A New Mathematical Model to Solve the Assignment Problems Caused by Multiple Heterogeneous Inputs and Outputs

Document Type : Research Paper

Authors

1 Prof. of Industrial Management, Tarbiat Modares University, Tehran, Iran

2 Assistant Prof. in Industrial Management, Ayatollah Haeri University of Meybod , Iran

3 Assistant Prof., Faculty of Management, Alzahra University, Tehran, Iran

4 Associate Prof., Faculty of Electrical Engineering, Yazd University, Yazd, Iran

Abstract

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.

Keywords

References

آذر، ع. (1394). تحقیق در عملیات: مفاهیم و کاربردهای برنامه‎ریزی خطی (چاپ ششم)، تهران: انتشارات سمت.
دانایی‌فرد، ح.، الوانی، س. م.، آذر، ع. (1392). روش‌شناسی پژوهش کمی در مدیریت: رویکردی جامع (چاپ دوم)، تهران: انتشارات صفار.
Azar, A. (2015). Operation Research: Concepts and applications of linear programming. Tehran: Oloume Novin. (in Persian) 
Bazaraa, M.S. & Jarvis, J.J. Sherali, H.D. (2010). Linear Programming and Network Flows. New Jersey: A John Wiley & Sons, Inc.
Campbell, G.M. & Diaby, M. (2002). Development and evaluation of an assignment heuristic for allocating cross-trained workers. Euro Journal Operation Research, 138(1), 9-12.
Chen, L.H. & Lu, H.W. (2007). An extended assignment problem considering multiple inputs and outputs. Applied Mathematical Modelling, 31(10), 2239-2248.
Chen, L.H. & Lu, H.W. (2008). Responses and comments to "A comment on An extended assignment problem considering multiple inputs and outputs".  Applied Mathematical Modelling, 32(11), 2463–2466.
Danaeifard, H. & Alvani, S.M. & Azar, M. (2007). Qualitative research methodology in management: a comprehensive approach. Tehran: Safar.
(in Persian) 
Dorf, R.C. & Svoboda, J.A. (2014). Introduction to Electric Circuits. California: Vaibhav Goel.
Fried, H.O. & Lovell, C.A.K. & Turner, J.A. (1996). An analysis of the performance of university-affiliated credit unions. Computer Operation Research, 23 (4), 375–384.
Hiller, G. & Liberman, B. & Frederick, S. (2002). Introduction to Operations Research. Mc Graw. Hill.
Jahanshahloo, G.R. & Afzalinejad, M. (2008). A comment on "An extended assignment problem considering multiple inputs and outputs". Applied Mathematical Modelling, 32(11), 2459–2462.
Kao, C. & Liu, S.T. (2000). Data envelopment analysis with missing data: an application to university libraries in Taiwan. Journal of Operation Research, 51(8), 897–905.
Lewin, A.Y. & Minton J.W. (1986). Determining organizational effectiveness: another look, and agenda for research. Management Science, 32(5), 514-538.
Marianoa, E.B. & Sobreirob, V.A. & Rebelattoc, D.A.N. (2015). Human development and data envelopment analysis: A structured literature review. Omega, 54, 33-49.
Nilsson, J.W. & Riedel, S.A. (2011). Electric Circuits. New Jersey: Prentice Hall.
Süer, G.A. & Bera, I.S. (1998). Optimal operator assignment and cell loading when lot-splitting is allowed. Computers & Industrial Engineering, 35(4), 431–434.
Industrial Management Journal
Volume 9, Issue 1
2017
Pages 1-18

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