Output deterioration with input reduction in data envelopment analysis

In most practical applications of Data Envelopment Analysis (DEA), it is recognized that there is a gap between the theoretical maximum reduction in inputs, e.g., 1 - theta, versus what is actually achievable. In this paper we examine this phenomenon in the context of productivity measurement of highway maintenance crews. Here, maintenance supervisors and geotechnical engineers estimate the maximum achievable reduction in resources without impacting the outputs from the process. Furthermore, they put bounds on the extent of output erosion that can result from input reduction beyond this maximum level. We present a modified version of the standard Banker, Charnes and Cooper (BCC) DEA model that explicitly addresses this erosion phenomenon. The resulting projections provide maintenance managers with a measure of the impact on system performance under excessive resource reduction, and aid in setting guidelines for maintenance budgeting at the patrol level.