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.