Efficiency measurement for hierarchical situations

Abstract

The measurement and monitoring of the efficiency of processes in organisations has become an important undertaking in today’s competitive environment. A fundamental tool for this undertaking is data envelopment analysis (DEA). The conventional setting for DEA views the decision-making unit (DMU) (school, hospital etc.) as a black box with inputs entering and outputs leaving. The current paper looks at a problem setting somewhat related to a multistage situation but pertaining to a particular form of hierarchical structure. Specifically, we examine a set of electric power units that act as sub-units or sub-DMUs, operating under the framework of set of power plants that play the role of DMUs. We develop a DEA-like methodology that evaluates, in a two-stage manner, both the efficiencies of the sub-units and of the aggregates of those sub-units (the plants). In so doing, the approach attempts to have the projected values of plant-level inputs and outputs match up with the corresponding aggregate values of the sub-unit projections, as is the case prior to projection to the frontier. Since such projections may in fact not match up as described, we introduce a goal-DEA methodology to minimise the extent of any failure to achieve this match up.

Keywords:

• DEA
• efficiency
• hierarchy
• power plants
• sub-units

Acknowledgement

The authors wish to thank two anonymous referees and an Associate Editor.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Wade Cook and Zhepeng Li were supported under grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) (A8966 and RGPIN-2017-05667). Joe Zhu acknowledges support from the National Natural Science Funds of China (No. 71828101).