University of TehranIndustrial Management Journal2008-58859120170421A New Mathematical Model to Solve the Assignment Problems Caused by Multiple Heterogeneous Inputs and OutputsA New Mathematical Model to Solve the Assignment Problems Caused by Multiple Heterogeneous Inputs and Outputs1186387110.22059/imj.2017.126879.1006872FAAdel AzarProf. of Industrial Management, Tarbiat Modares University, Tehran, Iran0000-0003-2123-7579Hossein MohebbiAssistant Prof. in Industrial Management, Ayatollah Haeri University of Meybod , Iran0000-0003-3859-8936Ameneh KhadivarAssistant Prof., Faculty of Management, Alzahra University, Tehran, IranAbasali HeydariAssociate Prof., Faculty of Electrical Engineering, Yazd University, Yazd, IranJournal Article20150625Nowadays assignment issues, as one of the optimization problems in the field of Operations Research is studied by many researchers. Assignment issue is known as a type of NP-Hard issues. However, in real applications, various inputs and outputs are usually concerned in an assignment problem. This paper, based on some of Electrical Engineering concepts that can be considered equivalent to the concept of efficiency in data envelopment analysis, provides a new linear programming model to resolve assignment problems with multiple diverse inputs and outputs for each possible assignment. The objective function in this model is maximum of comparative efficiency rather than cost or profit. The main advantages of this new mathematical model include faster convergence to the optimum solution, focusing on a single mathematical model at the same time not several models, stability in the number of variables and constraints of the proposed model considering any increase in the number of inputs or outputs of problem and also less computational time compared to the other conventional approaches. The proposed model was described along with an applied example, then the results were compared with that of the model proposed by Chen and Lu.Nowadays assignment issues, as one of the optimization problems in the field of Operations Research is studied by many researchers. Assignment issue is known as a type of NP-Hard issues. However, in real applications, various inputs and outputs are usually concerned in an assignment problem. This paper, based on some of Electrical Engineering concepts that can be considered equivalent to the concept of efficiency in data envelopment analysis, provides a new linear programming model to resolve assignment problems with multiple diverse inputs and outputs for each possible assignment. The objective function in this model is maximum of comparative efficiency rather than cost or profit. The main advantages of this new mathematical model include faster convergence to the optimum solution, focusing on a single mathematical model at the same time not several models, stability in the number of variables and constraints of the proposed model considering any increase in the number of inputs or outputs of problem and also less computational time compared to the other conventional approaches. The proposed model was described along with an applied example, then the results were compared with that of the model proposed by Chen and Lu.https://imj.ut.ac.ir/article_63871_4e184dd2264acd394ee6ab2ad7e33118.pdf