Cost, Revenue efficiency with integer-valued

Estimation of efficiency of firms that characterized by heterogeneous inputs and outputs along with their prices is questionable in data envelopment analysis ( DEA ). In practice, production is costbased. In traditional Data Envelopment Analysis (DEA) all inputs and outputs are assumed to take real values. However, this is not realistic in many practical situations and in some applications, there might be need to work with integer variables and parameters. Empirical studies of production technologies using directional distance function. In this paper, initially, cost efficiency and revenue efficiency are commonly introduced, then the set of production possibilities is limited to integer setsand the model is rewritten. After these in case study, we comparison between the general cost efficiency, cost efficiency withinteger sets. And comparison between the general revenue efficiency model and the revenue efficiency with integer sets.