A mixed-integer linear programming model for aggregating multi–criteria decision making methods

Selecting an MCDM method to use in any decision-making problem is always a difficult issue regarding that there is no agreement generally on which method is the most appropriate one. This paper addressed a proposal of a hybrid approach for this problem. Under the assumption that there is no superiority among well-established and accepted MCDM methods, we defined a minimax strategy based on the fact that the highest total rank deviation between MCDMs and the proposed hybrid approach in terms of alternative rankings should be as low as possible. Even though MCDM methods often rank the alternatives differently, many methods perform similar ranking due to sharing alike mathematical operations. To avoid positive bias towards these methods in an integrated approach, we focused on a prioritizing scheme that supports differentiated rankings from others. This prioritizing scheme also contributed to hindering the problem of selecting MCDMs with constraining the compound effect of similar rankings. We developed a hybrid decision-making model combining different MCDM methods with prioritizing them by using a mixed-integer linear programming model. We compared the proposed approach with some well-known prioritizing methods and the results revealed that the proposed approach produced better outcomes in obtaining the desired outputs.