Marginal rates in DEA using defining hyperplanes of PPS with CRS technology

Data envelopment analysis (DEA) was proposed in a highly influential paper by Charnes et al. (J Oper Res 2:429–444, 1978), who developed the Farrell seminal research (J R Stat Soc 120:253–290, 1957). The aim of the present research is calculating marginal rates for strong and weak efficient decision making units (DMUs) using the defining hyperplanes of the production possibility set (PPS). Toward this end, there are three essential objectives in the current study: (1) Implement Farrell’s idea to construct a new PPS called the Farrell PPS. In doing so, important relationships were discovered between the PPSs with constant returns to scale (CRS), non-increasing returns to scale, and non-decreasing returns to scale technologies. (2) Apply the newly constructed Farrell PPS as a catalyst to obtain strong and weak efficient DMUs and explicit form equations of strong and weak defining hyperplanes for the PPS with CRS technology. In order to do this task, a multiple objective linear programming problem is proposed whose structure for the decision space of the criterion space is similar to the proposed Farrell PPS. (3) Calculate the marginal rates for strong and weak efficient DMUs using the obtained explicit form equations of strong and weak defining hyperplanes for the PPS with CRS technology. Finally, an empirical study in the Iranian banking sector is used to show the applicability of the proposed methods.