On alternative optimal solutions in the estimation of returns to scale in data envelopment analysis

Zhu and Shen show that alternative optimal solutions in the estimation of returns to scale (RTS) are caused by a particular linear dependency among a set of extreme efficient decision making units (DMUs) when one employs the concept of most productive scale size in data envelopment analysis (DEA). This paper demonstrates that the presence of weakly efficient DMUs may also lead to alternative optima and extends the results of Zhu and Shen to the entire frontier. Necessary and sufficient conditions for the presence of multiple optimal solutions for constant returns to scale (CRS) DMUs are established.