Investigate the relationship between the super-efficiency and fixed input in the presence of infeasibility

The fixed input allocation is an important topic in the management science field. Previous data envelopment analysis (DEA) studies consider the problem based on the constant return to scale (CRS) framework (called CCR DEA model). However, the return to scale relationship between inputs and outputs includes three cases: CRS, increasing return to scale (IRS) and decreasing return to scale (DRS). Therefore, it is necessary to study the problem based on DEA under the variable return to scale (VRS) assumption (called BCC DEA model). This paper has two contributions: one is presenting an approach to solve the infeasibility problem when a new variable is added into the super-efficiency BCC DEA model, and the other is investigating the basic relationship between the BCC efficiency scores and the allocated fixed input. Both of them are significant for allocating the fixed input under the VRS DEA framework. Finally, the proposed approach is illustrated by an example of allocating the subsidy among urban public transport enterprises.