creating full envelopment in data envelopment analysis with variable returns to scale technology

in this paper, weak defining hyperplanes and the anchor points in dea, as an important subset of the set of extreme efficient points of the production possibility set (pps), are used to construct unobserved dmus and in the long run to improve the envelopment of all observed dmus. there has been a surge of articles on improving envelopment in recent years. what has been done first is in constant returns to scale (crs) environment for single input multiple output cases, and the latter study is in variable returns to scale (vrs) environment for multiple input and output cases, but none of them guarantees full envelopment. we provide a short summary of what has been done in vrs environments to improve envelopment we then devise an algorithm to create full envelopment of all observed dmus under vrs technology. we illustrate our algorithm using a numerical example.