Conditions for rank reversal in supplier selection

Supplier selection is the process of selecting the best bid among a number of bids submitted by different suppliers. The bids are all evaluated against a set of predetermined criteria. If there are more criteria, the bids receive a score on each criterion. The bid with the best total score over all criteria wins. \ud A common and sometimes even mandatory scoring rule per criterion is to assign the maximum score to the best bid on that criterion and to relate all other scores on that criterion to that best bid. This is a form of relative scoring, which is well known to open the way to rank reversal, the phenomenon that the ranking between two bidders is reversed. This may happen when, for example, an additional bid is taken into account, or when one of the original bids is removed. \ud In supplier selection this is especially harmful when the rank reversal involves the winning bid. In this paper we investigate under which conditions rank reversal with regard to the winning bid can occur