An Application of Mathematical Programming to Assess Productivity in the Houston Independent School District

A school may be viewed as an enterprise in which the professional staff provide the operating conditions for converting quantifiable resources or inputs into pupil learning (outputs). The resources are determined by budgets, teacher assignments, and student assignments while learning is determined by various outputs scored according to standardized tests such as the Iowa Test of Basic Skills. Following the work of Charnes, Cooper, and Rhodes (Charnes, A., W. W. Cooper, E. Rhodes. 1981. Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through. Management Sci. 27 (6) 668--697.), we use a ratio definition of efficiency that takes account of all outputs and inputs without requiring a priori specification of weights. Instead a series of mathematical programs are applied to determine "virtual multipliers" from actual data. The multipliers produce values that can be regarded as the "most favorable weights" for each school being evaluated. If the resulting optimum virtual multipliers for a given school yield an efficiency ratio of one, then that school is said to be efficient. If the ratio is less than one then that school is said to be inefficient relative to the other schools in the analysis. The ratio is also accorded operational significance---it is not merely an index number---so that the resulting values and the associated virtual multipliers make it possible to locate where improvements may be made along with their relative magnitudes. This analysis was applied to 167 elementary schools in the Houston Independent School District. Of these schools, 78 were found to be inefficiently utilizing their resources as compared to the 89 efficient schools. Based on this pilot study, an Educational Productivity Council has been formed at the University of Texas at Austin to provide an annual analysis for all of its member schools. At present 285 Texas schools in 22 districts are scheduled for participation in the annual analysis as described in this investigation.