Relative retrofit efficiency depends on the assumed production set: A data envelopment analysis of cumulative renovation packages and cost boundaries

Data envelopment analysis (DEA) can compare the resource intensity of renovation packages, but its scores depend on which scaled or combined alternatives are admitted as benchmarks. This paper examines that dependence using five cumulative packages from an anonymised nonresidential energy assessment. Investment is the single input, while modelled reductions in final energy and nitrogen-oxide emissions relative to baseline are two desirable outputs. Input-oriented constant-returns-to-scale and variable-returns-to-scale models are solved as small linear programmes. Total investment and additional energy-related cost are analysed separately. Under total investment, the first package is the only constant-returns reference and the remaining scores range from 0.5396 to 0.6410. The corresponding variable-returns scores are 1.0000, 0.9085, 0.8192, 0.8846 and 1.0000. The final package thus changes from a below-frontier score under unrestricted scaling to a frontier endpoint under convex combinations. Replacing total investment with additional cost makes the second package a further variable-returns frontier member. An audit of reference intensities shows that the constant-returns benchmark for the final package requires 5.455 copies of the first package, a mathematical construction that is not a feasible instruction for a single building. The paper demonstrates why efficiency scores must be accompanied by their reference packages, output slacks and cost definitions. These are deterministic relative comparisons of model scenarios, not evidence of managerial inefficiency, attainable procurement savings or realised environmental benefits.