Solving Three Objectives Single-Machine Scheduling Problem Using Fuzzy Multi-Objective Linear Programming
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Abstract
In this paper, three criteria scheduling problem of n jobs on a single machine is considered. Each of these n jobs is to be processed without interruption and becomes available for processing at time zero. The problem is to minimize three objectives simultaneously, which are the completion time, maximum tardiness, and maximum earliness. Here, we develop a fuzzy multi-objective linear programming (FMOLP) model for solving multi-objective scheduling problem in a fuzzy environment by using piecewise linear membership function (PLMF). A numerical example demonstrates the feasibility of applying the proposed model to scheduling problem, and yields a compromised solution to help the decision maker’s overall levels of satisfaction. The algorithm is tested to show the ability of applying this model to three criteria.
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References
[1] Nearchou, A. (2018). Multicriteria scheduling optimization using an elitist multiobjective population heuristic: the h-NSDE algorithm. Journal of Heuristics, 24(6):817-851.
[2] Sule, D. R. (1997). Industrial Scheduling, PWC Publishing Company.
[3] Tavakkoli-Moghaddam, R. et al. (2010). The use of a fuzzy multi-objective linear programming for solving a multi-objective single-machine scheduling problem. Applied Soft Computing, 10: 919–925.
[4] Loukil, T.; Teghem, J. and Tuyttens, D. (2005). Solving multi-objective production scheduling problems using meta-heuristics. European Journal of Operational Research, 161: 42–61.
[5] Murata, T.; Ishibuchi, H. and Tanaka, H. (1996). Multi-objective genetic algorithm and its applications to flow shop scheduling. Comput. Ind. Eng., 30 (4): 957–968.
[6] Toktas, B.; Azizoglu, M. and Koksalan, S.K. (2004). Two-machine flow shop scheduling with two criteria: maximum earliness and makespan. Eur. J. Oper. Res., 157:286–295.
[7] Lee, H.T.; Chen, S.H. and Kang, H.Y. (2002). Multi-criteria scheduling using fuzzy theory and tabu search. International Journal of Production Research, 40 (5):1221–1234.
[8] Adamopoulos, G.I. and Pappis, C.P. (1996). A fuzzy linguistic approach to a multi-criteria sequencing problem. European Journal of Operational Research, 92:628–636.
[9] Ishi, H. and Tada, M. (1995). Single machine scheduling problem with fuzzy precedence relation. European Journal of Operational Research, 87:284–288.
[10] Chanas, S. and Kasperski, A. (2003). On two single machine scheduling problems with fuzzy processing times and fuzzy due dates. European Journal of Operational Research, 147:281–296.
[11] Chanas, S. and Kasperski, A. (2004). Possible and necessary optimality of solutions in the single machine scheduling problem with fuzzy parameters. Fuzzy Sets and Systems, 142:359–371.
[12] Toktas, B.; Azizoglu, M. and Koksalan, S.K. (2004).Two-machine flow shop scheduling with two criteria: maximum earliness and makespan. Eur. J. Oper. Res, 157:286–295.
[13] Huo, Y.; Leung, J.Y. -T. and Zhao, H. (2007). Bi-criteria scheduling problems: number of tardy jobs
and maximum weighted tardiness. European Journal of Operational Research, 177 (1):116–134.
[14] Tavakkoli-Moghaddam, R.; Javadi, B. and Safaei, N. (2006). Solving a mixed-integer model of a single machine scheduling problem by a fuzzy goal programming approach. Wseas Transactions on Business and Economics, 3 (2):45–52.
[15] Zimmermann, H.J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1: 45–56.
[16] Zimmermann, H.J. (1976). Description and optimization of fuzzy systems. Int. J. Gen. Systems, 2: 209–215.
[17] Bellman, R.E. and Zadeh, L.A. (1970). Decision-making in a fuzzy environment. Management Science, 17:141–164.
[18] Hannan, E.L. (1981). Linear programming with multiple fuzzy goals. Fuzzy Sets and Systems, 6: 235–248.
[19] Leberling, H. (1981). On finding compromise solutions in multicriteria problems using the fuzzy min-operator. Fuzzy Sets and Systems, 6: 105–118.
[20] Luhandjula, M.K. (1982). Compensatory operators in fuzzy programming with multiple objectives. Fuzzy Sets and Systems, 8:245–252.
[21] Sakawa, M. (1988). An interactive fuzzy satisfying method for multiobjective linear fractional programming problems. Fuzzy Sets and Systems, 28: 129–144.
[22] Jawad, A. A.; Ali, F. H. and Hasanain, W. S. (2020). Using heuristic and branch and bound methods to solve a multi-criteria machine scheduling problem. Iraqi Journal of Science, 61(8): 2055-2069.
[23] Ali, F. H. and Jawad, A. A. (2020). Minimizing the total completion time and total earliness time functions for a machine scheduling problem using local search methods. Iraqi Journal of Science, Special Issue: 126-133.
[24] Cheachan, H.Ch. and Kadhim, (2021). M.T. Exact method for solving single machine scheduling problem under fuzzy due date to minimize multi-objective functions. Ibn Al-Haitham International Conference for Pure and Applied Sciences (IHICPS), Journal of Physics: Conference Series 1879, 022126 IOP Publishing doi:10.1088/1742-6596/1879/2/022126.
[25] Chachan, H. A. and Hameed, A. S. (2019). Exact methods for solving multi-objective problem on single machine scheduling. Iraqi Journal of Science, 60(8): 1802-1813.
[26] Aneed, J. S. (2013). Minimizing three Simultaneous Criteria in Machine Scheduling Problem. Thesis, university of Thi-Qar, Thi-Qar,Iraq.
[27] Hassan, D., Amiri, N. and Ramadan, A., 2022. A heuristic approach to minimize three criteria using efficient solutions. Indonesian Journal of Electrical Engineering and Computer Science, 26(1), p.334.