Accounting, life cycle assessment (LCA) and data envelopment analysis (DEA) are examples of various research areas that independently develop and apply diverse methodologies to evaluate performance. Though, many methods have in common that the results to be assessed are mainly determined by the inputs and outputs of the activities which are to be evaluated. Based on both production and decision theory, our comprehensive framework integrates and systematically distinguishes specific types of production-based performance assessment. It allows to examine and categorise the existing literature on such approaches. Our review focuses on sources which explicitly apply concepts or methods of multiple criteria decision analysis (MCDA). We did not find any elaborated methodology that fully integrates MCDA with production theory. At least, a basic approach to multicriteria performance analysis, which generalises the methodology of data envelopment analysis, appears to be well-grounded on production theory. It was already presented in this journal in 2001 and has rarely been noticed in the literature until now. A short overview outlines its recent insights and main findings. A key finding is that a category mistake prevails among well-known methodologies of efficiency measurement like DEA. It may imply invalid empirical results because the inputs and outputs of production processes are confused with resulting impacts destroying or creating values (to be minimised or maximised, respectively). We conclude by defining open problems and by indicating prospective research directions.