Title: Multi-objective unbalanced assignment problem with restriction of jobs to agents via NSGA-II

Authors: Amiya Biswas; Asoke Kumar Bhunia; Ali Akbar Shaikh

Addresses: Department of Mathematics, A.B.N. Seal College, Cooch Behar-736101, India ' Department of Mathematics, The University of Burdwan, Burdwan-713104, India ' School of Engineering and Sciences, Tecnológico de Monterrey, Ave. E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, Nuevo León, México

Abstract: In this paper, an approach based on genetic algorithm has been proposed for solving multi-objective unbalanced assignment problems with restriction of job(s) to different agents which may arise due to the inability/poor efficiency of performing certain jobs by some agents dealing with an additional constraint on the maximum number of jobs that can be performed by an agent. As the cost and time are considered as the most important factors for managerial decision in economic/industrial establishments, so here the total cost of assignment of jobs to agents and the total time of completion of jobs by the agents are considered as the two prime objectives. This gives rise to an NP-hard 0-1 programming problem and to solve this problem, we have equipped NSGA-II with a newly developed crossover having the capability of repairing infeasible solution and two new mutation schemes. Also, for comparison of the results obtained from this algorithm, some other variants of this algorithm with existing crossover and mutation schemes have been considered. Finally, to illustrate the performance of proposed approach, a set of test problems have been solved and the results have been analysed for different variants of NSGA-II and some potential future research directions has been discussed.

Keywords: multi-objective optimisation; unbalanced assignment problem; UNB-AP; genetic algorithm; non-dominated sorting; Pareto-optimal solution.

DOI: 10.1504/IJMOR.2018.092967

International Journal of Mathematics in Operational Research, 2018 Vol.13 No.1, pp.107 - 127

Received: 04 Mar 2016
Accepted: 09 Dec 2016
Published online: 04 Jul 2018 *

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