## 2 Literature Review
### Multi-Criteria Analysis Methods in Healthcare  
In making a comprehensive decision, the decision maker should take into account a combination of mentioned scenarios and criteria that sometimes conflict. In this situation, multi-criteria decision making (MCDM) methods are useful to help the manager to find the best decision. In [20], the authors carried out a literature review on the applications of these methods in healthcare, performed a comparison between these methods, and applied them to a hypothetical case study. Some of these methods were applied to structure decision-making in healthcare areas such as the AHP method [21]. AHP can be used also as a weighting method and its results can be used as an input for another MCDM method [5]. TOPSIS [22], ELECTRE [23], PROMETHEE [24], and PROMETHEE II [25] are widely used in healthcare areas. According to [PERSON] et al. [26], there are no better or worse techniques, but for some decision problems, there is always a method that is more appropriate than others.  
One of the commonly used MCDM methods is the VIKOR method. This method focuses on ranking and selecting alternatives and determining the solution or compromise that is the closest to the ideal by analyzing different scopes and weights of the criteria. In [27], the authors provided a review on the applications of the VIKOR method in several application areas. Thus, the number of papers related to VIKOR method increased from a single article in 2004 to 180 articles in 2015. However, only 2.84% of these papers used the VIKOR technique in healthcare fields.  
Along with the successful deployment of VIKOR method for solving complex decision-making problems, other variants of it, such as comprehensive VIKOR, fuzzy VIKOR, regret theory-based VIKOR, modified VIKOR, and interval VIKOR methods, have come into the picture depending on the type of decision problem and requirements of the concerned DM. They have been applied in different decision-making scenarios and have typical characteristics and mathematical formulations. However, a comparative analysis of the VIKOR method and its variants ([4]) showed that for any decision problem, the original VIKOR is the best method for a solution without unnecessarily complicating the related mathematical computations.  
This state of the art allows us to see that the resource allocation problem in healthcare systems is still a topical issue. Modeling and simulation methods has been mostly used to understand the functioning of the complex ED system and to predict its reactions to the various changes it faces.  
This study allows analysis of the complex trade-off between resources allocation and cost minimization when optimizing healthcare systems.  
The main contributions of this paper can be summarized as follows:  
* To develop a decision making tool for healthcare management based on an efficient simulation-optimization approach;
* To develop an efficient DES model for performance evaluation;
* To carry out a large experimental study through the test of 145 scenario, hence creating a new benchmark that does not exist in the literature;
* To analyze the complex trade-off between resource allocation and cost minimization when optimizing healthcare systems. The VIKOR multi-criteria analysis method and the entropy method are used to this aim.