Applying a multi-criteria group decision-making method in a probabilistic environment for supplier selection (Case study: Urban railway in Iran)

Supplier selection of urban train signaling equipment is one of the main problems in urban railways due to the serious impact of this equipment on the safety of travelers. The supplier's selection is a multi-criteria decision-making (MCDM) problem, in which the preferences over criteria are highly dependent on the opinions of decision-makers (DMs). The focus of the present study is to provide an appropriate model of multi-criteria group decision making in a probabilistic setting to effectively combine DMs' judgments. For this purpose, the Bayesian hierarchical model with the best-worst method (BWM) is used to determine the weights of criteria and the Vise Keriterijumska Optimizacija I Kompromisno Resenje (VIKOR) is used to prioritize suppliers. Bayesian BWM aggregates the opinions of all DMs at once, instead of averaging the individual opinions of the DMs that underlie MCDM methods. In this method, the probability of preference of one criterion over one another is calculated using Markov-chain Monte Carlo (MCMC), in addition to the weight of criteria, so that the confidence between pairs of criteria is revealed and ranking of criteria become more certain. Given that the average obtained confidence levels are 0.95, the validity of the Bayesian BWM results is confirmed. For different values of the VIKOR parameter, the third supplier will have the highest rating and the fifth supplier will have the lowest rating. The introduced multi-criteria decision model in this research will help the decision-makers of the urban railway company and other organizations with several suppliers to be able to select the best supplier by considering the relevant criteria.