Supply chain management environmental and social criteria are practical and research concerns due to regulatory, stakeholder, and economic pressures. Effective holistic sustainable supply management schemes require the evaluation and selection of suppliers. Supplier evaluation requires the balancing of multiple criteria. Multiple criteria tools, each with advantages and limitations, are necessary for the supplier evaluation and selection problem. This paper introduces a new methodological approach including complementary, analytic hierarchy process (AHP), decision-making trial and evaluation laboratory (DEMATEL) techniques and Bayesian networks (BN). The combination of DEMATEL, AHP and Bayesian approaches, although they are supportive and complementary methods, has seen limited investigation. The Bayesian network approach can complement DEMATEL and AHP to help improve the accuracy of AHP input data. Alternatively, DEMATEL and AHP can provide expert and more objective inputs for intangible factors, used in the Bayesian network approach. The validity and efficacy of this approach is demonstrated through a real industrial case using decision-makers’ inputs and outputs. The study shows the advantages and disadvantages of each method. Finally, we present results with managerial and research implications and future research directions.