Process mining can be used to discover different variants of a business process, each variant being a specific way in which the business process has been executed. To optimise the performance of the process, the best variant needs to be identified. However, process performance is multidimensional – a process might perform well on one dimension and poor on another – and it is often not known how these dimensions weigh out against each other to find the best performing process. This paper proposes to use conjoint analysis and regression analysis to assess the overall performance of different process variants discovered by process mining. In contrast to existing performance assessment techniques for process mining like conformance checking, the proposed approach does not require a benchmark process model to identify the best variants. The approach has been implemented in a visual tool and has been applied to an industrial case study.