Title: Solution of fuzzy multi objective generalised assignment problem

Authors: Supriya Kar; Aniruddha Samanta; Kajla Basu

Addresses: National Institute of Technology, Mahatma Gandhi Avenue, Durgapur-713209, India ' National Institute of Technology, Mahatma Gandhi Avenue, Durgapur-713209, India ' Department of Mathematics, National Institute of Technology, Mahatma Gandhi Avenue, Durgapur, 713209, India

Abstract: In this paper, multi objective generalised assignment problem (MOGAP) with fuzzy parameters has been solved using three different approaches. Here, we consider three objective functions which are to be minimised. In the first approach, weighted sum method has been used and the problem is converted into a single objective one and then solved by extremum difference method (EDM) to get the optimal assignment. In the second one, modified fuzzy programming technique (MFPT) has been used for the same problem. Application of linear and exponential membership functions give comparative results with the goal that the better alternative can be obtained. The third one describes multi objective genetic algorithm (MOGA) to find the solution surface and the Pareto optimal front including the optimal assignment. The methods are demonstrated by a suitable numerical example.

Keywords: FMOGAP; extremum difference method; EDM; modified fuzzy programming technique; MFPT; multi objective genetic algorithm; MOGA.

DOI: 10.1504/IJMOR.2019.101611

International Journal of Mathematics in Operational Research, 2019 Vol.15 No.1, pp.33 - 54

Received: 12 Jul 2017
Accepted: 08 Feb 2018
Published online: 14 Aug 2019 *

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