Multi-Period DEA-R Efficiency for Decision Making Units Using Network Structure

Abstract

Purpose: In this paper, P tage network that contains relative data is studied in different time periods and the aim is to evaluate the technical efficiency of such a structure in each time period and overall efficiency after several desired time periods. Also, the efficiency of each stage of such a structure is evaluated in each time period and after several time periods.

Method: Considering a subsystem corresponding to each time period, we have a network system with a parallel structure of T subsystems, in which each subsystem consists of P processes connected in series. Using the proposed multi-period DEA-R model and also the mathematical relationships in overall efficiencies of  the overall system, subsystems and sub- processes, overall efficiency and the multi-period sub-processes efficiency of the system network are measured after several time periods and  in any time period.

Results: Out of 10 decision units, units D and H were efficient after three time periods, unit D was efficient in the first and second time periods, and unit H was efficient in the third period.

Conclusion: It has been shown that overall efficiency scores and the efficiency of each process obtained from this model after several desired time periods are higher than or equal to overall efficiency scores and the efficiency of each process in each time period.  Also, a unit becomes efficient after several periods of time if it is efficient in at least one period of time