evaluating the efficiency of two-stage network data envelopment analysis with non-discretionary inputs for centralized resource allocation by means of the modified russell model

In evaluating the efficiency of organizations, there are situations inwhich all units exactly under consideration of a centralized manager that direction them.this situation is important when all of the units belong to the same organizations toobtain their outputs. in this study, we introduce a centralized resource allocation modelfor two-stage network data envelopment analysis (dea) with inputs which managerscannot change the inputs in evaluating the efficiency of dmus in network systems,which these inputs are called non- discretionary inputs. if non- discretionary inputs existin evaluating the efficiency of sub-dmus and dmus, it is important to take intoaccount the inputs in evaluating the efficiency of sub-dmus and dmus, because thenon- discretionary inputs can affect the system’s efficiency. in such situation, thecentralized manager wants to minimize the all inputs consumption and also to maximizethe all outputs production in evaluating the efficiency of network dea, while thecentralized manager cannot minimize consumption of non- discretionary inputs inevaluating the efficiency of network dea. we propose a model for such situations,which it has not been discussed in previous studies of network dea so far. we illustratethe ability of implementation of the presented model in this study by using an appliedexample of evaluating the efficiency of a road construction company in iran, that hasbeen discussed in this study.