A stochastic cross-efficiency DEA approach based on the prospect theory and its application in winner determination in public procurement tenders

As an encouraged award rule in public procurement tenders, the ‘‘Most Economically Advantageous Tender’’ rule aims to determine the winning bidder considering quantitative and qualitative factors simultaneously by a group of experts. In such a rule, how to maintain a transparent procedure in accordance with governmental procurement regulations as well as guaranteeing fair evaluations of all bidders considering the risk behaviors of experts is a challenge. To fill this challenge, this study proposes a stochastic cross-efficiency data envelopment analysis (DEA) approach based on the prospect theory to determine the winner in public procurement tenders. Firstly, two cross-efficiency DEA models to maximize gains and minimize losses based on the prospect theory are developed to derive the cross-efficiencies of bidders. Next, a stochastic Benefit-of-the-Doubt (BoD) model, carried out by Monte Carlo simulation, is used to aggregate the diverse cross-efficiencies derived from the evaluations of different experts. The model can deduce a robust ranking of bidders without a priori setting of attribute weights and expert weights. For the challenging issue that experts cannot make evaluations precisely for qualitative factors with uncertain information, the hesitant fuzzy linguistic term set is applied to express the vagueness of expert judgments. An illustrative example is given to demonstrate the applicability and effectiveness of the proposed approach.