This chapter proposes a method for estimating what may be called benchmark, or best practice unit and marginal cost rates. These rates provide plausible operational goals for the management of the units being compared. This method also provides efficiency measures and suggests which organizational units or time periods are more or less efficient, as well as an estimate of the degree of such inefficiency. Efficient units or time periods provide benchmarks for imitation by other units or can be studied for continuous improvement possibilities. As far as the authors can determine, the proposed methodology is the first technique with the capability to suggest plausible benchmark cost rates.
A principle of maximum performance efficiency (MPE) was proposed as a generalization of the maximum decisional efficiency estimation principle in Troutt (1995). This principle is more broadly applicable than the MDE principle. Also, a gamma distribution based validation criterion was proposed for the new MPE principle. The earlier MDE principle appealed to the maximum likelihood estimation principle for model aptness validation, but required relatively inflexible density models for the fitted efficiency scores.
The estimation models derived here reduce to straightforward linear programming models and are therefore widely accessible. A case was made that an optimal cost rate estimate of zero for some activity may be indicative of generally poor efficiency across the units with respect to one or more activities. Modifications based on reduced costs and augmented objective functions were proposed to compensate in that case.
In these models, the unknown cost rate parameters resemble the coefficients of linear regression models. However, the maximum performance efficiency estimation principle is employed rather than a criterion such as ordinary least squares. This principle assumes that for each organizational unit and time period, the unit intends to minimize these costs. Model adequacy with respect to this assumption was judged by a test of normal-like-or-better performance effectiveness for the estimated efficiency scores.
These results are also consistent with Noreen and Soderstrom (1994) who found that costs were not generally proportional to activity levels in a cross-sectional study of hospital accounts. The results of this chapter suggest that one source of such non proportionality, in addition to the possibly non-linear form of the basic cost model, is what we call performance inefficiency.
The proposed estimation criterion was applied to a published data set previously analyzed by a modified data envelopment analysis method. The resulting estimates were compared with the average costs obtained by the previous method. The estimated benchmark cost rates were uniformly and strictly lower than their average rate counterparts, consistent with their definitions and providing a strong measure of face validity.
Benchmarking estimation models, such as discussed here, provide a new tool for data mining when the emphasis is on modeling the best performers.