MEASURING THE EFFICIENCY OF NETWORK STRUCTURES UNDER INTERMEDIATE VARIABLES CONTROL CONDITION

The traditional models of data envelopment analysis (DEA) have used only nal inputs and outputs for ef- ciency measuring of decision making units (DMUs) in network structures, and they have considered its all operations as a black box. Hence, they are not able to determine accurately the ineciency source within structure. The dierent network models in two separate spectrum, multiplier and envelopment are presented to solve this problem. Multiplier models, also known as relational models, study network eciency and its parts and as well as relationship between the amounts of their ef- ciency in a model, while envelopment models, verify the points projected of non ecient units in addition to study of network eciency and its parts. Having envelopment approach, this article develops some production possibility sets (PPS) due to the concept of the link value determination controlling (intermediate variable) by network parts. Some Scenarios presented in each production possibility set with the aspect of kind and control power which determining link value that shown as 1.link control by previous part, 2.Link control by next part, 3.Link control by previous and next part as the same (non-cooperative approach- type 1), 4.Link control by previous and next part as the same (non- cooperative approach- type 2), 5.Link control by none of previous and next part (advanced approach). The results show when parts related to link have no control over its value (scenario 5) or all of them have the same control over the link (scenario 3and 4), the parts eciency and consequently the whole network eciency will be more than parts have one-way or unequal control. Furthermore, it can be inferred from the article that there is more eciency in network structure when a part of network has more control over the link value determination to related part. Therefore, it can be used to design network structure in order to increasing parts and consequently the whole network eciency.