Abstract
The job shop scheduling problem is generally divided into two types according to production environments, the job shop scheduling problem with deterministic processing times and the job shop scheduling problem with uncertain processing times. Regarding the job shop scheduling problem with deterministic processing times, the shop parameters such as processing times are constant throughout the realization of a schedule. In the job shop scheduling problem with uncertain processing times, the actual processing time is uncertain until the operation is completed. In practice, the process may take less or more time than originally scheduled, which makes it a challenging task. In this paper, an approach integrating the artificial immune system into ordinal optimization is designed to look for a near-optimal schedule in a relatively short time. The job shop scheduling problem with uncertain processing times is first formulated as a stochastic constraint optimization problem to minimize the summation of tardiness penalty costs and storage costs. Next, the artificial immune system supported by a rough estimate is adopted to determine a selected subset within a limited computing time. Finally, the optimal computing budget allocation is utilized to look for a near-optimal schedule. The proposed approach is applied to two test examples: the medium-size with six jobs and six machines, and the large size with ten jobs and ten machines. The uncertain processing times are modeled by three probability distributions: truncated normal, exponential, and uniform. Test results demonstrate that the near-optimal schedule obtained by the proposed approach has significant improvements in terms of both efficiency and solution quality.
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Zhang, J.; Ding, G.F.; Zou, Y.S.; Qin, S.F.; Fu, J.L.: Review of job shop scheduling research and its new perspectives under Industry 4.0. J. Intell. Manuf. 30, 1809–1830 (2019)
Gao, K.Z.; Cao, Z.G.; Chang, L.; Chen, Z.H.; Han, Y.Y.; Pan, Q.K.: A review on swarm intelligence and evolutionary algorithms for solving flexible job shop scheduling problems. IEEE-CAA J. Automatic. 6(4), 904–916 (2019)
Baykasoglu, A.; Madenoglu, F.S.; Hamzadayi, A.: Greedy randomized adaptive search for dynamic flexible job-shop scheduling. J. Manuf. Syst. 56, 425–451 (2020)
Sun, L.; Lin, L.; Li, H.J.; Gen, M.S.: Cooperative co-evolution algorithm with an MRF-based decomposition strategy for stochastic flexible job shop scheduling. Mathematics 7(4), 318 (2019)
Haddadzade, M.; Razfar, M.R.; Zarandi, M.H.F.: Integration of process planning and job shop scheduling with stochastic processing time. Int. J. Adv. Manuf. Tech. 71, 241–252 (2014)
Gu, J.W.; Gu, M.H.; Lu, X.W.; Zhang, Y.: Asymptotically optimal policy for stochastic job shop scheduling problem to minimize makespan. J. Comb. Optim. 36, 142–161 (2018)
Turker, A.K.; Aktepe, A.; Inal, A.F.; Ersoz, O.O.; Das, G.S.; Birgoren, B.: A decision support system for dynamic job-shop scheduling using real-time data with simulation. Mathematics 7(3), 278 (2019)
Tamssaouet, K.; Dauzere-Peres, S.; Yugma, C.: Metaheuristics for the job-shop scheduling problem with machine availability constraints. Comput. Ind. Eng. 125, 1–8 (2018)
Yang, X.P.; Gao, X.L.: Optimization of dynamic and multi-objective flexible job-shop scheduling based on parallel hybrid algorithm. Int. J. Simul. Model. 17(4), 724–733 (2018)
Wang, Z.; Zhang, J.H.; Yang, S.X.: An improved particle swarm optimization algorithm for dynamic job shop scheduling problems with random job arrivals. Swarm Evol. Comput. 51, 100594 (2019)
Zadeh, M.S.; Katebi, Y.; Doniavi, A.: A heuristic model for dynamic flexible job shop scheduling problem considering variable processing times. Int. J. Prod. Res. 57(10), 3020–3035 (2019)
Rahmati, S.H.A.; Ahmadi, A.; Govindan, K.: A novel integrated condition-based maintenance and stochastic flexible job shop scheduling problem: simulation-based optimization approach. Ann. Oper. Res. 269, 583–621 (2018)
Lin, L.; Gen, M.: Hybrid evolutionary optimisation with learning for production scheduling: state-of-the-art survey on algorithms and applications. Int. J. Prod. Res. 56(1–2), 193–223 (2018)
Li, D.; Liu, S.L.; Gao, F.R.; Sun, X.: Continual learning classification method with new labeled data based on the artificial immune system. Appl. Soft. Comput. 94, 106423 (2020)
Aldhaheri, S.; Alghazzawi, D.; Cheng, L.; Alzahrani, B.; Al-Barakati, A.: DeepDCA: novel network-based detection of IoT attacks using artificial immune system. Appl. Sci. 10(6), 1909 (2020)
Chou, F.I.; Ho, W.H.; Chen, Y.J.; Tsai, J.T.; Chang, C.W.: Detecting mixed-type intrusion in high adaptability using artificial immune system and parallelized automata. Appl. Sci. 10(5), 1566 (2020)
Sharmila, L.; Sakthi, U.: An artificial immune system-based algorithm for abnormal pattern in medical domain. J. Supercomput. 76, 4272–4282 (2020)
Ho YC, Zhao QC, Jia, QS 2007 Ordinal Optimization: Soft Optimization for Hard Problems. Springer, New York, USA
Ma, T.; Tian, F.; Dong, B.: Ordinal optimization-based performance model estimation method for HDFS. IEEE Access 8, 889–899 (2020)
Liu, A.D.; Luh, P.B.; Bragin, M.A.; Yan, B.: Ordinal-optimization concept enabled decomposition and coordination of mixed-integer linear programming problems. IEEE Robot Autom. Let. 5(4), 5051–5058 (2020)
Xiao, H.; Gao, F.; Lee, L.H.: Optimal computing budget allocation for complete ranking with input uncertainty. IISE Trans. 52(5), 489–499 (2020)
Choi, S.H.; Kim, T.G.: Enhancing the noise robustness of the optimal computing budget allocation approach. IEEE Access 8, 25749–25763 (2020)
Zhang, Q.; Manier, H.; Manier, M.A.: A modified shifting bottleneck heuristic and disjunctive graph for job shop scheduling problems with transportation constraints. Int. J. Prod. Res. 52(4), 985–1002 (2014)
Burdett, R.L.; Kozan, E.: A disjunctive graph model and framework for constructing new train schedules. Eur. J. Oper. Res. 200(1), 85–98 (2010)
Horng, S.C.; Lee, C.T.: Integration of ordinal optimization with ant lion optimization for solving the computationally expensive simulation optimization problems. Appl. Sci. 11(1), 136 (2021)
Horng, S.C.; Lin, S.S.: Coupling elephant herding with ordinal optimization for solving the stochastic inequality constrained optimization problems. Appl. Sci. 10(6), 2075 (2020)
Horng, S.C.; Lin, S.S.: Embedding ordinal optimization into tree–seed algorithm for solving the probabilistic constrained simulation optimization problems. Appl. Sci. 8(11), 2153 (2018)
Horng, S.C.; Lin, S.S.: Bat algorithm supported by ordinal optimization for solving discrete probabilistic bicriteria optimization problems. Math. Comput. Simul. 166, 346–364 (2019)
Chen, C.H.; Lee, L.H.: Stochastic simulation optimization: an optimal computing budget allocation. World Scientific, NJ, USA (2010)
Sule, D.R.: Production Planning and Industrial Scheduling: Examples, Case Studies and Applications, Vol. 2. CRC Press, Boca Raton (2007)
Wisner, J.D.: Operations Management: A Supply Chain Process Approach. SAGE Publications, Calif, LA, USA (2016)
Ryan, T.P.: Sample Size Determination and Power. John Wiley and Sons, New Jersey, NJ, USA (2013)
Abualigah, L.; Diabat, A.; Mirjalili, S.; Abd Elaziz, M.; Gandomi, A.H.: The arithmetic optimization algorithm. Comput. Methods Appl. Mech. Eng. 376, 113609 (2021)
Abualigah, L.; Yousri, D.; Abd Elaziz, M.; Ewees, A.A.; Al-qaness, M.A.A.; Gandomi, A.H.: Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput. Ind. Eng. 157, 107250 (2021)
Abualigah, L.; Diabat, A.; Elaziz, M.A.: Intelligent workflow scheduling for big data applications in IoT cloud computing environments. Cluster Comput. (2021). https://doi.org/10.1007/s10586-021-03291-7
Abd Elaziz, M.; Abualigah, L.; Attiya, I.: Advanced optimization technique for scheduling IoT tasks in cloud-fog computing environments. Future Gener. Comput. Syst. 124, 142–154 (2021)
Abualigah, L.; Diabat, A.: Advances in Sine Cosine algorithm: a comprehensive survey. Artif. Intell. Rev. 54(4), 2567–2608 (2021)
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This research work is supported in part by the Ministry of Science and Technology in Taiwan, R.O.C., under Grant MOST110-2221-E-324-018.
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Horng, SC., Lin, SS. Apply Ordinal Optimization to Optimize the Job-Shop Scheduling Under Uncertain Processing Times. Arab J Sci Eng 47, 9659–9671 (2022). https://doi.org/10.1007/s13369-021-06317-9
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DOI: https://doi.org/10.1007/s13369-021-06317-9