Designing a Dynamic two-stage data envelopment analysis model to calculate partial and periodic efficiency

The measurement of organizational efficiency has always been discussed by various researchers. Data envelopment analysis, taking the inputs and outputs of the decision-making units into account, makes it possible to calculate the relative efficiency for each unit. Many organizations have a two-stage structure, and their performance in successive periods depends on each other. In evaluating such a structure, partial and periodic efficiency must be calculated. Early models and network and dynamic models are not able to calculate this performance alone. Models of existing dynamic networks are also unable to provide a projection for inefficient units or solve all challenges. In this study, by defining the PPS, an input-oriented dynamic two-stage DEA was developed.  In this model, the optimal value of the intermediate and carryover variables is determined by the next stage and period, and the stages and periods become efficient backward from the last stage of the last period. In addition to the total structure, the model makes efficient all stages and periods and only becomes an efficient unit if it is efficient in all stages and periods. It was also proved that the projection of the unit to be evaluated is partial, periodic, and total efficient. How to use the model to calculate efficiency was expressed by a practical three periodical example.