Evaluating the efficiency of relief centers in disaster and epidemic conditions using multi-criteria decision-making methods and GIS: A case study

Abstract

Disaster response refers to any action taken and performed by disaster team managers after and during a disaster. According to the prevalence of the coronavirus and the unpredictability of the behavior of this virus, the capacities of hospitals and medical centers have been overshadowed by this epidemic. Governments have set up temporary rehabilitation centers to control the epidemic, make better use of resources, and quarantine COVID-19 patients. The Tehran (Iran) Disaster Management Organization has designated centers to house the injured and displaced during natural disasters such as floods and earthquakes. In this study, the efficiency and sustainability of the evaluation criteria of selected disaster management centers were evaluated in three scenarios: disaster conditions (natural disasters), epidemic conditions, and disaster-epidemic situations. Firstly, the research criteria were classified by experts using the fuzzy Delphi method and weighted using the triangular fuzzy aggregation method. In addition, the criteria are evaluated as information layers in the Geographic Information System (GIS) and the relief locations determined by the disaster management are evaluated against the research criteria. By forming a decision matrix, the alternatives in all three scenarios were prioritized using the PROMETHEE Method and evaluated in terms of efficiency. As a results, the main ways criterion shown with an impact factor of 13% among the evaluation criteria of centers in disaster situations. Additionally, the security criterion with an impact factor of 22% among the evaluation criteria of centers in epidemic conditions achieved the most important criteria in the PROMETHEE ranking.

1. Introduction

Disaster management is a process that can prevent a disaster or, if it does occur, try to reduce the damage, create the necessary preparedness, deal with it, provide immediate relief, and improve the situation until normalcy and reconstruction are achieved. Nowadays, Pre-disaster planning is one of the most important issues for managers and planners, especially in the field of disaster management.

Generally, after an earthquake or when the danger of an earthquake is felt, in order to create a safe environment for residents and citizens and get them out of dangerous conditions and avoid the dangers of aftershocks or secondary hazards such as fire, a safe evacuation operation must be carried out. Safe evacuation can be done spontaneously or at the request of the relevant authorities. In the event that the authorities determine the need for a safe evacuation for the above reasons, they will then issue a safe evacuation order. Safe evacuation centers include all safe evacuation places and spaces where asylum seekers are accommodated for safe evacuation if needed and have the basic facilities to meet the needs and requirements of asylum seekers for 72 h. The Tehran disaster Management Organization, during a study conducted by the Japan International Cooperation Agency (JICA) team on the Tehran earthquake, has identified suitable locations in all 22 districts of Tehran so that people can use these shelters in times of disaster [1].

During the COVID-19 pandemic in China and its spread in the world, which became a global concern, the World Health Organization declared a pandemic [2]. The outbreak of this disease in developing countries has also caused a number of compatriots to be infected with this disease and has drastically increased the number of referrals and hospitalizations in the affected provinces. Hospital capacity is rapidly increasing. Since the behavior of this disease has not been predictable so far, it is difficult to predict the number of patients and people in need of hospitalization in the coming days and months. Rehabilitation centers that are set up temporarily outside of hospitals provide all accommodation and basic nursing services to patients who do not need specialist services in the hospital or whose conditions are such that they do not need hospitalization at all., be able to receive quarantine services, receive primary medical care until recovery, and return to the community without the possibility of transmitting the disease to others. These centers can reduce the burden of hospitalization and facilitate resource management. Therefore, in order to make optimal use of human and financial resources, the relief centers considered by disaster management can also be used to accommodate COVID-19 patients. Regarding that the most critical requirement of an earthquake victims is to have a shelter and supply rescue services to the public as soon as possible, and since it's not possible to provide suitable shelters for the victims immediately after the earthquake, prior to such crises, providing suitable places for the earthquake victims is a must in terms of accessing the urban uses, security, distance from dangerous zones, etc., because the injured person would be on the verge of serious physical injuries without conventional shelter [3]. That's why the role of locating relief centers at the time of crises is critically important for crisis management and reducing the due financial and human losses. On the other hand, with the COVID-19 pandemic outbreak and its worldwide prevalence, the number of the referrals and hospitalizations has significantly increased and concerning the disease's unpredictability, many governments have got into a challenge to manage the capacity of hospitals. The question posed here is whether the study area locations (which often include stadiums, parks, universities, and barren land) introduced as the crisis centers by the Crisis Management Organization are appropriate in terms of accommodating the patients as suitable for care and hospitalization? Can these centers be used to accommodate the COVID-19 sufferers during an epidemic? Do the intended locations have the essential efficiency to be employed at the times of crisis? Regarding the aforementioned cases and assuming that the locations considered by the Crisis Management Organization have the necessary accommodation conditions in emergencies and critical situations, the locations considered by the Crisis Management in three scenarios: crisis time, epidemic and crisis-epidemic conditions are evaluated separately and their effectiveness is measured.

In this study, according to the standard criteria and applying the Geographic Information System (GIS) and Multi-Criteria Decision-Making methods (MCDM), relief centers considered by the Tehran Disaster Management in terms of flexibility and efficiency to accommodate the injured and patients in disaster and epidemic conditions will be assessed.

In recent years, a lot of research has been done on the location of the relief base and evaluating the relief centers in times of disaster [4]. used GIS and a p-median-based modeling framework to locate disaster relief facilities taking into account the age of the sufferers [5]. designed a system theory-based planning framework and GIS in China for urban emergency shelters during natural disasters. The results showed that their framework was a suitable tool for planning urban emergency shelters [6]. used GIS, the TOPSIS method, a simple clustering method, and two meta-heuristic algorithms to locate relief centers [7]. evaluated the relief centers considered by the Urmia City Disease Management. They used the ANP method to weight the criteria and the PROMETHEE method to prioritize the alternatives. Safety criteria, time of use, and coverage level were the most important research criteria [8]. developed models for identifying the optimal distribution of emergency evacuation centers such as schools, colleges, hospitals, and fire stations to improve emergency flood planning in the Sylhet area of northeastern Bangladesh. The results demonstrated that their proposed models can be used to improve distribution planning and the use of these models can help reduce human losses, property losses and improve emergency performance [9]. identified multi-purpose shelters and places in times of disaster using GIS and MCDM methods. They utilized the criteria of experts to determine the weight of the criteria and used the Simple Additive Weighting (SAW) model GIS to integrate the information layers. Ahmadi Choukolaei et al. (2021) evaluated using multi-criteria decision making and GIS methods, the relief centers considered by disaster management, and the favorable areas proposed by the GIS in terms of efficiency and optimality. The results indicated that among their alternatives, only four were optimal and efficient [10]. used a TOPSIS assessment model using GIS to assess the open space of Canadian cities as an emergency shelter in times of disaster [11]. investigated a medical supply chain network during the COVID-19 epidemic considering sustainability. They suggested some meta-heuristic methods to solve their model. Finally, to show the performance and efficiency of their network and model, a real case study in Iran was provided [12]. proposed a bi-level mathematical model for the location, routing, and allocation of medical centers to distribution depots during the COVID-19 epidemic considering game theory. A real case study was suggested to indicate the performance of their model, where the Lagrangian relaxation method was used to solve their problem. [13] evaluated the city of Babol using data and documentary and field information in ArcGIS software environment with the aim of analyzing the risk and vulnerability of urban infrastructure during earthquakes. Their research innovation has been the study of earthquake risks. The results showed that urban facilities respond to critical situations. Also, some areas of Babol with high earthquake risk were identified and solutions for crisis management were provided in these areas.

[14] evaluated the city of Sisakht in Kohgiluyeh and Boyer-Ahmad Provinces of Iran at the time of the earthquake. The novelty of their research was the use of a descriptive-correlation design to describe the study area at the time of the earthquake without the intervention of variables. The results showed that practical and rapid management, in addition to playing a decisive role in reducing casualties and material damage, can minimize the problems that occur in the medium and long term after the earthquake. [15] evaluated seven neighborhoods in Istanbul using 15 criteria in order to determine areas of safe accumulation after the earthquake. Their research novelty was a multi-criteria decision-making approach, GIS and a hierarchical analytical process. The results of the study show that not every open area is safe to be a gathering place after the earthquake. Dervishi et al. (2022) evaluated the relief centers of Tehran 18th district, which were mostly parks and stadiums, using GIS and PROMETHEE method. It was used for housing in times of crisis. They used Shannon's entropy method to weight the criteria and PROMETHEE method to prioritize options. The use of PROMETHEE 5 and the application of constraints to determine optimal locations were among their research innovations. The results showed that more than half of the considered locations were not optimal and did not perform well. [16] assessed the city of Mashhad with the aim of locating rescue centers based on efficient quality. They selected and prioritized the best location for rescue centers in the area, taking into account the criteria of distance from residential uses, medical centers, fire stations, proper access to roads and distance from dangerous urban facilities. Their research was using hierarchical analysis method and GIS software. [17] presented a simulation-optimization model for estimating the number of relief commodities and locating distribution centers in crisis situations. The location of distribution centers in pre-crisis conditions is done by GIS. Minimizing pre-crisis costs and maximizing post-crisis coverage levels are among the research objectives. Attention to cascade disasters such as floods, earthquakes, and nuclear crises is among their novelties.

Considering the importance of discussing the location of relief centers in times of crisis and considering the spread of Corona and the importance of discussing crisis management, by evaluating more than 1500 articles in the field of location and COVID-19, the gaps in past papers have been examined and the research objectives in were considered to cover this gap. This evaluation was done by VOSviewer analytical software. VOSviewer can be used to create networks of scientific publications, scientific journals, researchers, research organizations, countries, keywords or terms. Fig. 1, Fig. 2 respectively show the results of research conducted in the field of location and COVID-19. Each circle represents the most frequent fields in recent years, and the size of these circles is directly related to the amount of research conducted in that field. In grid visualization, items are shown with their label and by default with a circle. Circles with larger sizes indicate a high number of researches conducted in that research field. Differentiated clusters with different colors indicate their close relationship to each other, which are connected to each other through lines. These lines show the number of connections of each research field with other fields. As can be seen in Fig. 1, Fig. 2, the lack of attention to important issues such as efficiency and sustainability in the location of aid centers is one of the things that have not been paid attention to in recent research. Also, by examining the recent research conducted in the field of COVID-19, it can be pointed out that there has been no attention to the issue of location, especially the location of aid centers since the outbreak of the epidemic.

Fig. 1.

The results of research conducted in the field of location.

Fig. 2.

The results of research conducted in the field of the COVID-19.

According to the existing gap, the contribution of the present research is as follows:

• •Lack of consideration for the efficiency of relief centers in times of disaster.
• •Reviewing and ranking relief centers in only one case and not evaluating relief centers considered in different scenarios such as epidemic conditions.
• •Lack of attention to the issue of sustainability in the selection of criteria and the feasibility of these centers in different scenarios.

According to the existing challenges, research contributions are listed as follows:

• •Evaluating the efficiency of relief centers considered in times of disaster and epidemic conditions separately and simultaneously using Data Envelopment Analysis (DEA)
• •Evaluate and prioritize criteria and alternatives in scenarios by GIS and PROMETHEE approaches
• •Considering multi-scenario planning includes: disaster conditions (natural disasters), epidemic conditions, and disaster-epidemic situations
• •Assessing the feasibility and sustainability of the criteria for evaluating relief centers considered by disaster management.

In the rest of the current paper, the methodology and problem statement in Section 2 are explained. In Section 3, the data and results are described. Finally, in Section 4, the conclusion and future works are stated.

2. Methodology and problem description

The methodology of this research includes two parts: the method of collecting and weighing the criteria and prioritizing the alternatives, along with the general process of the research. In this study, the fuzzy Delphi method has been used to find the opinions of experts on the criteria and their classification. Also, the triangular fuzzy method has been used to weigh the research criteria and the PROMETHEE method has been employed to prioritize the alternative. Performing the evaluation process on a limited set of finite alternatives, as a partial or complete ranking, the clear effect of each criterion and its weight on the answers and the high efficiency of the algorithm in this method despite its simplicity and based on the importance of performance differences between two answers (distinguishing it from the hierarchical structure method) are among the advantages of the PROMETHEE method. The triangular fuzzy aggregation has been used to weigh the criteria and the PROMETHEE method has been used to prioritize and evaluate research options. In the PROMETHEE method, the options are ranked by pairwise comparison of the options in each index and the comparison is measured based on a predefined superiority function with a range of [0,1]. PROMETHEE method is one of the MADM methods and as an efficient method seeks to select the best option. In this research, PROMETHEE II has been used for the complete ranking of discrete options. In the final evaluation stage of the research options, Visual PROMETHEE software has been used, in which the input information has been entered quantitatively and qualitatively according to the output of the GIS and the opinions of experts. The weight of the criteria, which is calculated from the triangular fuzzy aggregation method, is also considered as the input of Visual PROMETHEE software.

2.1. Triangular fuzzy aggregation method

Fuzzy numbers are very popular due to their high computational efficiency. In addition, calculations with this type of numbers are very simple and understandable. Fuzzy logic became effective by introducing fuzzy sets and then fuzzy numbers. Meanwhile, the introduction of triangular fuzzy numbers has played an important role in the development of fuzzy calculations. For example [18], proposed the fuzzy hierarchical analysis process with these numbers. One of the reasons for using the triangular fuzzy aggregation method is to use the opinions of relevant experts for proper evaluation to achieve more accurate results. The traditional process of quantifying the individuals' perspectives does not fully reflect the human thinking style. To put it better, using fuzzy sets is more compatible with the linguistic and sometimes ambiguous human explanations. Thus, it's better to deal with long-term forecasting and real-world decision-making utilizing fuzzy sets (with fuzzy numbers). The use of fuzzy sets is more compatible with linguistic and sometimes ambiguous human explanations. Therefore, it is better to use long-term predictions and real-world decisions using fuzzy numbers. Each triangular fuzzy number consists of three parameters F = (l, m, u). The lower limit (l) and the upper limit (u) are the minimum and maximum values that a fuzzy number F can take, respectively. In addition, m is the most probable value of a fuzzy number [19].

$${\mu }_F\left(x\right)=\{\begin{array}{c}\frac{x-l}{m-l}l<x<m\\ \frac{u-x}{u-m}m<x<u\\ 0otherwise\end{array}$$ (1)

In this weighing step, the sum of triangular fuzzy numbers is obtained according to Equation (2).

$$F_1=\left(l_1.m_1.u_1\right)F_1+F_2=\left(l_1+l_2.m_1+m_2.u_1+u_2\right)F_2=\left(l_2.m_2.u_2\right)$$ (2)

After collecting the criteria and evaluating them, the experts evaluated the fuzzy criteria (VH, H, M, L, VL). Then, the weight of the indicators is calculated and normalized.

2.2. PROMETHEE multi-criteria decision-making method

In research that was conducted to select the best statistical distribution using the PROMETHEE and GAIA method, the results showed that the PROMETHEE method is an acceptable method to select the best statistical distribution, and for this reason, it was recommended to use this method [20]. In another study, the implementation of the PROMETHEE method with multi-criteria decision making was discussed. Among the advantages of the PROMETHEE method are comprehensibility, the ability to deal with uncertainty, giving value to decision-makers, the power of visual display of data, reliability and high flexibility, which can be done by using charts such as GAIA chart and Rainbow chart. It will be easier. Also, in higher versions of PROMETHEE (PROMETHEE V), it is possible to apply restrictions to determine optimal options [21,22]. The PROMETHEE method is a superior method for a limited set of alternatives [23]. In this method, each decision criterion is examined based on a separate function and without relation to other criteria. Prioritization of the PROMETHEE method is done during the following steps [24]:

Step 1

Creating the decision matrix;

Step 2

Creating a pairwise weight comparison matrix;

Step 3

Assigning the $P_j$ preference function to each of the criteria j. The value of $P_j$ (a, b) is calculated for each pair of alternatives. This value varies between zero and one. If the relation $F_j$ (a) = $F_j$ (b) is established, the value of $P_j$ (a, b) becomes zero, and with increasing $F_j$ (a) = $F_j$ (b) this value increases;

Step 4

The total priority $\pi$ (a, b) for each alternative “a" is calculated on alternative b. Although π (a, b) is higher, alternative “a” is more preferable. $\Pi$ (a, b) is calculated as follows [25]:

$$\pi \left(a،b\right)=\sum _{j=1}^{{\rm K}}wjpj\left(a،b\right)،\left(\sum _{j=1}^{{\rm K}}wj=1\right)$$ (3)

where $\pi$ (a, b) indicates the degree of priority of alternatives “a” over alternatives “b”.

Step 5

Calculating the positive rating flow or output flow, that demonstrates in Equation (4).

$${\varnothing }^{+}\left(a\right)=\frac{1}{n-1}\sum _{x\epsilon A}\pi \left(x.a\right)$$ (4)

In Equation (4), the flow shows the priority of alternative $″a″$ over other alternatives. A larger ${\varnothing }^{+}\left(a\right)$ means the best alternative.

Step 6

Calculating the negative rating flow or input flow, that shows in Equation (5).

$${\varnothing }^{-}\left(a\right)=\frac{1}{n-1}\sum _{x\epsilon A}\pi \left(x.a\right)$$ (5)

where ${\varnothing }^{-}\left(a\right)$ is a negative rating flow or input flow, which is called the preference of other alternatives over alternative “$a^{″}$. The lower the negative flow, the better the alternative.

$$\varnothing \left(a\right)={\varnothing }^{+}\left(a\right)-{\varnothing }^{-}\left(a\right)$$ (6)

Step 7

Calculate the net flow for complete ranking. For complete ranking of alternatives, you should define the net ranking flow for each alternative (See Equation (6)) [22]. This flow is the result of a balance of positive and negative ranking flows, and the higher the net flow, the better that alternative [26,27].

Among the merits of PROMETHEE method are comprehensibility, ability to cope with uncertainty, appreciate decision makers, able to visually display the power of data, and high reliability and flexibility. Also, in higher versions of PROMETHEE (PROMETHEE 5), it is possible to apply constraints to determine the optimal alternatives.

2.3. Fuzzy Delphi method

Fuzzy Delphi method collects ideas through several stages by creating coordination between the views, attitudes and judgments of people and expert groups without the need to be present at a specific place and only by using a questionnaire. Delphi is mentioned as a combined method, that is, a combination of qualitative and quantitative methods [28]. Delphi provides a platform for discussion and sharing of opinions among the members of the expert group and gives them the opportunity to modify their views [29]. The Delphi method is based on the logical assumption that several thoughts are better than one thought [30]. In the Fuzzy Delphi Method (FDM), the members of the participating group require to be equipped with 4 properties: knowledge and experience in the question problem, willingness to cooperate, sufficient time for participating in the process, and communication skills [31]. In order for the Delphi method to be successful in achieving the objectives and the credibility of the participants’ cooperation, the group members should be selected out of the relevant field experts. As stated by Ref. [32]; Delphi participants being experts reflect their knowledge and perception while being impartial in their findings [32]. Regarding the number of experts, there are various opinions; for instance Ref. [33], reported the number of experts ranging from 10 to 1685 [33]. The number of participants would vary according to the scope of the problem and sources at hand. The sources such as time and money are so important and influential in selecting the number of participants; however, the magnification of the problem under consideration and approving the solutions proposed by the expert group depend on the interpretation of the researcher and the commentator [34]. believed that being a representative of society is stated based on the quality of the expert group, not on their number. The statistical community and sample of the present study include the experts of the Crisis Management Organization, the senior managers, and university faculty members and the data have been collected through interviews and questionnaires. The fuzzy Delphi method was proposed by Ref. [35]. The advantages of the fuzzy Delphi method over the Delphi method include reducing the number of polls, using reversible fuzzy in interviews with experts to get logical and appropriate answers, achieving higher economic efficiency in the time and cost required to conduct surveys, simple calculation process, handling multi-level decision problems, and multiple features and multiple solutions [36]. This technique is dealt with in several steps by coordinating the views, attitudes, and judgments of the individuals and expert groups without requiring them to attend a certain place and merely using a questionnaire to collect the opinions. Delphi has been mentioned as an integrated method, i.e., a combination of qualitative and quantitative methods [28]. Delphi provides the ground for discussion and sharing the opinions among the members of the expert group and allows them to refine their views [37]. The Delphi method is based on the logical assumption: Several thoughts are better than one thought [38]. In the FDM, the questionnaire is performed in two or more steps and the results from the previous courses are employed for the new period of developing and modifying the questionnaire.

In this study, the fuzzy Delphi method has been used to find the opinions of experts about the criterion. It is assumed that the evaluation value of criterion $j$ from the expert point of view is number $i$ among $n$ experts ${\mathrm{W}}_{ij}$ =(${\mathrm{a}}_{ij}$, ${\mathrm{b}}_{ij}$, ${\mathrm{c}}_{ij}$) that the value of $j$ is equal to $j=1‚2‚3‚\dots ‚m$ and the value of $i$ is equal to $i=1‚2‚\dots ‚n$. Thus, the fuzzy value of the criterion $j$ is calculated based on Equations (7), (8), (9).

- FDM Steps:

• 1.Identifying research indicators using a comprehensive review of the research theoretical foundations.
• 2.Collecting the decision-making experts' opinions: A decision-making group made up of the research topic experts has been formed and in order to detect the identified indicators being associated with the main research topic and screening, the questionnaires have been sent to them, in which the language variables of Table 1 are utilized to state the importance of each indicator being ranked as Very High (VH), High (H), Medium (M), Low (L) and Very low (VL), respectively.
• 3. Verifying and Screening the Indicators: To extract the final desired indicators, it's necessary to use the threshold limit for the defuzzified numbers. If the defuzzified value of the triangular fuzzy number is 0.7 or more depending on the opinion of the experts and specialists, it will be agreed upon as an acceptable indicator, otherwise, it will be removed from the questionnaire [39]. For this purpose, first off, the triangular fuzzy values of the experts ‘opinions have to be calculated, then to calculate the average of the n respondents' opinions, their fuzzy average is calculated. The fuzzy number is calculated for each of the indicators using the following equations.

$${\mathrm{a}}_j=\min \left\{a_{ij}\right\}$$ (7)

$${\mathrm{b}}_j=\frac{1}{n}\sum _{i=1}^n{b}_{ij}$$ (8)

$${\mathrm{c}}_j=\max \left\{c_{ij}\right\}$$ (9)

Table 1.

Fuzzy linguistic variables for the weight of each criterion.

VH	0.75	1	1
H	0.5	0.75	1
M	0.25	0.5	0.75
L	0	0.25	0.5
VL	0	0	0.25

Then, Equation (10) is used for de-fuzzy.

$${\mathrm{S}}_j=\frac{{\mathrm{a}}_j+{\mathrm{b}}_j+{\mathrm{c}}_j}{3},j=\mathrm{1,2},\dots .,\mathrm{m}$$ (10)

• 4Consensus and Fuzzy Delphi Termination: By consensus, it means that the respondents have reached a general decision about the factors. And the step after which nothing special happens in the criteria.

Fig. 3 depicts a schematic diagram of the Fuzzy Delphi DM's threshold. In this study, 30 experts of the Disaster Management Organization (DMO) have cooperated in the evaluation of criteria. All experts have a master's and doctoral degree, as well as more than ten years of work experience. Table 2 demonstrates the current study statistical community including Delphi members, the work or management experience of the members, the degree of Delphi group members, and their gender.

Fig. 3.

The Fuzzy Delphi (Decision Makers) DM's threshold.

Table 2.

Composition and characteristics of fuzzy Delphi group members.

Fuzzy Delphi Group Members
Characteristics of the statistical community	Senior Managers	Crisis Management Organization Experts	University professors
Number of Delphi members	4	17	9
Work or managerial experience	Between 10 and 20 years of experience	Between 10 and 20 years of experience	More than 10 years of experience
Degree	Ph.D	M.Sc., Ph.D.	Ph.D
Gender	Number of men: 3	Number of men: 12	Number of men: 6
	Number of women: 1	Number of women: 5	Number of women: 3

Table 3 shows the frequency distribution of age of experts. It is clear that 17% of experts are between 25 and 35 years old, 53% are between 36 and 45 years old, 20% are between 46 and 55 years old and 10% are between 56 and 65 years old.

Table 3.

The frequency distribution of age of experts.

Age	Frequency	Percentage
25–35	5	17%
36–45	16	53%
46–55	6	20%
56–65	3	10%

Table 4 indicates the frequency distribution of experts' degrees. As it turns out, 70% of the experts between the Master of Science and 30% of the experts have a Ph.D.

Table 4.

Frequency distribution of experts' degrees.

Age	Frequency	Percentage
Associate Degree	0	0%
Bachelor of Science	0	0%
Master of Science	21	70%
Ph.D.	9	30%

Table 5 reports the frequency distribution of experts' work experience. It is clear that 30 of the experts are between 11 and 15 years old, 40% of them are between 16 and 20 years old, 20% are between 26 and 30 years old and 10% are between 26 and 30 years old.

Table 5.

Distribution of work experience of experts.

Work experience (year)	Frequency	Percentage
11–15	9	30%
16–20	12	40%
21–25	6	20%
26–30	3	10%

Fig. 4 shows the frequency distribution of Delphi members by sex. As it turns out, 30% of the experts are women and 70% are men.

Fig. 4.

Percentage distribution of Delphi members by sex.

2.4. Problem description

The strategic goal of establishing relief bases is to provide a suitable operational and tactical platform for the implementation of prevention, preparedness, and response measures in various disasters, especially large natural disasters such as earthquakes and to make the city disaster management system tactical. Relief centers include all safe places and evacuation areas where asylum seekers can be accommodated if needed and have basic facilities to meet their needs for 72 h. The Tehran Disaster Management Organization has identified suitable locations in all 22 districts of Tehran, including the first District of Tehran so that people can use these shelters in times of disaster. With the spread of the coronavirus in late 2019 in Wuhan, China, there was concern and confusion in the world [40]. Due to the unpredictability of the disease in the community and the number of infected people in the city, as well as the optimal use of resources and manpower to control the epidemic, new capacities are needed to isolate patients and increase the capacity of care centers and Identify treatment. Therefore, this study, uses standard criteria of places considered by disaster management in three scenarios including (1) use of these centers in times of disaster and natural disasters, (2) use of relief places during the COVID-19 epidemic, and (3) the use of relief places during the COVID-19 epidemics and natural disasters will be evaluated for efficiency and usability. In this study, first, the necessary criteria for locating relief centers and using these centers as isolated accommodation centers during the epidemic were identified and selected by the fuzzy Delphi method, and after classification as information layers in ArcGIS have been prepared. The Arc GIS Toolbox tool was used to analyze the collected layers in the ArcGIS software. The triangular fuzzy aggregation method was used to weigh the research criteria and then 10 proposed disaster management centers were employed as relief centers in times of disaster and as isolated shelters during the epidemic according to the research criteria. After forming the matrix using the PROMETHEE Method, the alternatives in each of the three scenarios are prioritized and analyzed. In the current research, the FDM has been used to measure the importance of decision-making indicators and screening the indicators by reaching a consensus. PROMETHEE is one of the MADM methods and an efficient one to select the best option. In this study, the PROMETHEE II version has been used for the complete ranking of the discrete alternatives. Actually, the criteria have been identified and evaluated using the FDM and the research alternatives, i.e., the very relief centers in the region, have been prioritized and evaluated in three scenarios: crisis conditions, epidemic conditions, and crisis-epidemic conditions by the Visual PROMETHEE.

Fig. 5 shows the overview of the research. Considering that evaluating the efficiency of relief centers considered by Tehran crisis management in three scenarios and dealing with the issue of sustainability in the location of relief centers was one of the most important goals of this research, and considering the importance of the issue of location in three scenarios, the conditions natural crisis (earthquake), epidemic conditions and earthquake-epidemic conditions, we tried to use appropriate criteria and methods for evaluations. In this research, using experts' opinions and library studies, the fuzzy Delphi method was used to determine and classify the criteria. Then, these criteria have been valued and weighted to determine their degree of importance using triangular fuzzy aggregation method. By using the geographic information system and forming information layers, the relief locations determined by the crisis management were evaluated. Finally, with the formation of the paired scale matrix, the research options were prioritized by the parametric method, and the effectiveness of the research options was also evaluated using data coverage analysis. In the following, the advantages of the used methods will be explained.

Fig. 5.

The general structure of the current research.

3. Data and results

Fig. 6 and Table 6 demonstrate an overview of the research process and the resources used in each section. In this research, first, using library studies, previous studies of [41] and [9]; etc. and using the output of the studies of the Japan International Cooperation Agency [1] evaluation criteria of crisis centers in crisis and epidemic conditions were collected and important criteria were identified using fuzzy Delphi method and evaluated by university professors, experts and senior managers of the Crisis Management Organization. After weighing the criteria by triangular fuzzy aggregation method, using GIS, the research criteria were evaluated (epidemic conditions criteria and crisis conditions criteria) and this information was used as a pairwise comparison matrix. It has been used as input for Visual PROMETHEE software to prioritize. Another source used in this study was the Tehran Crisis Management site (https://tdmmo.tehran.ir/), which has designated crisis relief centers in each region. Also, the site and announcements of the Ministry of Health and Medical Education (https://behdasht.gov.ir/) of Iran have been used to identify the basic criteria for evaluating relief centers during an epidemic. This information was collected in the first six months of 2021.

Fig. 6.

Overview of the research process and resources used in each section.

Table 6.

General information about the research process and references used.

No	Data	Data collection method	References
1	Evaluation criteria for relief centers	Library studies and previous papers	JICA Ahmadi Choukolaei et al. (2021), Borhani et al. (2021) https://behdasht.gov.ir/ https://tdmmo.tehran.ir/
2	Evaluate and select the collected criteria	Fuzzy Delphi Method	Evaluation by experts (Authors calculations)
3	Information layers and evaluation of options relative to criteria	GIS	ArcGIS software (Authors calculations)
4	Criteria weighting	Triangular fuzzy aggregation	MATLAB software (Authors calculations)
5	Prioritization and evaluation of relief centers	Output of GIS, Criteria weight and Qualitative data obtained from expert evaluations	software Visual PROMETHEE (Authors calculations)

Criteria and alternatives in this study to evaluate the best relief centers in times of disaster and epidemic are considered. The research criteria are based on previous studies and have been collected and evaluated using the fuzzy Delphi method. Hence, the Delphi questionnaire, the pairwise comparison questionnaire was designed and distributed, and also collected among experts. Table 7 reports the evaluation criteria of relief centers at the time of natural disasters.

Table 7.

The considered criteria for evaluating relief centers at the time of natural disasters.

Criteria classification		Criteria	Description	Very good	Good	Average	Bad	Very bad
1	Environmental	Area	Area of relief centers	3000	2000–3000	2000	1000–2000	0–1000
		Wells and aqueducts	Distance to wells and aqueducts	300	200–300	100–200	50–100	0–50
		Rivers	Distance to the river	700	500–700	200–500	100–200	0–100
		Parks and gardens	Distance to parks	0–200	200–400	400–600	600–1000	1000
2	Social	Hospital	Distance to hospitals	0–500	500–1000	1000–1500	1500–2000	2000
		Population	Population density	120	90–120	60–90	30–60	0–30
		Educational centers	Distance from educational centers	0–150	150–300	300–500	500–700	700
3	Economic	Main ways	Distance with main roads	0–100	100–200	200–300	300–400	400
4	Incompatible neighborhood	Gas station	Distance to the gas station	400	200–400	100–200	50–100	0–50
		CNG & fuel station	Distance to the CNG & fuel station	400	200–400	100–200	50–100	0–50
		Electric post	Distance to electric post	100	80–100	60–80	30–60	0–30
		Fault	Distance with fault	400	200–400	200	100–200	0–100
5	Compatible neighborhood	slope percent	Percentage of land slope of relief centers is considered	1–4	4–6	6–10	10–12	+12
		Fire station	Distance from the fire department	0–500	500–1000	1000–1500	1500–2000	2000

These criteria are divided into five sections including environmental, social, economic, incompatible neighborhood, and compatible neighborhood.

• •Environmental criteria are factors that may have a direct impact on the environment in the disaster condition. For example, non-compliance with a proper distance between the ventilation system and the sewers of the relief centers and the aqueducts and rivers may cause their pollution. Also, non-compliance with health issues and lack of waste control will lead to the accumulation of waste in the relief centers (which are mostly parks and stadiums), which will cause damage to the environment and the spread of various diseases.
• •Social criteria include closeness to hospitals, population density, and closeness to educational centers, which are directly related to the social and welfare characteristics of natural disasters for the injured and displaced. Social criteria are often considered in order to comply and pay attention to educational, medical, and welfare issues.
• •Closeness to the main roads is one of the economic criteria considered in this research. It is very important that temporary centers be accessible to operational and relief forces.

The three criteria considered above are criteria related to sustainability.

• •Roads play an essential role in accelerating the relief process, and the closer the relief centers are to the main roads, the better and more appropriate the relief and service operations for the affected and displaced people will be. In addition, the closeness of roads to relief centers will reduce the golden time of relief and reduce fuel consumption, which in turn will reduce the cost of relief.
• •Incompatible neighborhood criteria are criteria that are better the farther away from the relief centers, and on the other hand, closeness and compliance with compatible neighborhood criteria are very important.

The considered score range is very good, good, average, bad, and very bad, which according to the evaluated intervals, the alternatives will be placed in one of the mentioned ranges. Also, the criteria for evaluating the centers during the epidemic are reported in Table 8 .

Table 8.

The considered criteria for evaluating centers during an epidemic.

NO	Criteria classification	Criteria	Description
1	Social	Security	Controllability of the input and output of the place is considered
		Closeness to medical centers	Use of facilities and equipment in urgent conditions
		Proper health facilities	Having a separate health service and proper health facilities
2	Economic	Establishment cost	Cost of equipping and preparing the place for use
		Isolation capability	The intended location should have the necessary structural space and facilities for isolating patients
3	Environmental	Control waste ability	Having the necessary facilities and infrastructure to control hazardous waste to prevent the spread of virus and damage to the environment

The evaluation criteria of relief centers during an epidemic consist of three sections: environmental, economic, and social criteria. These criteria include security, closeness to medical centers, isolation capability, cost of commissioning and preparation for use, having sufficient facilities to control hazardous waste (which causes the spread of viruses and damage to the environment), and having appropriate sanitary facilities.

• •Security, closeness to medical centers, and having proper health facilities are among the criteria related to social issues in an epidemic situation. Due to the epidemic situation, paying attention to the social aspect of the people is vital. Control of the entrance and exit of the centers and the closeness of the medical centers to receive services are among the important issues to control the spread of the disease in the community and relief centers.
• •The established cost and the isolation capability of patients are related to the economic criteria. Although the relief centers in the area have some conditions for the accommodation of patients in epidemic conditions. According to international restrictions and standards, some spaces and facilities should be provided to comply with these requirements as much as possible. The better the conditions for these relief centers in terms of established costs and isolation capability, the lower the cost of using these centers.
• •The criterion of waste control ability is one of the most important criteria in epidemic conditions. Due to the nature of the epidemic and the possibility of transmitting the virus through this waste, their lack of proper control and recycling will cause disaster in the community. Waste types of protective masks, medical equipment, etc. can be among the factors that transmit the virus in relief centers and the community.

It should be noted that the combination of the criteria of the first and second scenarios constitutes the criteria of the third scenario. Hence, there are 20 criteria, of which 14 criteria are for scenario 1 and 6 criteria are for scenario 2 in the third scenario.

3.1. Area of study

District 1 of Tehran Municipality is one of the urban areas of Tehran, which is located at the northeastern tip of this city and is considered the northernmost point of Tehran. The population of this region, according to the 2016 census of Iran, includes 487,508 people (166,881 households). According to a study conducted in the field of earthquake disaster management in Tehran by the Japan International Cooperation Agency (JICA) team, this area is considered a relatively high degree of damage due to the active fault north of Tehran. These evaluations were performed in four models including the North Tehran fault model, the Shahr Rey fault model, the Mosha fault model, and the floating model. The results of the assessments indicate the vulnerability of the urban fabric and buildings in the region in the North Tehran fault model, which is why the Tehran Disaster Management Organization has identified and introduced suitable places in the region to accommodate displaced people and affected people. Natural disasters, including earthquakes, should be used to house displaced persons and provide first aid. Fig. 7 shows Relief sites in the study area and Fig. 8 demonstrates the distribution of structural damage ratios in the North Tehran fault model, which was the result of the JICA team evaluation [1].

Fig. 7.

Relief sites in the study area.

Fig. 8.

Dispersion ratio of construction damage in the study area.

The statistical population of the study includes all places identified by the Crisis Management Organization for use as relief centers in times of crisis and natural disasters such as earthquakes (Fig. 5). These places include sports complexes, parks, barren lands, and universities, which can be identified on the Tehran Crisis Management website (https://tdmmo.tehran.ir/). In this research, a stratified sampling method has been used [42]. According to the number of statistical population and maintaining the dispersion of samples in the study area and refusing to select options with common features, 10 places were selected from the existing statistical population and were evaluate the performance of these centers in times of crisis and epidemic.

3.2. Layer valuation and GIS output evaluation

In today's cities, with the complexities and uncertainties and many factors that affect its development, traditional methods for solving spatial problems such as manual compilation of maps can no longer be the answer. The speed of growth and transformation of cities, as well as the mass of factors influencing spatial issues in the city, has left no other choice but to use a codified framework based on GIS to solve spatial issues in urban planning. The geographic information system is a coherent system of hardware, software, and data that allows the data entered into the computer to be stored, analyzed, transferred, evaluated, and retrieved and disseminated in the form of maps, tables, and models of geographic areas. GIS with its capabilities and capabilities in collecting, analyzing, modeling and displaying geographic data can be a powerful tool in the hands of managers and planners for optimal use of resources [43]. Using GIS, it is possible to perform various types of processing and analysis by saving money and time [44]. GIS is a special form of the information system or database management system (DBMS) that combines geographically referenced data as well as non-location attribute information [45]. In other words, these systems are used to collect and analyze all information that is somehow related to geographical location. [46]. Indeed, the combination of GIS and spatial science is at the forefront of advances in spatial analysis capabilities and offers considerable potential for continuous theoretical and empirical evolution [47]. GIS enables a wide range of techniques to be applied to spatial information. The GIS analysis component includes the application of query, proximity, and centrality functions to one or more spatial spaces. In this research, first, standard criteria for the optimal location of relief bases are defined intermittently and information layers are prepared in ArcGIS. In this research, the Raster Calculator tool has been used to merge layers. In general, a GIS is used to collect, store, and analyze data whose geographic location is a major and important feature. In other words, these systems are used to collect and analyze all information that is somehow related to geographical location [48]. Spatial processing and Geo Processing are some of the important features of ArcGIS. Geographic information systems (GIS) offer many facilities for integrating, storing, editing, analyzing, sharing, and displaying spatial and non-spatial information [49]. The combination of GIS and spatial science is at the forefront of the advances in spatial analysis capabilities and provides an outstanding potential for continuous theoretical and experimental evolution [47]. GIS enables applying a wide range of techniques to spatial information. Considering the mentioned capabilities, it is obvious that GIS can play an important role in supporting us to make decisions in the location science area. Using hundreds of tools in the ArcToolbox section, it can perform many spatial processes such as privacy, layer cutting, location, routing, conversions between different formats, and more. The ultimate goal of a GIS is to support decisions based on geographic data, and its primary function is to obtain information that is obtained by combining different layers of data in different ways and with different perspectives. Various evaluated layers were stored as layers using GIS capabilities. Information layers are obtained from various data, such as land use and surface area, which are the result of the field collection of private companies or government organizations, and road maps, which are obtained from the national layers of the country. In fact, for each of the research criteria for the evaluation of aid centers, an information layer must first be formed. In the second step, the distance or proximity is determined for each element. For example, distance and Euclidean Distance tools are used to determine the degree of proximity or distance to faults. Then, the classify tool was used to obtain the desired sizes. In the third step, layers are overlapped and the distance of each option is determined with respect to the criteria. After preparing all the maps and classifying them, using Map Algebra and Raster Calculator, all the prepared maps are overlapped (by multiplying each map by the weight of that criterion) and after determining the optimal areas, the distance of each of the criteria have been evaluated. In this research, the purpose of using the geographic information system was to evaluate the options compared to the research criteria to form a matrix of pairwise comparisons, and these data were used as input to the Visual PROMETHEE software to evaluate and prioritize the data. Fig. 9 shows an example of these information layers.

Fig. 9.

Map of the information layer related to the distance criterion to the river.

To unify and compare the uses and the amount of impact, the layers are classified as intervals based on the buffer created in ArcGIS software (see Table 9 ). After the formation of information layers, the considered places (alternatives) are evaluated about the generalized indicators of research in Table 6, in which VG, G, A, B, and VB mean very good, good, average, bad, and very bad, respectively. Also, with the help of experts and GIS, these places were evaluated in epidemic conditions according to the criteria introduced in Table 8. The results of this evaluation are shown in Table 9, Table 10 .

Table 9.

Evaluation of area locations in relation to the classified criteria of the research.

Alternatives	Laleh Park	Aboozar Park	Mehregan Park	Darabad Coastal Park	Industry Sports Complex	Niavaran Park	Yas Sport Complex	Qeytarieh Park	Beheshti University	Wasteland
Criteria
Area	VG	VG	VG	VG	VG	VG	VG	VG	G	VG
Main ways	VG	VG	VG	G	G	VG	VG	VG	VG	VG
Gas station	VG	VG	VG	VG	VG	VG	VG	VG	VG	VG
CNG station	VG	VG	VG	VG	VG	VG	VG	VG	VG	VG
percent slope	A	B	A	VG	A	VB	VB	VB	VB	A
wells and aqueducts	G	VG	VG	VG	VG	VG	VG	VG	VG	VG
Hospital	VB	VB	A	G	A	VG	G	B	G	G
Fire station	VB	A	G	G	VG	A	G	VB	VB	VG
Electricity post	VG	VG	VG	B	VG	VG	VG	VG	VG	VG
Population	VB	VB	A	VB	VG	VB	B	A	VG	VG
Fault	VG	VG	VG	VG	VG	VG	VG	VG	VG	B
Rivers	VG	VG	G	B	VG	G	VG	VG	VB	VG
Educational centers	VB	VG	B	G	VB	VB	B	B	VB	VG
parks and gardens	VG	VG	VG	VG	VG	VG	VG	VG	VG	VG

Table 10.

Evaluation of area locations according to epidemic criteria.

Criteria	Security (controllable input and output)	Proximity to medical centers	Isolation capability	Establishment cost	Ability to control waste	Proper health facilities
Alternative
Laleh Park	Bad	Very bad	Average	Good	Average	Average
Aboozar Park	Bad	Very bad	Bad	Bad	Bad	Bad
Mehregan Park	Average	Very bad	Bad	Bad	Average	Bad
Darabad Coastal Park	Average	Average	Bad	Average	Average	Good
Industry Sports Complex	Good	Very bad	Average	Good	Good	Average
Niavaran Park	Good	Very bad	Average	Average	Average	Good
Yas Sport Complex	Very good	Very bad	Good	Good	Good	Good
Qeytarieh Park	Bad	Bad	Average	Average	Good	Good
Beheshti University	Very good	Average	Good	Very good	Very good	Very good
Wasteland	Very bad	Bad	Very bad	Bad	Bad	Very bad

3.3. Weighting criteria in disaster and epidemic conditions

The weight of the research criteria was obtained using the opinion of Decision-Makers (DM) and by the method of triangular fuzzy aggregation. Table 11 illustrates the fuzzy linguistic variables for the weight of each criterion. As VH has the highest score value and VL has the lowest value. For more information on fuzzy numbers and how to use them, refer to Ref. [50]. Table 12 also shows the opinion of experts to determine the weight of the criteria.

Table 11.

Fuzzy linguistic variables for the weight of each criterion.

VH	0.75	1	1
H	0.5	0.75	1
M	0.25	0.5	0.75
L	0	0.25	0.5
VL	0	0	0.25

Table 12.

Matrix of evaluation of research criteria by experts (in crisis scenario).

	Criteria	DM1			DM2			DM3
1	Area	0.25	0.5	0.75	0.5	0.75	1	0.25	0.5	0.75
2	Main ways	0.5	0.75	1	0.75	1	1	0.75	1	1
3	Gas station	0.75	1	1	0.75	1	1	0.75	1	1
4	CNG station	0.75	1	1	0.75	1	1	0.75	1	1
5	percent slope	0.5	0.75	1	0.25	0.5	0.75	0.25	0.5	0.75
6	wells and aqueducts	0.25	0.5	0.75	0.25	0.5	0.75	0.25	0.5	0.75
7	Hospital	0.5	0.75	1	0.75	1	1	0.75	1	1
8	Fire station	0.5	0.75	1	0.5	0.75	1	0.25	0.5	0.75
9	Electricity post	0.75	1	1	0.25	0.5	0.75	0.75	1	1
10	Population	0.5	0.75	1	0.25	0.5	0.75	0.25	0.5	0.75
11	Fault	0.75	1	1	0.75	1	1	0.75	1	1
12	Rivers	0.75	1	1	0.5	0.75	1	0.5	0.75	1
13	Educational centers	0.75	1	1	0	0.25	0.5	0	0.25	0.5
14	parks and gardens	0.25	0.5	0.75	0	0.25	0.5	0.25	0.5	0.75

The opinions of some experts and decision makers (DM1, DM2, & DM3) have been given to weigh the research criteria (under epidemic and crisis circumstances) in Table 11, Table 13 . After being evaluated in MATLAB software, the experts' opinions and extracted information has been coded and the final weight of the criteria has been calculated by the triangular fuzzy aggregation method.

Table 13.

Matrix of evaluation of research criteria by experts (in epidemic scenario).

NO	Criteria	DM1			DM2			DM3
1	Security (controllable input and output)	0.75	1	1	0.75	1	1	0.75	1	1
2	Proximity to medical centers	0.5	0.75	1	0.5	0.75	1	0.25	0.5	0.8
3	Isolation capability	0.75	1	1	0.5	0.75	1	0.5	0.75	1
4	establishment cost	0.25	0.5	0.75	0.25	0.5	0.75	0.25	0.5	0.8
5	Ability to control waste	0.5	0.75	1	0.25	0.5	0.75	0.5	0.75	1
6	Proper health facilities	0.5	0.75	1	0.5	0.75	1	0.5	0.75	1

3.4. The evaluation of the results

After applying the opinions of experts and forming a matrix of pairwise comparisons, the weights of the criteria were obtained by the triangular fuzzy aggregation method. The weights of the criteria in disaster conditions are shown in Table 14 and the weights of the criteria in epidemic conditions are indicated in Table 15 . As can be seen, during the disaster, distance from the fault and distance from the gas pump, and distance from the gas station has been the most important criteria evaluated by experts. Also, in an epidemic situation, the security and isolation capacity of the place is among the important criteria.

Table 14.

Calculated weight of criteria in disaster situations.

No	Criteria	Weight	Final normal weight
1	Area	0.625	0.68
2	Main ways	0.792	0.86
3	Gas station	0.917	1.00
4	CNG station	0.917	1.00
5	percent slope	0.625	0.68
6	wells and aqueducts	0.5	0.55
7	Hospital	0.792	0.86
8	Fire station	0.625	0.68
9	Electricity post	0.6394	0.70
10	Population	0.625	0.68
11	Fault	0.917	1.00
12	Rivers	0.792	0.86
13	Educational centers	0.4729	0.52
14	parks and gardens	0.375	0.41

Table 15.

Calculated weight of criteria in epidemic situations.

	Criteria	Weight	Final normal weight
1	Security	0.92	1.00
2	Proximity to medical centers	0.63	0.68
3	Isolation capability	0.79	0.86
4	Establishment cost	0.50	0.55
5	Ability to control waste	0.63	0.68
6	Proper health facilities	0.75	0.82

After weighting the criteria, according to the pairwise comparison matrix obtained from the evaluation of alternatives and using the perimeter method, alternatives were prioritized. Table 16, Table 17 show the number of positive currents ${\varnothing }^{+}$ and negative ${\varnothing }^{-}$ and the net flow $\varnothing$ obtained in disaster and epidemic conditions and the ranking of these flows. A higher net flow ($\varnothing$) indicates the superior alternative. As can be seen in the disaster conditions, Industry Sports Complex with a net flow of 0.1904, Wasteland with a net flow of 0.0456, and Darabad Park with a net flow of 0.0303 are in the first to third ranks, Beheshti University with a net flow of 0.9385, Yas Sports Complex with a net flow of 0.5226 and Industry Sports Complex with a net flow of 0.1818 are ranked first to third, respectively.

Table 16.

Prioritization of alternatives in disaster situations.

Alternatives	$\varnothing$	${\varnothing }^{+}$	${\varnothing }^{-}$	RANK
Industry Sports Complex	0.1904	0.3105	0.1201	1
Wasteland	0.0456	0.2706	0.2250	2
Darabad Park	0.0303	0.2821	0.2518	3
Beheshti University	0.0261	0.2787	0.2527	4
Yas Sport Complex	0.0195	0.1914	0.1719	5
Mehregan Park	−0.0072	0.2054	0.2126	6
Niavaran Park	−0.0125	0.2397	0.2522	7
Aboozar Park	−0.0802	0.1534	0.2336	8
Laleh Park	−0.0990	0.1546	0.2536	9
Qeytarieh Park	−0.1130	0.1352	0.2482	10

Table 17.

Prioritization of alternatives in epidemic situations.

Alternatives	$\varnothing$	${\varnothing }^{+}$	${\varnothing }^{-}$	RANK
Beheshti University	0.9385	0.9385	0.0000	1
Yas Sport Complex	0.5226	0.6381	0.1155	2
Industry Sports Complex	0.1818	0.4667	0.2849	3
Qeytarieh Park	0.1348	0.4442	0.3094	4
Niavaran Park	0.1058	0.4006	0.2948	5
Darabad Coastal Park	0.0608	0.4214	0.3607	6
Laleh Park	−0.1513	0.2798	0.4311	7
Mehregan Park	−0.4152	0.1704	0.5856	8
Aboozar Park	−0.6185	0.0813	0.6998	9
Wasteland	−0.7594	0.0988	0.8581	10

Fig. 10, Fig. 11 of the GAIA charts show the ranking in disaster and epidemic conditions. In this chart, the alternatives are shown with points and criteria with concentric diagrams, and the longer the axis length, the more important that criterion is. Additionally, the alternatives that have the same function are closer to each other and the alternatives that have the same preferences for the criteria are located in the direction and close to that criterion, and in case of poor performance, they will be in the opposite direction of that criterion. For example, in a disaster situation (Fig. 10) where the alternatives are highlighted in black and the criteria in blue, Beheshti University performed well in terms of CNG station criteria but did not perform well in terms of Fire station criteria. Also, in the epidemic situation (Fig. 11) where the alternatives are indicated in blue and the criteria in red, the alternative of Laleh Park, Aboozar Park, Mehregan Park, and Wasteland performed poorly compared to the considered criteria.

Fig. 10.

GAIA chart in disaster condition.

Fig. 11.

GAIA chart in epidemic condition.

It is clear that Fig. 12, Fig. 13 show the effects of the criteria weight on the ranking of alternatives. At the bottom of these figures is the relative weight (percentage) of the criteria and at the top is the ranking of alternatives according to their net flow. As can be seen in Fig. 12, the highest weight effect in the ranking of alternatives in disaster situations is related to the criterion of proximity to the main roads (13%) and the lowest effect is related to the criterion of proximity to parks with a weight of 4%. Also, in epidemic conditions, Security, Isolation capability, and health facilities criteria with 19%, 22%, and 18% by weight importance, respectively, had the greatest impact on the ranking in epidemic conditions.

Fig. 12.

Impact weight of criteria in ranking alternatives in disaster situations.

Fig. 13.

Impact weight of criteria in ranking alternatives in epidemic situations.

After ranking and analyzing the relief places considered by disaster management in disaster and epidemic conditions, these places have been evaluated in the third scenario, in the combined state of disaster and epidemic conditions. Table 18 shows the information on ranking alternatives in disaster-epidemic situations. The alternatives of Yas Sports Complex with a net flow (0.2457), Industry Sports Complex with a net flow (0.1340), and Beheshti University with a net flow (0.1292) are in the first to third ranks of the evaluation of relief places in disaster-epidemic conditions, respectively.

Table 18.

Prioritization of research alternatives in disaster-epidemic conditions.

Actions	$\varnothing$	${\varnothing }^{+}$	${\varnothing }^{-}$	RANK
Yas Sport Complex	0.2457	0.3639	0.1182	1
Industry Sports Complex	0.134	0.3312	0.1972	2
Beheshti University	0.1292	0.3923	0.2631	3
Qeytarieh Park	0.0355	0.2658	0.2303	4
Darabad Coastal Park	−0.0142	0.2976	0.3119	5
Niavaran Park	−0.0509	0.2515	0.3024	6
Mehregan Park	−0.0585	0.2312	0.2897	7
Wasteland	−0.1216	0.2547	0.3763	8
Laleh Park	−0.1231	0.1887	0.3117	9
Aboozar Park	−0.1761	0.1629	0.3391	10

Fig. 14 shows a PROMETHEE rainbow diagram in a disaster-epidemic situation in which the research alternatives are prioritized from left to right. Each slice from the rectangular surface of each alternative determines the performance of the criteria of that alternative, where the blue sections are related to the disaster situation and the red sections are related to the epidemic situation. Positive criteria are at the top of the rectangular surface and negative criteria are at the bottom. For instance, the Yas Sports Complex alternative, which ranks first and has a positive flow, has performed positively in 17 of the 20 research criteria, Security is the most important of these criteria, and only in the Population, Proximity to medical centers, and percent slope criteria has not been good. On the other hand, the Aboozar Park alternative, which was ranked last, had a poor performance in half of the important research criteria.

Fig. 14.

The rainbow diagram to show the performance of the alternatives in meeting the criteria in a disaster-epidemic.

According to the selected centers disaster management (alternatives) are considered only in disaster situations. In addition, the purpose of this study was to evaluate these places during the epidemic, and the evaluation criteria of these centers in epidemic conditions in terms of sustainability are examined. Fig. 15, Fig. 16, Fig. 17, Fig. 18, Fig. 19, Fig. 20 indicate the sustainability charts of alternatives in the disaster-epidemic condition. In these charts, the horizontal dimension corresponds to the weight of the selected criterion and the vertical dimension corresponds to the net flow score (∅). For each operation, a line is drawn that shows the net flow score as a function of the standard weight. On the right side, the weight of the criterion is equal to 100% and the actions are graded according to that unit criterion. At the left edge, the weight of the criterion is equal to 0%. The position of the green and red vertical bars corresponds to the current standard weight, and the WSI means the same weight sustainability distance. For example, in Fig. 12, which shows the stability chart of the health facilities standard, the weight of the Wasteland and Aboozar Park alternatives decreases as the weight of the health facilities benchmark increases, while the score of the Beheshti University alternative increases. This alternative will have the highest performance by increasing the standard weight of health facilities.

Fig. 15.

Sustainability chart of health facilities criterion.

Fig. 16.

Sustainability chart of control waste criterion.

Fig. 17.

Sustainability chart of establishment cost criteria.

Fig. 18.

Sustainability chart of isolation capability criterion.

Fig. 19.

Sustainability chart of security criterion.

Fig. 20.

Sustainability chart of medical centers criterion.

The presented method has been validated by applying the test on the equality of the means at the confidence interval 95%. The real system data are also acquired from the Ministry of Health of Iran. This data has been tested for an epidemic scenario. It can be stated that with 95% reliability, the presented model can have a proper estimate of the real system. The Mann Whitney nonparametric test has also been utilized to determine whether the two populations (the real relief center place and the estimated relief center place) are equal ($H0$) or not ($H1$). Thus, the test statistics value is 0.365. According to the $p-value$ > 0.05, there is no sufficient evidence to reject zero hypotheses (See Fig. 21 ).

Fig. 21.

Comparison of simulation results with real system.

Finally, according to the scores of inputs and outputs, the efficiency of each alternative in the disaster-epidemic condition was evaluated. When measuring the efficiency of operating units (or DMUs - decision units in the DEA (Data Envelopment Analysis)), compare input metrics (various resources allocated to units) with output metrics (results of unit activity) and look for a “best” output/input ratio [51,52]. Suppose we have $n$ $DMU$, where ${DMU}_j$ ($j$ = 1, …, $n$) uses $x_{ij}$ inputs ($i$ = 1, …, $m$) to generate $s$ output $y_{rj}$ ($r$ = 1, …, $s$). The DEA uses the following model to evaluate the return performance of the $DMU$:

$$\mathit{Min}\theta s.t:\sum _j{\lambda }_j{x}_{ij}\le \theta x_{io}\forall i\sum _j{\lambda }_j{y}_{rj}\ge y_{ro}\forall r$$ (11)

Fig. 22 indicates the effectiveness of alternatives in disaster-epidemic situations as calculated by the DEA method. This is a two-dimensional representation of the input and output currents. The efficiency boundary is marked in red and the actions located at the efficiency boundary (red line) have a net input and output current rating that is not affected by any other action. In these graphs, the horizontal dimension corresponds to the amount of output, which has an increasing trend from the bottom up, and the vertical dimension corresponds to the amount of output, which has a decreasing trend from left to right. It is clear that the alternatives of Beheshti University, Yas Sports Complex, and Industry Sports Complex are the most efficient.

Fig. 22.

Efficiency of alternatives in the disaster-epidemic.

4. Conclusion and future work

Disaster management is the process of preventing a disaster or minimizing its effects when it occurs. According to the preventive role of disaster management and its importance in the event of natural disasters such as earthquakes, preparedness and capacity identification are important issues in disaster management. The Tehran disaster Management Organization has planned places to house the victims during the disaster so that the affected people can be settled in these centers in the event of natural disasters. Due to the global epidemic of coronavirus and its unpredictable behavior, some governments are facing a shortage of resources and manpower.

Managers' lack of awareness of damages before crises lead to confusion and inappropriate decision-making during crises. This issue is so important that developed countries devote an important part of their comprehensive and national plans to it. With the start of the COVID-19 epidemic in China and its spread to all continents of the world, and due to the unpredictability of crises such as earthquakes and epidemics, pre-crisis preparation to minimize financial and life losses will become more important. Although managers and related organizations try to prepare as much as possible in times of crisis, but the review and evaluation of management decisions taken during crises can affect management performance and relief in crisis situations. The purpose of this research was to evaluate the relief locations considered by the crisis management of Tehran to accommodate the injured and displaced people during the crisis, in terms of efficiency and optimality in three scenarios. Considering the issue of sustainability and humanitarian and environmental criteria, the results of this research can be used to better manage crises such as earthquakes and epidemics. The results of this research are used to increase the awareness of managers of crisis management organizations, rescue and rescue organizations, Red Crescent organizations, municipal officials and environmental organizations for planning during earthquake and epidemic crises with the aim of reducing loss of life and making maximum use of resources and suitable people. Also, by using the methods used in this research, the researchers or the relevant managers can evaluate other relief places considered for the accommodation of refugees in other cities and other areas and considering weaknesses and strengths of each of the relief places considered by the crisis management to prepare as well as possible with crises in different scenarios.

This study aimed to evaluate the relief centers considered by the disaster management of Tehran Region 1 in disaster conditions (occurrence of natural disasters), epidemic conditions, and disaster-epidemic conditions simultaneously. In this study, 14 criteria were considered for evaluating the relief centers in the region in disaster conditions and 6 criteria for evaluating the centers in epidemic conditions. First, the criteria were evaluated and classified by experts using the method of triangular fuzzy aggregation, their weights were calculated and evaluated as information layers in the GIS.

Then, the research alternatives were evaluated by experts and the GIS against the research criteria. By forming a decision matrix that was quantitative and qualitative, the alternatives in all three scenarios were prioritized using the PROMETHE method and the weight significance coefficient and stability of the criteria were determined. Among the research alternatives, sports complexes and universities have been among the top alternatives in all scenarios. The reason for this result can be their good performance in criteria of high importance such as safety (1.00), having space and isolation (0.86) in epidemic conditions and distance from fault lines (1.00), distance to gas pump (1.00), and Know the distance to the gas station (1.00). Also, these centers were evaluated in terms of performance, with the Beheshti University, Yas Sports Complex, and Industry Sports Complex alternatives being the most efficient compared to the other alternatives. A closer look at the PROMETHEE Rainbow Chart (see Fig. 11) reveals that even low-ranking PROMETHEE prioritization alternatives such as Aboozar Park and Laleh Park meet almost half of the research criteria, including high-importance criteria such as fault lines, distance to the gas pump and the distance to the gas station had a positive performance. According to the weighting coefficient of the criteria in the final ranking and the degree of compliance with the important criteria of the research by the alternatives, it can be concluded that the places considered by disaster management can be used in addition to disaster conditions and natural disasters in epidemic conditions. The proposed model is considered for 3 scenarios disaster conditions (natural disasters), epidemic conditions, and disaster-epidemic situations. But due to the comprehensiveness of the model and its results, it can be used for other scenarios. For example, the PROMETHEE model can be implemented for any other criteria and alternative, and the DEA model can be implemented for any other input and output. Also, due to the comprehensiveness of the proposed model, organizations such as Crisis Relief Organizations, Fire Department, Emergency, Municipalities, etc. are among the evidence of this research. In this research, a case is also examined, but it can be implemented for other cases as well.

One of the limitations of the research is the lack of evaluation of all centers in the region due to epidemic conditions and preventive laws and the lack of necessary permission to evaluate these centers during operational and executive time due to the sensitivity of these centers and control issues. In addition, due to the epidemic conditions for evaluating and selecting research criteria, questionnaires were provided to experts through cyberspace, and evaluations were performed online. Due to the existing limitations and lack of access to some layers of information such as gas pipelines, oil pipes, sewage network, military centers, dangerous places and sensitive centers, it has not been possible to evaluate relief centers with more criteria. Also, considering the conditions of the epidemic and the lack of direct access to experts to evaluate the criteria, it has been one of the limitations of the research that may affect the results of the evaluations. According to the strength of the proposed model, the number of research options can be increased and more places can be evaluated.

For future work, it is suggested that the relief centers considered in the region be evaluated in terms of operation and efficiency in different scenarios, including the amount of Richter and the type of fault, etc. Also, using simulation and modeling, the number of relief commodities and the most optimal warehouse location in the three scenarios are to be evaluated to use the most optimal resources in times of disaster.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.