Multicriteria Decision Analysis, MCDA is a tool capable of supporting decisions utilizing multiple criteria. The use of MCDA as a method to support the definition of priorities in health care is not new, researchers have shown its growing importance in the health field [1,2,3,4] especially within public health systems [5,6,7,8]; including recent studies that highlight the contribution of MCDA in the context of epidemic events such as COVID-19 [9,10,11,12,13,14,15]. The potential for the application of MCDA in the health field is due to the combination of restricted resources and the growing demands that have led decision-makers to address this issue more directly than in the past [16].
Despite the proven value of MCDA’s support in the health field, no models were found that used a multicriteria method to assist in prioritizing victims’ decisions at Emergency Medical Services, EMS. This is one of the most important health services, as it plays a vital role in saving people’s lives and reducing the rate of mortality and morbidity [17].
Despite the fact that the importance and sensitivity of decision-making in the field of EMS has been recognized by Operations Research scientists, emergency medical planners and health professionals who have studied strategic, tactical and operational problems for EMS since the 1960s [18], only monitoring, forecasting and location problems have been widely discussed [19,20,21,22,23]. Carvalho et al. [24] presents two generic approaches to optimize dispatch; and Belanger et al. [25] relocation decisions and thereby maximize the preparation of the system and a recursive simulation-optimization framework; however, it does not take into account fundamental criteria for the ambulance dispatch decision, such as those related to the victim’s severity and conditions, leaving a gap in the literature.
In Brazil, the solution for these problems is still a manual task, with responsibility for the dispatch decision attributed to the regulating physicians of the Mobile Emergency Care Service, SAMU/192, which is the mobile prehospital component of the Emergency Care System and Brazilian emergencies, in municipalities and regions throughout the national territory. The model proposed by the present work supports the decision to prioritize victims of SAMU/192 regulating doctors, and focuses on the so-called level 1 (red code of absolute priority), since they have the highest number of occurrences. Thus, throughout the text we will use SAMU/192 as a term equivalent to the Brazilian EMS.
The SAMU/192 strategy for sending ambulances follows protocols that are formulated based on criteria related to the victim’s severity level. Based on this information, generally, the victim who is closest to the available ambulance is treated. However, in an environment in which the demand exceeds the capacity of the available resources, a greatest number of attributes related to the alternatives ought to be evaluated; given that from a system overview, this decision can lead to a better area coverage, considering not only the immediate situation, but also possible future emergencies.
For instance, on considering two calls, in a scenario of scarcity of resources, in which the victims suffer from epileptic attacks [26, 27]; after assessing the victim’s health status, the regulatory physician (RP) classifies the call as Level 1, red code and authorizes the ambulance to be dispatched. However, only one ambulance is available to assist the victims. Given this scenario, when the regulatory protocols are not sufficient for the decision to prioritize victims, how to make the decision? What are the steps to be followed? Which victim to prioritize? When the protocol advises the ambulance to be sent and the doctor does not have the resources to care for the victims, what criteria would be used to assist this decision? The prioritization of victims must be carried out, making use of guiding criteria (protocols - dealing with criteria related to the victim’s health status) and criteria that influence the decision-making process (criteria related to the health system; support tools; victims’ details and external factors).
In such cases, which involve different criteria, the use of the multicriteria model developed will bring greater clarity, transparency and rationality, maximizing the benefit and minimizing the risk in the SAMU/192 environment. Hence, the current study presented the dispatch problem as a decision to prioritize victims and developed a new model for prioritizing victims of SAMU/192, in an environment of scarcity of resources based on multicriteria decision support methodology. The analysis and structuring of the problem revealed important criteria in the field of EMS. Mathematical modeling, with FITradeoff, suggested the best alternative amongst those analysed. It is believed that the proposed model could improve the efficiency of victim prioritization in the context of SAMU/192.
Multicriteria decision
A multicriteria decision problem occurs when the Decision Maker, DM, an individual over whom power and responsibility over the decision are attributed, is faced with a situation with at least two alternatives for action, so that choice between the courses of action available is driven by the desire to meet multiple objectives, conflicting with each other [28,29,30].
Before selecting and implementing any MCDA method, the limits of the problem to be addressed should be defined, given that the better the problem is defined, the more accurate the analysis result will be [31, 32]. This can be achieved by reviewing the literature on decision-making criteria, conducting qualitative research, and consulting experts [3].
As long as the problem was pre-defined, the objectives and criteria to assist in decision making were identified, and the decision maker’s rationality established, a multicriteria assessment method can be chosen to meet the conditions and needs to address the problem [29, 33].
Multicriteria model of deterministic additive aggregation
An additive model for aggregation uses a single synthesis criterion MCDA method, which presents as the main characteristic the aggregation of multiple criteria in a single synthesis [29], thus being situated in the context of compensatory rationality. In such model, uncertainty is considered in obtaining the vector of consequences x for each alternative a.
For the problem of choice, which defines the class of problems in which the objective is to support the decision through the choice of a subset of the action space, the solution of the additive model consists in the selection of the alternative that presents the highest global value v(a) [30]. As the contribution of the additive model to the single criteria methods of synthesis lies in the process of aggregating the criteria, in these methods the evaluation of the alternatives is carried out through the value function defined on the consequences, considering that each alternative is associated with a consequence vector x [29].
The greatest difficulty faced by the multicriteria decision support methodology lies in the evaluation and modelling of preferences [30]. However, preferences can be modelled by rules and logical relations [34,35,36]. With the knowledge about the preferences of the decision maker, a problem can be solved based on the additive model, being necessary two types of evaluation: the intracriteria and the intercriteria. The intracriteria evaluation aims to evaluate each alternative i for each criterion j, which leads to the value function \(v_j(a_i)\), the construction of the value function for each element is based on the evaluation of the consequences to be obtained. In the Intercriteria evaluation with the information \(v_j(a_i)\), the information that considers the combination of the different criteria is sought, and to find it, it is necessary to choose a method of aggregating criteria [29]. When the criteria are represented by different units, it is necessary to normalize these values, so that they are redefined on a scale from 0 to 1. Prior to the final recommendation, sensitivity analyses can be carried out to investigate whether the preliminary conclusions are robust or whether they are sensitive to changes in aspects of the model [32].
FITradeoff
Almeida et al. [37] proposed the Flexible and Interactive Tradeoff, FITradeoff method to address the problem of eliciting scale constants, which will occasionally be referenced also by criteria weights. In FITradeoff the scaling of the scale constants is based on the tradeoff procedure in which the values tradeoff are to be achieved, which is defined by the moment when the decision maker is indifferent to two consequences and you can be willing to exchange them [29, 37]. This procedure is adopted in the Tradeoff method [38, 39], which makes FITradeoff to be considered an extension of this.
In compensatory methods, the DM considers the compensations by criterion when comparing the alternative consequences [38, 39]. Operationalization through the Decision Support System (DSS), includes the following steps: 1. Intracriteria assessment; 2. Classification of criteria weights; 2.1. Attempt to solve the problem using the set of weights available; 3. The DM’s preferences are evaluated to arrive at the results [37].
The first part allows the weight space to be defined. Subsequently, the second part is started, it is possible to see the difference between the procedure and the traditional model, the DM is not required to define an exact value of \({(x_{l}^{i})}\), which denotes the result of the i criterion for which indifference is obtained between consequences, whereas the traditional method requires this procedure.
If the solution is not found, then the third stage begins, that is, that of assessing the preferences of the DM that can be divided into four stages: 3.1. Define values to test the weight distribution; 3.2. Asking the DM to indicate their preferences; 3.3. LPP computing; and 3.4. Finalization. Upon completion, these four steps constitute the main stage of FITradeoff. Thus, the objective is to find an alternative, based on the vector of the alternatives, which has the maximum value according to the weight of the criteria space [40]. Therefore, LPP is performed until an ideal alternative is found. If it does not occur, the dominated alternatives are eliminated and the process is started again, starting from step 3.1. Now, only the alternatives identified as potentially optimal are considered in the subsequent steps, otherwise the process is finalized [37]. In the finalization step, the weight ranges supporting the solution are computed and produced in a report with the final recommendation.