Fuzzy Type-II Resource Allocation and Target Setting in Data Envelopment Analysis: A Real Case of Gas Refineries

Data envelopment analysis (DEA) is a linear programming method to measure the relative efficiency of a set of decision-making units (DMUs) with multiple inputs and outputs. Some DEA models are used to allocate resources and to set targets. Previous studies in resource allocation and target setting have used deterministic data; however, in real problems resources and targets are not deterministic. In this paper, a type-II fuzzy DEA approach is developed for resource allocation and target setting. A numerical example and a real case study including 11 gas refineries with two inputs and three outputs are provided to illustrate the performance of the proposed approach. The results demonstrate that the proposed method efficiently allocates resources and sets targets in presence of uncertainty. Sensitivity analysis is accomplished based on the variation of the value of targets and resources and the variation of the footprint of uncertainty (FOU) of resources and targets.