  In data envelopment model (DEA), while either the most or least distance
based frameworks can be implemented for targeting, the latter is often more
relevant than the former from a managerial point of view due to easy
attainability of the targets. To date, the two projection-dependent problems of
reference set identification and returns to scale (RTS) measurement have been
extensively discussed in DEA literature. To the best of our knowledge,
nonetheless, there exists only one study which uses a closest projection for
identifying reference set and accomplishes this task through a primal-dual
linear programming based method. Motivated by this, we investigate the two
aforementioned problems in a least distance based framework. First, we propose
a lexicographic multiple-objective programming problem to find a unique closest
projection for an inefficient decision making unit (DMU). Associated with the
founded projection, we then identify all the possible closest reference DMUs by
developing a linear programming model in the envelopment form. For an
inefficient DMU, we next define closest RTS (CRTS) as the RTS of its least
distance projection and measure the CRTS in two stages. Finally, we illustrate
our proposed approach by a numerical example and compare the results with those
found in the most distance based framework.

Optimization and Control