Application of DEA-SBM for Identifying Water-Quality Risk Pipes in Water Distribution Networks

Abstract

This article presents a comparative study of data envelopment analysis (DEA) models for identifying water-quality risk pipes, focusing on how input-output variable definitions and the choice of efficiency model govern the results. Seven sedimentation- and exfoliation-related factors are integrated into an input-oriented Banker-Charnes-Cooper (BCC) model, with the stagnation-time ratio, velocity difference, and change of flow direction redefined as continuous rather than threshold-based or binary indicators. This redefinition assigns positive output values to low-velocity pipes and thereby increases the pipes tied at an efficiency score of unity, leaving the radial score limited in refining the priority of the risk pipes. To overcome this limitation, we use a DEA-SBM (slacks-based measure) model that embeds the input slacks directly into the efficiency score. Unlike the two-stage procedure that computes slacks separately after the radial analysis, this differentiates the pipes within a single model. When applied to an actual network of 479 pipes, the radial BCC model classifies 120 pipes as equally high-risk pipes, whereas the SBM differentiates them into 62, 5, 14, and 33 pipes as risk-pipe Levels 1, 2, 3, and 4, respectively, enabling a finer quantitative prioritization of water-quality risk pipes.