Linear fractional radial graph measure of efficiency of production

Abstract

The linear fractional radial graph efficiency measure developed in this article is consistent with the definition of efficiency itself as a ratio of output to input, and has an interpretation of profitability as a ratio of revenue to cost. This measure embeds input and output radial efficiency measures which have cost and revenue interpretation respectively. As this graph measure does not have any path constraint, it can also be adapted to hyperbolic graph efficiency measure, generalised distance function, and directional distance function by imposing a path constraint. This measure, under a variable returns to scale assumption about the technology, provides feasible ways of scale inefficiency improvement within production possibility set. It also provides flexible ways of inefficiency improvement under constant returns to scale assumption. Profitability is maximised within technical efficiency context whenever scale efficiency is attained.

Keywords:

• Data envelopment analysis
• efficiency
• fractional programming
• linear programming

Acknowledgements

The author is grateful to the comments of anonymous referees and appreciates advices of C.A. Knox Lovell, Rolf Färe, D.S. Prasada Rao, and Henry Burley.

Disclosure Statement

No potential conflict of interest was reported by the author(s).