Modification of Classic Linear Assignment Method Including the Impact of the Distance between the Performances of Alternatives for Alternatives Evaluation and Ranking

Document Type: Research Paper


Department of Industrial Engineering, Arak Branch, Islamic Azad University, Arak, Iran


This paper introduces a new method for incorporating the performance of alternatives into their ultimate ranking in a linear assignment method. This method is one of multi-criteria decision-making methods, in which the weight of criteria is incorporated in ranking the alternatives, and the distance between the performances of alternatives do not affect in ranking the alternatives. In order to modify the linear assignment method with the aim of incorporating the distance between the performances of the alternatives, some intervals are defined first, and each alternative is primarily ranked based on the interval that belongs to. In the ultimate ranking of the alternatives, the interval to which each alternative belongs to will be considered as the ranking criterion. Hence, not only the weight of the criteria, but also the distances between the performances of the alternatives has affected the ranking. The results of the modified method are compared to the TOPSIS method, as one of the most popular multi-criteria decision-making methods, and the outcome shows a better consistency between the modified model and TOPSIS.


Main Subjects

1-    Rezaei, J. ( 2015)."Best_Worst multi-criteria decision-making method." Omega., Vol.53, PP.49-57.

2-    Wallenius, J., Dyer, J.S., Fishburn, P.C., Steuer, R.E., Zionts ,S. and  Deb , K. (2008)."Multiple criteria decision making,multi attribute utility theory: recent accomplishments and what liesahead."Management Science., Vol.54, PP.1336-49.

3-    Hwang, C.L. and Yoon, K. (1981)."Multiple attribute decision making: methods and applications: a state-of-the-art survey."Springer-Veriag.

4-    Triantphyllou, E. (2000)."Multi-criteria decision making methods: a comparative study.Dordrecht."Kluwer Academic Publisher.

5-    Zopounidis, C. (1999)."Multi criteria decision aid in financial management."European Journal of Operational Research., Vol.119, PP.404-15.

6-    Hajkowicz, S. and Higgins, A. (2008)."A comparision of multiple criteria analysis techniques for water resources management." European Journal of Operational Research., Vol.184, PP.225-65.

7-    Zanakis, S.H., Solomon, A., Wishart, N. and Dublish, S. (1998)."Mutiple attribute decision making: a simulation comparision of select methods." European Journal of Operational Research., Vol.107, PP.507-29.

8-    Bernardo, J.J. and  Blin, J.M. (1977)."A Programming Model of Consumer Choice among multi-attributed Brands."Journal of Consumer Research., Vol.4, No.2, PP.111-118.


9-    Gass, S.I  .( 1984)." Linear Programming." fifth ed., McGraw-Hill Book Company.

10-  Pfaffenberger, R.C. and Walker, D.A. (1976)."Mathematical Programming for Economics and Business." first ed., The Iowa State University Press.

11-  Xian-ying, M. (2012)." Application of assignment model in PE human resources allocation." Energy Procedia.,Vol. 16,PP.1720-3.

12-  Campell, J.F . and Langevin, A. (1995)." The snow disposal assignment problem." J. Oper. Res. Soc.,Vol. 48, PP.919-929.

13-  Dessouky, M.M. and Kijowski, B.A. (1997)." Production scheduling on single-stage multiproduct batch chemical process with fixed batch sized." IIE Trans.,Vol. 29,No. 5,PP. 399-408.

14-  Leblanc, L.J. and Farhangian, K. (1981)."Efficient algorithm for solving elastic demand traffic assignment problem and mode split-assignment problem." Transport. Sci.,Vol. 15,No. 4,PP. 306-317.

15-  Mckeown, P. and Workman, B. (1976)." A study in using linear programming to assign students to schools." Interfaces .,Vol. 6,No. 4,PP. 96-101.

16-  Soumis, F., Ferland, J. and  Rousseau, J. (1980)."  A model for large-scale aircraft routing and scheduling problems." Transport. Res. Part B: Meth.,Vol. 14,No. 1,PP. 191-201.

17-  Balinski, M.L. (1986)."A competitive (dual) simplex method for the assignment problem." Math. Program.,Vol. 34,No. 2,PP. 125-141.

18-  Barr, R.S., Glover, F. and  Klingman, D. (1977)."The alternating basis algorithm for assignment problems." Math. Program.,Vol. 13,No. 1,PP. 1-13.

19-  Hung, M.S. and  Rom, W.O. (1980)." Solving the assignment problem by relaxation." Oper. Res.,Vol. 28,No. 4,PP. 969-982.

20-  McGinnis, L.F. (1983)." Implementation and testing of a primal-dual algorithm for the assignment problem."Oper. Res.,Vol. 31,No. 2,PP. 277-291.

21-  Burkard, R., Dell'Amico, M. and Martello, S. (2009)."Assignment problems."Society for Industrial Mathematics.

22-  Lovasz, L. and  Plummar, M.D. (1988)."Matching theory."Annals of Descrete Mathematics., Vol.29.North-Holland.

23-  Schrijver, A. (2003)."Combinatorial Optimization.Polyhedra and efficiency.Algorithms and combinatorics."Springer_Verlag,Berlin., Vol.24.

24-  Asgharpour, M.J. (1390)."Multiple Criteria Decision Making." 10th. Ed. Tehran University Press, Tehran.

25-  Mianabadi, H. and  Afshar, A. (1387)." Multiple Criteria Decision Making in Projects of Municipal Water Preparation."Water and Sewage, No.66, PP.34-45.

26-  Razavi, S.H., Hashemi, S.S. and  Zavadskas,E.K. (2012)."Prioritization of Expert Promotion Programs by Fuzzy Linear Assignment Method."Engineering Economics., Vol.23, No.5, PP.462-470.

27-  Amiri, M., Zandieh, M., Soltani, R. and Vahdani, B. (2009)."A Hybrid Multi-Criteria Decision-Making Model for Firms Competence Evaluations."Expert Systems with Applications., Vol.36, No.10, PP.12314-12322.

28-  Bashiri, M., Badri, H. and Hejazi, T.H. (2011)."Selecting Optimum Maintenance Strategy by Fuzzy Interactive Linear Assignment Method."Applied Mathematical Modelling., Vol.35, No.1, PP.152-164.

29-  Komijan, A.R. and  Koupaei, M.N. (2012)."A Multi_Attribute Decision_Making and Mathematical Model for University Examination Timetabling."Journal of Basic and Applied Scientific Research., Vol.2, No.10, PP.10258-10262.

30-  Foroughi, A. and Esfahani, M.J. (2012)."An Empirical study for ranking risk factors Using linear Assignment : A Case Study of road construction."Management Science Letters., Vol.2, PP.615-622.

31-  Norouzi, S.A. and Shariati, A.R. (2013)."Study of Locating Fire Stations using Linear Assignment Method:Case study Maku City."Global Journal of Human Socail Science., Vol.13, No.3.

32-  Nguyen, V., Emmanuel, F., Jacques_Antoine, G., Marlene, S. and Eric, D.W. (2010)."Optimizing the marriage market: An application of the linear assignment model." European Journal of Operational Research., Vol.202, PP.547-553.

33-  Bashiri,M. and  Badri,H. (2011)." A group decision making procedure for fuzzy interactive linear assignment programming."Expert Systems with Application.,Vol. 38,PP. 5561-8.

34-  Chen,T. (2013)."A linear assignment method for multiple criteria decision analysis with interval type 2 fuzzy sets."Applied Soft Computing.,Vol. 13,PP. 2735-48.

35-  Danchick,R. (2005)."A ranked linear assignment approaches to Bayesian classification."Applied Mathematics and Computation.,Vol. 162,PP. 265-81.

36-  Burkard,R.E. (2002)."Selected topics on assignment problems."Discrete Applied Mathematics.,Vol. 123,PP. 257-302.

37-  Ehsanifar,M. and Bakhtiarnezhad,S. (2012)."Selection of Portfolio by using Multi Attributed Decision Making (Tehran Stock Exchange)." American Journal of Scientific Research. , Issue. 44,PP. 15-29.

38-  Ehsanifar,M., Bakhtiarnezhad,S., Anvari,F.,Anvari,N., Farahani,H.R., Mohajerfar,M., et al. (2012)."Linear assignment and its application in financial management and portfolio." Archives Des Sciences.,Vol. 65,No. 7,PP. 333-58.

39-  Chakraborty,S. (2011)." Applications of the MOORA method for decision making in manufacturing environment." Int J Adv Manuf Technol.,Vol. 54,PP. 1155 -66.

40-  Barros,C.P. and Wanke,P. May-June (2015)." An analysis of African airlines efficiency with two-stage TOPSIS and neural networks."Journal of Air Transport Management., Vol. 44-45, PP. 90-102.

41-  Dymova,L., Sevastjanov,P. and Tikhonenko,A. July (2015)." An interval type-2 fuzzy extension of the TOPSIS method using alpha cuts ." Knowledge-Based Systems., Vol. 83, PP. 116-127.

42-  Hwang, C.L., Lai, Y.J. and Liu, T.Y. (1993)." A new approach for multiple objective decision making." Computers & Operations Research., Vol. 20 ,PP. 889-99.

43-  Lai, Y.J., Liu, T.Y. and Hwang, C.L. (1994)." TOPSIS for MODM." European Journal of Operational Research., Vol. 76, PP. 486-500.

44-  Olson, D. (2004)." Comparison of weights in TOPSIS models." Mathematical and Computer Modelling., Vol. 40, PP. 721-7.

45-  Yoon, K. (1987)." A reconciliation among discrete compromising solutions." The Journal of the Operational Research Society, Vol. 38, PP. 277-86.

46-  Behzadian,M., Khanmohammadi Otaghsara,S., Yazdani,M. and  Ignatius,J. December( 2012 )."A state-of the-art survey of TOPSIS applications ."Expert Systems with Applications., Vol. 39, Issue 17, PP. 13051-13069.

48-  Datta,A., Saha,D., Ray,A. and Das,P. December (2014)."Anti-islanding selection for grid-connected solar photovoltaic system applications: A MCDM based distance approach ."Solar Energy., Vol.110, PP. 519-532.

49-  Gauthier, T.D. (2001)." Detecting Trends Using Spearman's Rank Correlation Coefficient." Environmental Forensics., Vol. 2,No. 4,PP. 359-362.