Determining an Assurance Non-Archimedean Epsilon in FDH Models with Variable Returns to Scale

Authors

Abstract

The use of epsilon form in free disposal hull (FDH) models
is essential for evaluating the performance of decision-making units
(DMUs). However, an inappropriate choice of the non-Archimedean
epsilon value may cause the multiplier side model to be infeasible and
therefore the envelopment side model to become unbounded. In this
paper, a method is presented to determine an assurance value of non-
Archimedean epsilon in FDH models with input orientation and assuming
variable returns to scale (FDH-VRS models). This value of epsilon
is calculated using only basic arithmetic on the input data, and guarantees
that the multiplier side become feasible and the envelopment side is
bounded. Following that, by providing numerical examples, the role of
epsilon in improving the accuracy of the evaluation of DMUs as well as
the computational efficiency of the model is shown. The results of running
the proposed model on real data from 25 supermarkets in Finland
show that this epsilon-based FDH model with VRS technology produces
the same results as the base model without epsilon with the same accuracy,
with fewer calculations (equal to the number of DMUs). This
research provides a practical and mathematical solution to overcome
the challenge of epsilon selection in non-convex FDH environments.

Published

2026-02-01

Issue

Vol. 20

Section

Vol. 20, No. 2, (2026)

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