On the linearisation of reference technologies for testing returns to scale in free disposal hull models

One of the methods of testing returns to scale (RTS) in data envelopment analysis is based on the use of specially constructed reference technologies. Recently Kerstens and Vanden Eeckaut constructed such technologies for testing RTS in the free disposal hull (FDH) model. The use of these technologies requires solving mixed integer non-linear programming models. In this note we construct equivalent linear models, which have an obvious computational advantage.