Measuring and evaluating efficiency and effectiveness using goal programming and data envelopment analysis in a fuzzy environment

Generally, in most situations optimal achievement of multiple goals is rarely possible for crisp mathematical programming techniques. In such cases, a compromise achievement of goals that leads to a satisfying solution rather than an optimal solution bears more relevance. The present research introduces a Fuzzy Goal Data Envelopment Analysis (Fuzzy GoDEA) framework to measure and evaluate the goals of efficiency and effectiveness in a fuzzy environment. Fuzzy GoDEA accommodates crisp input and output data but allows imprecise specification of the aspiration levels for the efficiency and effectiveness goals. A membership function is defined for each fuzzy constraint associated with the efficiency and effectiveness goals and represents the degree of achievement of that constraint. Further, the Fuzzy GoDEA framework is extended into several variations that (i) allow the assignment of relative importance to the goals of efficiency and effectiveness and (ii) model scenarios where one of the goals of efficiency and effectiveness is crisp and the other fuzzy. The Fuzzy GoDEA framework is implemented for a newspaper preprint insertion process.