Improved Proximity Indexed Value MCDM Method for Solving the Rank Reversal Problem: A Simulation-Based Approach

Multiple criteria decision-making methods have been extremely useful for identifying the optimal alternative in complicated decision problems. However, in dynamic decision situations, they often suffer from rank reversal problem (RRP). For minimising the RRP, various improvements in existing methods have emerged in recent times. The proximity-indexed value (PIV) method is one method that promises to minimize the rank reversal problem. However, a detailed investigation of the RRP issue for the PIV method does not exist. In this paper, the PIV method has been taken up for a detailed examination of RRP using a MATLAB simulation-based framework by generating a sample of 10,000 random decision matrices. Seven approaches have been used to detect the existence of rank reversal. It is found that a sizeable prevalence of rank reversal remains in the PIV method. A new, improved PIV (IPIV) method is also proposed in this paper, which has been demonstrated to be effective in reducing the prevalence of rank reversal to almost zero. The effect of varying the number of criteria and the number of alternatives is also evaluated while considering the variation in criteria weights, i.e. equal and unequal criteria weights. Analysis of variance using the concept of blocking has been carried out on the results obtained at a 5% level of significance. The study also identifies more effective approaches from the seven approaches used to detect rank reversal. In addition, the application of the IPIV method is demonstrated in a real-world problem.