computation of economic efficiency of units under evaluation with integer-valued

In data envelopment analysis, estimation of the efficiency of firms characterized by heterogeneous inputs and outputs along with their prices is questionable. all inputs and outputs are assumed to take real values in traditional data envelopment analysis. however, in many practical situations and in some applications, this is not realistic, as there might be need to work with integer variables and parameters. this paper introduces cost efficiency and revenue efficiency models which are common with real values. thereafter, the set of production possibilities is restricted to integer values and the cost and revenue efficiency models are presented. subsequently, cost efficiency and revenue efficiency models with directional distance function which tend to constant returns to scale are introduced. a comparison was made between the three types of cost efficiency and revenue efficiency. the values of the target function were derived from the models in this paper, which are extracted using lingo programming as illustrated.