Non-convex Technologies and Economic Efficiency Measures with Imprecise Data

The economic efficiency (EE) measure in non-convex technologies requires the data ofinput/output vectors and prices to be known deterministically. But as regards the dataof the production process in many real-world applications, rather than dealing with crispreal numbers and crisp intervals, one has to deal with”approximate” numbers or intervalsof the type that can be described as”numbers that are close to a given real number.” Forthe aforementioned reason, development of the economic efficiency models in such a way that they can deal with imprecise data, has become an issue of great interest. To thisend, the notion of bounded data and fuzziness has been introduced. This paper developsa procedure to compute the economic efficiency measures with non-convex technologies in the presence of uncertain data. In this study, uncertain EE formulas are transformed into a family of crisp EE formulas and LP models, based on comparison intervals and −cuts.To obtain the bounds of the membership functions of efficiencies, we propose a family ofparametric two-level programs. This pair of parametric programming problems gives thelower and upper bounds of  − cuts corresponding to the membership function of EE.Then, we prove that the lower bound is computed by some closed form expressions, but to obtain the upper bound we solve a LP model. Since the efficiency measures are expressed by membership functions rather than by crisp values, more information is provided for the management. Moreover, two examples are provided for illustrating the proposed approaches.