maximizing total efficiency by resource reallocation in dea: a case study on tehran stock exchange

Data envelopment analysis is a technique based on mathematical planning for specifying the efficiency of decision making units (dmus). dmus are units which produce similar outputs using similar inputs. so far, the issue of allocating a new resource to decision-making units has been discussed as a challenging issue in several articles. in some cases, manager is not going to add a new resource but to reallocate one of the previous resources. reallocating a resource may be done for different purposes and has different benefits. for example, without adding a new resource and only using the same resources, is it possible to increase the efficiency of one unit or even increase the efficiency of the whole system? this is the main idea of the present article. in this paper, a mathematical model is presented that can be used to reallocate one of the previous available resources between units in such a way that the total efficiency of decision-making units reaches the maximum possible value. in this model, in order to prevent excessive reduction of the share of each unit of the desired source, restrictions have been considered. in these constraints, a lower bound for the share of each unit is specified. also, reallocating a resource is likely to lead some changes in output values of decisionmaking units. fortunately, this issue has not been neglected in our model. in the presented model, some constraints are considered that specify an upper bound for outputs produced by the units. there are other restrictions in this model. the first is that the total share of units from the desired resource should not exceed the amount available of it and the second is that the total output produced by all units should be at least equal to the total output produced before reallocation. the model presented in this article, in addition to considering the restrictions described, all of which are unavoidable, has been transformed into a linear programming model that can be solved by many existing software. finally the mentioned model has been utilized in two examples. the first example is numerical and the second one is related to tehran stock exchange. in both examples, after the reallocation of the resource in question, the total efficiency of the units has increased significantly.