International Journal of Industrial Mathematics
Volume:3 Issue: 4, Autumn 2011

This paper proposes a method for evaluating the efficiency of decision making units(DMUs) by using principal component analysis. This efficiency deals with undesirableoutputs and simultaneously reduces the dimensionality of data set. First, we change theundesirable outputs to be desirable by reversing. Then we do PCA on the ratios of a singledesirable output to a single input.In order to reduce the dimensionality of data set, the required principal components areselected out of the generated ones according to the lowest eigenvalues. Finally these chosen principal components are treated as virtual data set into data envelopment analysis(DEA). Then the utility of proposed approach is applied to real data set of some branchesof an Iranian bank.

The economic efficiency (EE) measure in non-convex technologies requires the data ofinput/output vectors and prices to be known deterministically. But as regards the dataof the production process in many real-world applications, rather than dealing with crispreal numbers and crisp intervals, one has to deal with”approximate” numbers or intervalsof the type that can be described as”numbers that are close to a given real number.” Forthe aforementioned reason, development of the economic efficiency models in such a way that they can deal with imprecise data, has become an issue of great interest. To thisend, the notion of bounded data and fuzziness has been introduced. This paper developsa procedure to compute the economic efficiency measures with non-convex technologies in the presence of uncertain data. In this study, uncertain EE formulas are transformed into a family of crisp EE formulas and LP models, based on comparison intervals and −cuts.To obtain the bounds of the membership functions of efficiencies, we propose a family ofparametric two-level programs. This pair of parametric programming problems gives thelower and upper bounds of  − cuts corresponding to the membership function of EE.Then, we prove that the lower bound is computed by some closed form expressions, but to obtain the upper bound we solve a LP model. Since the efficiency measures are expressed by membership functions rather than by crisp values, more information is provided for the management. Moreover, two examples are provided for illustrating the proposed approaches.

This paper is aimed at proving the existence of a solution to the Volterra-Hamerstainintegral equations in partially-ordered spaces. To this end, some fixed point theorems areproved in this kind of spaces.

In this paper, a Burgers-Huxley equation is solved by using variety of the Adomian’s decomposition method, modified Adomian’s decomposition method, variationaliteration method, modified variational iteration method, homotopy perturbation method,modified homotopy perturbation method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series whose components are computed by applying a recursive relation. Consequently, the existence and uniqueness of the solution and the convergence of the proposed methods are proved. Furthermore, a the accuracy of the presented methods.

In sciences and industries such as signal optimization, traffic assignment, economic marketand etc, many problems have been modeled by bilevel programming (BLP) problems,where in each level one must optimize some objective functions. There are so many algorithms in order to find the global optimum of the linear version of BLP problems.This paper addresses multi-objective linear bilevel multi-follower programming (MOLBMFP)problems in which there is no sharing information among followers. It presents a newmethod for solving these problems.

In this paper, we consider the problem of evaluating the efficiency of a company, DMU,initially having sub-units, DMSU, for fulfilling their requirements in these internal subunits.This is similar to the methods of producing different items in a chain system, inwhich all the parts are provided in other related sections of the chain system. In fact, theoutput of every sub-unit in this system produces the internal input for the following subunits in the chain. We demonstrate the efficiency of all sub-units and finally the aggregate efficiency of them at large.