Features of the efficiency frontier and its application in Inverse DEA without solving a model

Abstract

The inverse data envelopment analysis is an inverse optimization problem, which can be used as an appropriate planning tool for management decisions. The typical DEA mainly focuses on post-operative evaluation of an organizational performance. Sometimes economic conditions such as economic prohibitions on exports or imports are imposed on a system. These prohibitions prevent decision-making units from best performance (efficiency one). In this case, if the system has the best performance (with a less than one efficiency score) then it will be considered as an efficient system. So, the efficiency frontier change’s problem must be studied. So by making change in definition of the best efficiency amount of a system, it still has the best performance. In these situations, the inefficient units can select a real pattern instead of reaching an unrealistic pattern that is presented in ideal terms to achieve the best conditions (the best efficiency value is one). So a long-term management plan can be developed. the efficiency frontier change will be expressed inputs and outputs as a coefficient of efficiency. The frontier change looks at the changes in inputs and outputs to reach the new frontier. One of the purposes of the data envelopment analysis is the investigation of input’s and output’s amounts by changing the amount of efficiency. So far, many models must be solved to calculating these changes. Efficiency frontier problem can replace a simple mathematical model with these models. All of these advantages can improve calculating input and output’s changes and RTS will be unchanged and decision maker can estimate unit’s RTS without solving any model. So a unit will be stayed MPSS by reducing inputs. In other frontier change methods some hyperplanes and extreme units had been deleting but our method transforms them on new frontier. So all extreme units and RTS can estimate easily. The efficiency frontier changes can delete some inefficient units so system’s cost will be reduced.  For this purpose, in this paper, the change in the efficiency frontier, its properties and its effect on the inverse data envelopment analysis is examined.