AN EXTENSION OF THE PARABOLIC DEA FRONTIER TO DEAL WITH INTEGER VARIABLES: A CASE STUDY IN BRAZILIAN RAILWAY STATIONS

Abstract

In this paper, we extend the Parabolic DEA frontier to deal with integer values. Thus, we propose a hybrid approach that
combines the Parabolic DEA frontier with the Sequential Algorithm to Resource Allocation in DEA. This is a two-phase
approach, in which the non-integer reallocation obtained by the parabolic DEA frontier is transformed into an integer
reallocation by the use of the Sequential Algorithm, while maintaining the highest DMUs’ efficiencies. We use this
hybrid approach to redistribute employees among 79 railway stations in Rio de Janeiro. By using this approach, all the
employees were redistributed respecting the integer values, and the system’s average efficiency has increased from 52%
to 96% through input redistribution.