Journal of Intelligent & Fuzzy Systems 33 (2017) 1687–1697 DOI:10.3233/JIFS-17086 IOS Press 1687 Solution of a class of generalized assignment problem Supriya Kar a,∗ , Kajla Basu b and Sathi Mukherjee c a Research Scholar, National Institute of Technology, Mahatma Gandhi Avenue, Durgapur, West Bengal, India b Department of Mathematics, National Institute of Technology, Mahatma Gandhi Avenue, Durgapur, West Bengal, India c Department of Mathematics, Gobinda Prasad Mahavidyalaya, Amarkanan, Bankura, West Bengal, India Abstract. The paper presents the solution of a multi objective multi-index generalized assignment problem using Fuzzy Programming Technique which is a new concept. It emphasizes on minimization of the job cost and time at different sites where the jobs are being performed using different machines (medium). Multi objective assignment problem or multi objective generalized assignment problem have been solved in different ways by different mathematicians. But they have considered only two indices (jobs and alternatives). Here we have considered more than two indices and so it becomes a multi-index generalized assignment problem which makes it superior to the previous methods. This type of problem has not been solved earlier by our proposed method. Moreover in this paper Fuzzy Programming Technique has been used considering linear, exponential and hyperbolic (non-linear) membership functions for getting optimal solutions. Finally a real life application has been presented. Keywords: MOMIGAP, FPT 1. Introduction Nowadays the industrial world is very much pro- fessional and its aim is to achieve the maximum profit out of minimum investment. To reach this goal, optimization is the most innovative way and research is going on, on a large scale in this field. For a real life Assignment Problem (AP) or Gen- eralized Assignment Problem (GAP), optimization depends on the cost, time, efficiency etc. of a worker who is being assigned for the job. The optimization model can be formulated in various ways for real life assignment problems. Multi Objective Assignment Problem (MOAP) or Multi Objective Generalized Assignment Problem (MOGAP) can be structured in ∗ Corresponding author. Supriya Kar, Research Scholar, National Institute of Technology, Mahatma Gandhi Avenue, Durgapur-713209, West Bengal, India. E-mail: supriyakar1234@ gmail.com. Linear Programming Problem (LPP) form so that the objective functions such as job cost, time etc. are min- imized. Also there are different algorithms for solving AP or GAP but in real life, Decision Makers (DM) do not have exact and complete information for the required parameters. The conventional approaches are applicable for crisp numbers and so unable to satisfy the need of the DMs. To overcome this prob- lem, the data for the objective functions are taken as fuzzy numbers, interval-valued fuzzy numbers, intu- itionistic fuzzy numbers, hesitant fuzzy numbers etc. This paper involves two objective functions (cost and time) and four indeces (jobs, alternatives, machines, sites). Many researchers have already proposed different methods to solve a single objective AP [1–8] and GAP [9–13]. For solving MOAP, Chiao-Pin Bao et al. [14] used 0-1 programming method to translate a MOAP into a LPP form. De and Bharti Yadav [15] solved 1064-1246/17/$35.00 © 2017 – IOS Press and the authors. All rights reserved