauma centers are established, 98% of EMS will be covered. While the present coverage of demands by Kerman EMS center is less than 30%.

How to cite this article:
Pourmoallem N, Nasab SJ, Barshan AR. Urban trauma centers locating using coverage supply-demand model.Int J Health Syst Disaster Manage 2013;1:85-91

How to cite this URL:
Pourmoallem N, Nasab SJ, Barshan AR. Urban trauma centers locating using coverage supply-demand model. Int J Health Syst Disaster Manage [serial online] 2013 [cited 2022 May 20 ];1:85-91
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Nowadays the consequences, financial problems, and health injuries caused by accidents, have a great effect on people's lifestyles and health. The fast social and economic improvement, enjoying technology and new facilities without considering the social and cultural foundations and fast changes in lifestyles without considering necessary needs to accept these changes, lead to increase in intentional and unintentional deaths and its psychosocial consequences and made it a global risk. [1] In medicine trauma is known as "injury", a physiological wound caused by an external source. The injuries are the consequences of a severe type of force applied to the body, which is higher than physiological tolerance of the body like accidents, falls, battery, and blunt trauma caused by building destroyed, etc., Recently, trauma is the main reason of death in the people aged 1-40 years in the developing countries. It is also one of the major causes of death in developed countries. As the deaths cause by injuries mostly happen among the youth, disability adjusted life years is more than other major factors of death. Road accidents are considered as one the major causes of trauma. They include 50% of trauma and are the second cause of death and the first cause of lost years of life. [2]

According to evidence, trauma system can be an appropriate solution for controlling the load of accidents in the country. Trauma system is an organized and coordinated effort in a geographical region in order to provide the injured with entire medical care. This system is coordinated with local healthcare system. Trauma system can decrease the number of predictable death up to 50%. It also can reduce the number of deaths caused by accidents up to 15-20%. This system is missioned to be the leader in providing optimal and affordable programs in preventing injuries. [3],[4],[5]

One of the most important factors in medical emergency services is locating the place of facilities and reducing the time of the trip to location of accident and transferring to an equipped clinic or hospital. One of the important factors in reducing the time is the location of ambulance transferring stations, and emergency treatment/health unitsin the city and the region which is under the control of such units. [6] The aim of the present study was to choose the optimal location of some trauma center with different levels of quality among candidate enters as facilitators of medical emergency services through coverage supply-demand models.

Literature review

According to previous researches the proposed models were divided in two main categories: The first ones were those which focused on covering demand areas at the time of standard and specified response. These models are called covering-based models. The second ones are the ones with the aim of minimizing the reaction time in the whole system which are called P-median models.

P-median problem was introduced by Hakimi in 1964. [7] After that many researchers tried to evaluate and develop different aspects of this model in order to set the location of different types of hospital facilities. [8],[9],[10],[11],[12],[13],[14],[15] Solving P-median problem, they concluded that the time of responding to some of the areas are unacceptably long. In order to solve this problem, covering-based models were proposed. By coverage we mean the presence of at least one of the facilities in the standard time or distance. [16]

The formulation of the primary and basic coverage-based models was proposed by Toregas et al., in 1971 through forming location set covering model (LSCM). This model was proposed as a result of minimizing the number of needed emergency vehicles in order to cover all of the demand areas. [17] Church and ReVelle 1974 developed LSCM model in the condition that the number of available facilities was less than the demanded facilities to cover all of the areas. This model was proposed as a result of covering the maximum population who demanded relieving services at a standard time or distance. It was called as maximal covering location problem (MCLP). It worked well in the areas which were not covered. [18] The coverage-based models of MLCP and LSCM were attended by other researchers in location setting and developed by them. [19],[20],[21],[22],[23],[24],[25]


The way of providing emergency services and their location setting depends on the amount of demand in that certain city and the amount of time needed to reach the trauma center. As a result gathering information is the first and the most important part of the research because entering wrong or incomplete information will lead to unrealistic results. In order to use the demand information, establishing street network in the city and gathering traffic information like the time of trip between two places were necessary. After that the demand centers were located and zoned. In order to establish a trauma center the suitable places should be specified and evaluated. Then the matrix covering areas were established vs the candidate areas of trauma center considering the standard time of help from the demand area to trauma center. In the next stage the necessity of trauma center zoning in different levels was inspected and the amount of demand and the number of needed centers were specified at each level. The optimal place was chosen according to selection and solution of a model aimed at providing maximum coverage for each level of trauma center.

Data collection and statistics

The first set of data for setting the location of trauma center was the map of the city network and traffic information like the time of trip in the network. The data was gathered through the Reorganization Plan of City Transport Traffic in Kerman and using the EMME/software. After that the demand of trauma center on the city networks was specified. In order to specify the demands we used the data gathered on traumatic events in the emergency centers of the city and the recorded accidents in Traffic Police Department.

The variables containing recorded data included the date and the time of the accident and its notification to the center, the vehicles involved in the accident, the kind of accidents based on the wrecks, being injured or dead, the number of injured or dead people, the reason of the accident according to the experts, the kind of injury, the place of hospitalization, the phone number of the caller, the time of sending the injured to the hospital, and the time of ambulance return to the center, the injured condition and the last but not the least, the location where the accident happened. Among the collected data the date, the place of accident, and the number of injured and dead people were used. [Figure 1] shows the overall structure of the study.{Figure 1}

Choosing a location set model

As the trauma centers are static and immobilized, using the static models are suitable. Among these models we chose MCLP model. In objective function of d i model, the demand of i and y i zone is a binary variable in a way that if zone i is covered by at least one of the facilities it would be equal to 1 otherwise it would be 0. If facilities are covered in zone j, the amount of x j would be equal to 1 otherwise it would be 0. The formulation of the model is as follows:


Demand covering matrix

In order to calculate the demand covering matrix (demand zones vs candidate zones), we used the trip time indicator; the time of the trip from demand zones to each of the candidate zones. The shortest amount of time was calculated through EMME/2 model.

Solving the model and choosing the best alternative

In order to solve MCLP linear programming model, WinQSB software was used. This software is one of the simplest and most complete series of softwares in which you can find many softwares from quality control to project control and linear programming. [Figure 2] and [Figure 3] show the problem solving process in WinQSB software.{Figure 2}{Figure 3}


In this part we tried to solve the main problem. Kerman city was chosen for the research and location setting of trauma center. The condition of relieving was assessed first and the gathered data was analyzed. Then location setting was performed for Kerman.

The condition of emergency services in kerman

Kerman has 11 hospitals and teaching centers. The emergency center of only one of these hospitals admits trauma patients injured in and out of the city accidents. [Figure 4] shows the location of hospitals in Kerman. The Disaster and Emergency Medical Center has six stations to send the ambulances all over the city. [Figure 5] displays the stations.{Figure 4}{Figure 5}

Preparing the map of the city road network

The first job to do was preparing the map of the road network of the city. The map was designed by AutoCAD software according to the studies done on reorganizing traffic in Kerman. This network included 492 nodes and 762 arcs (one-sided and two-sided). [Figure 6] shows the roads in Kerman.{Figure 6}

Zoning the demand areas

During the next phase, the trauma patients' demand zones (the place of traumatic accidents) were inserted into the map of the city street network at different levels according to the time of accident (different months of the year), the kind of the accident (intentional or unintentional), the data of the uncovered accidents. One hundred and four intracity zones and six suburban areas with high emergency demands were considered totally. [Figure 7] shows the administration of the demand zones in the network and the way of zoning.{Figure 7}

Choosing the candidate zones

The aim of this research was to set locations for some level-I and level-II trauma centers in each of the candidate hospitals in Kerman. Therefore, each of the 11 hospitals was considered as a potential candidate to be changed into a trauma center.

Forming coverage: Based matrix vs. candidate zones

After zoning the demand zones and specifying candidate places in the network through the map of Kerman road network, the coverage-based matrix was designed. The criterion for the zones to be covered was the time of trip to the considered trauma center. The standard time from the time of accident announcement till the time of reaching the trauma centers is 30 min for big cities (over one million population) and 60 min for suburbs in America. Considering that the population of Kerman is 600,000 people and the standard time of responding in emergency cases is 8 min in Iran, 10 min is needed to take the patient from the place of accident to the trauma center.

Each candidate zone is specified to the nearest node in order to appoint the amount of covering in each area through the candidate zones. The central node in each of these zones is considered as the representative of that zone. Since the shortest time of the trip between two nodes was calculated before, the trip time could be computed from any demand zone to any candidate zone. A part of the covering matrix of 104 intracity demand zones is shown in [Table 1].{Table 1}

Identifying number and level of trauma systems

In trauma system, the trauma centers are classified to four levels based on the number of trauma patients ad missioned in a year and the quality of services provided.

Appointing the amount of demand for each level of trauma center

The demand for the level-I trauma center is considered for acute injuries. All of the demands for the intercity accidents are considered as the demands for level-I trauma centers because of the possible serious injuries. In addition half of the intercity accidents are also considered as the demands for level-I trauma centers because of the significant presence of motorcycles and pedestrians in such accidents. Moreover, the head injuries and falls can cause serious problems to the brain and body. In general 10% of traumatic injuries are added and the remaining 90% as well as intracity accidents are considered as demands for level-II trauma centers.

Administration of the model and the results

Regarding the population of Kerman and its need to trauma center, among 11 hospitals in the city one was chosen for level-I and two were chosen for level-II trauma centers. In order to do this job the city network was divided into 110 zones (104 intercity zones and six suburban zones) with demands for any level of trauma center. The shortest trip time from any zone to any of 11 candidate hospitals was computed and the matrix of covering demand areas was at hand. Using MCLP, the optimal place was chosen. The problem of location setting for level-I trauma centers with the capacity of covering suburban areas included an objective function of 110 variables and 110 constraints and the problem of level-II trauma centers included an objective function of 104 variables and 104 constraints.

For solving the problem the objective function of any of the candidate zones was computed by WinQSB software. The candidate zone with the highest objective function would be the optimal zone. The results are shown in [Table 2] and [Table 3]. As it is shown, hospital number 6 with the highest covering for demands was chosen as level-I trauma center. According to the results presented in [Table 3], candidate zones 2 and 3 are optimal to be a trauma center. As a result hospitals 2 and 9 with 98% of covering demands are the best places to become level-II trauma centers. [Figure 8] and [Figure 9] display the locations of level-I and level-II trauma centers.{Figure 8}{Figure 9}{Table 2}{Table 3}

 Results and Discussions

Benefitting a comprehensive management system as a macro strategy at the time of disasters like earthquake, flood, famine, etc., will improve the functions of any responsible organization. One of the main goals of such organizations is to attend and reduce the injuries and trauma system is an optimal way to reach this goal. The results show that trauma system and the location setting in Kerman is not proportional with the needs for covering demands.

Using the location set model with the aim of maximizing the covering in Kerman and establishing a level-I trauma center in Arjomand hospital, will cover 1,214 demands out of 1,400 ones. This will cover 87% of level-I demands. Establishing two other level-II trauma centers in Raziye Firooz and Shafa hospitals will cover 98% of demands at the level of medical emergencies, while the entire coverage of demands by the center of disaster and emergency medical services is fewer than 30%.


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