The inverse data envelopment analysis with imprecise data

Data envelopment analysis (DEA) measures the relative efficiency of a set of decision making units (DMUs) based on available input-out data. Inverse DEA models try to answer such a question: if the outputs need to be increased to a certain level and the efficiency of the DMU remains unchanged, how much more inputs should be provided to the DMU. In many real world applications full information about input-output data may not be available. This article deals with the inverse DEA problem in an uncertain environment. As a matter of fact, inverse DEA models are extended for the case that input-output data are imprecise and they are available only as intervals. Two multiple-objective linear programming (MOLP) are proposed for estimating the required upper/lower inputs for producing requested outputs and preserving efficiency scores. Proposed models preserve the upper/lower efficiency scores of not only the DMU under consideration but also other DMUs. A numerical example is provided to illustrate proposed methods.