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Abstract
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Data envelopment analysis (DEA) has been shown to be a very useful mathematical programming
tool to measure the relative efficiency of decision making units (DMUs), especially
when the so-called internal network structure of the production process is taken
into account. Under a network structure, however, two standard directions of modeling
the production process may generally lead to a pair of multiplier and envelopment DEA
models so that the outcomes are not necessarily equivalent, i.e. a network duality problem
occurs. Although, the duality problem has recently been addressed for specific cases of network
structures, for more complex structures, DEA models have only been able to be developed
by following either the envelopment form or multiplier form. Investigating this
duality problem, this paper also proposes DEA models for general network structures with
two additional properties. Due to the first property, all factors in a general network structure
including main inputs/outputs and/or intermediate inputs/outputs can be shared
among the divisions while the second property assumes that a factor in a structure may
be considered as both intermediate input/output and main input/output simultaneously.
We will show that the proposed network DEA models cannot only deal with the already
existing general network structures in the literature, but are also represented by dual multiplier
and envelopment linear programming-based problems by which consistent outcomes
can be obtained. A comprehensive numerical example will be presented to
explain the properties and features of the suggested models.
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