A Zero-One Programming Model for Preventing Rank Reversal Phenomena in Ranking of Decision Alternatives

Many methods have been proposed in the literature for solving Multiple Attribute Decision Making (MADM) problems, which may create different prioritization for a unique problem. The validity of the methods depends on preserving the rankings in the case of adding or removing irrelevant alternatives. Irrelevant alternatives are those which their evaluations regard to any attribute is worse than the best selected alternative or any other alternative which has not been chosen. In other words, the validity of prioritization not only depends on not to create a different prioritization with removing the worst alternative, but also depends on to create an upward prioritization for other alternatives when the best alternative elemintates from the set of alternatives. Furthermore, when diverse normalization process use for the problem, the results must not change. Furthermore, different normalization processes do not have any effect on the rankings. In this paper, a zero-one programming model with a weighted sum minimization objective function has been constructed. Any constraint which relates to each attribute needs to have a slack or surplus variable for standardization. These constraints with real world constraints (for instance, budget constraint) forms the model constraints. Three case studies adapted from literature review, which have been normalized with different normalization procedures, solved with new model. The results demonstrate rank reversal phenomena has not been occurred.