Abstract
In this study, we investigate an unrelated parallel batch processing machines scheduling problem (UPBPMSP). A set of jobs with non-identical sizes and arbitrary ready times are scheduled on unrelated parallel batch processing machines with different capacities to minimize the makespan (i.e., the completion time of the last batch). Existing studies have either decomposed the scheduling problem into two sub-problems and employed population-based heuristic interaction for searching the best solutions or used neighborhood search algorithms to search the current solution’s neighborhood to find a better solution. However, the performances of these methods are not quite satisfactory due to the complicated interactions or oversimplified neighborhood search strategies, especially for large-scale UPBPMSPs. In this study, we propose a novel tabu-based adaptive large neighborhood search (TALNS) algorithm to obtain high-quality solutions for the UPBPMSP. To avoid complex interactions, we propose a new solution structure, and the proposed TALNS is applied to obtain the optimal solution structure of the UPBPMSP. Extensive experiments are conducted to evaluate the performance of the proposed algorithm on a total of 360 instances from the literature and 30 new instances. Numerical results demonstrate that the proposed TALNS outperforms the neighborhood search methods, which outperforms the population-based methods. With the proposed TALNS, 55 out of 360 instances’ best-known solutions are updated from this study.
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References
Almeder C, Mönch L (2011) Metaheuristics for scheduling jobs with incompatible families on parallel batching machines. J Oper Res Soc 62(12):2083–2096. https://doi.org/10.1057/jors.2010.186
Arroyo JEC, Leung JYT (2017a) An effective iterated greedy algorithm for scheduling unrelated parallel batch machines with non-identical capacities and unequal ready times. Comput Ind Eng 105:84–100. https://doi.org/10.1016/j.cie.2016.12.038
Arroyo JEC, Leung JYT (2017b) Scheduling unrelated parallel batch processing machines with non-identical job sizes and unequal ready times. Comput Oper Res 78:117–128. https://doi.org/10.1016/j.cor.2016.08.015
Chang PY, Damodaran P, Melouk S (2004) Minimizing makespan on parallel batch processing machines. Int J Prod Res 42(19):4211–4220. https://doi.org/10.1080/00207540410001711863
Chen H, Du B, Huang GQ (2010) Metaheuristics to minimise makespan on parallel batch processing machines with dynamic job arrivals. Int J Comput Integr Manuf 23(10):942–956. https://doi.org/10.1080/0951192x.2010.495137
Cheng BY, Wang Q, Yang SL, Hu XX (2013) An improved ant colony optimization for scheduling identical parallel batching machines with arbitrary job sizes. Appl Soft Comput 13(2):765–772. https://doi.org/10.1016/j.asoc.2012.10.021
Chiang TC, Cheng HC, Fu LC (2010) A memetic algorithm for minimizing total weighted tardiness on parallel batch machines with incompatible job families and dynamic job arrival. Comput Oper Res 37(12):2257–2269. https://doi.org/10.1016/j.cor.2010.03.017
Chung SH, Tai YT, Pearn WL (2009) Minimising makespan on parallel batch processing machines with non-identical ready time and arbitrary job sizes. Int J Prod Res 47(18):5109–5128. https://doi.org/10.1080/00207540802010807
Damodaran P, Chang P (2008) Heuristics to minimize makespan of parallel batch processing machines. Int J Adv Manuf Technol 37(9–10):1005–1013. https://doi.org/10.1007/s00170-007-1042-8
Damodaran P, Vélez-Gallego MC (2012) A simulated annealing algorithm to minimize makespan of parallel batch processing machines with unequal job ready times. Expert Syst Appl 39(1):1451–1458. https://doi.org/10.1016/j.eswa.2011.08.029
Damodaran P, Vélez-Gallego MC, Maya J (2009) A GRASP approach for makespan minimization on parallel batch processing machines. J Intell Manuf 22(5):767–777. https://doi.org/10.1007/s10845-009-0272-z
Damodaran P, Diyadawagamage DA, Ghrayeb O, Vélez-Gallego MC (2011) A particle swarm optimization algorithm for minimizing makespan of nonidentical parallel batch processing machines. Int J Adv Manuf Technol 58(9–12):1131–1140. https://doi.org/10.1007/s00170-011-3442-z
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197. https://doi.org/10.1109/4235.996017
Fowler JW, Mönch L (2021) A survey of scheduling with parallel batch (p-batch) processing. Eur J Oper Res 298(1):1–24. https://doi.org/10.1016/j.ejor.2021.06.012
Garey MR, Johnson DS (1979) A GUIDE to the theory of NP-completeness. Computers and intractability. W. H. Freeman, San Francisco
Jia ZH, Leung JYT (2015) A meta-heuristic to minimize makespan for parallel batch machines with arbitrary job sizes. Eur J Oper Res 240(3):649–665. https://doi.org/10.1016/j.ejor.2014.07.039
Jia ZH, Li K, Leung JYT (2015) Effective heuristic for makespan minimization in parallel batch machines with non-identical capacities. Int J Prod Econ 169:1–10. https://doi.org/10.1016/j.ijpe.2015.07.021
Jia ZH, Li XH, Leung JYT (2017) Minimizing makespan for arbitrary size jobs with release times on P-batch machines with arbitrary capacities. Futur Gener Comput Syst 67:22–34. https://doi.org/10.1016/j.future.2016.07.017
Kashan AH, Karimi B, Jenabi M (2008) A hybrid genetic heuristic for scheduling parallel batch processing machines with arbitrary job sizes. Comput Oper Res 35(4):1084–1098. https://doi.org/10.1016/j.cor.2006.07.005
Lausch S, Mönch L (2016). Metaheuristic approaches for scheduling jobs on parallel batch processing machines. In Heuristics, Metaheuristics and Approximate Methods in Planning and Scheduling (187–207). Springer, Berlin
Lee CY, Uzsoy R, Martin-Vega LA (1992) Efficient algorithms for scheduling semiconductor burn-in operations. Oper Res 40(4):764–775. https://doi.org/10.1287/opre.40.4.764
Li SG (2017) Approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities. Eur J Oper Res 263(3):815–826. https://doi.org/10.1016/j.ejor.2017.06.021
Li XL, Huang YL, Tan Q, Chen HP (2013) Scheduling unrelated parallel batch processing machines with non-identical job sizes. Comput Oper Res 40(12):2983–2990. https://doi.org/10.1016/j.cor.2013.06.016
Mathirajan M, Sivakumar A, Chandru V (2004) Scheduling algorithms for heterogeneous batch processors with incompatible job-families. J Intell Manuf 15(6):787–803. https://doi.org/10.1023/b:jims.0000042664
Mönch L, Balasubramanian H, Fowler JW, Pfund ME (2005) Heuristic scheduling of jobs on parallel batch machines with incompatible job families and unequal ready times. Comput Oper Res 32(11):2731–2750. https://doi.org/10.1016/j.cor.2004.04.001
Muter İ (2020) Exact algorithms to minimize makespan on single and parallel batch processing machines. Eur J Oper Res 285(2):470–483. https://doi.org/10.1016/j.ejor.2020.01.065
Ozturk O, Begen MA, Zaric GS (2016) A branch and bound algorithm for scheduling unit size jobs on parallel batching machines to minimize makespan. Int J Prod Res 55(6):1815–1831. https://doi.org/10.1080/00207543.2016.1253889
Pinedo ML (2012) Scheduling: Theory, Algorithms and Systems, 3rd edn. Springer Science+Business Media Prentice-Hall, Upper Saddle River, NJ
Ropke S, Pisinger D (2006) An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transp Sci 40(4):455–472. https://doi.org/10.1287/trsc.1050.0135
Shaw P (1997) A new local search algorithm providing high quality solutions to vehicle routing problems. Dept of Computer Science, University of Strathclyde, APES Group, Glasgow, Scotland, UK
Sung CS, Choung YI (2000) Minimizing makespan on a single burn-in oven in semiconductor manufacturing. Eur J Oper Res 120(3):559–574. https://doi.org/10.1016/S0377-2217(98)00391-9
Tang M, Ji B, Fang XP, Yu SS (2022) Discretization-strategy-based solution for berth allocation and quay crane assignment problem. J Marine Sci Eng 10(4):495. https://doi.org/10.3390/jmse10040495
Trindade RS, de Araújo OCB, Fampa MHC, Müller FM (2018) Modelling and symmetry breaking in scheduling problems on batch processing machines. Int J Prod Res 56(22):7031–7048. https://doi.org/10.1080/00207543.2018.1424371
Trindade RS, de Araújo OCB, Fampa M (2021) Arc flow approach for single batch-processing machine scheduling. Comput Oper Res 134:105394. https://doi.org/10.1016/j.cor.2021.105394
Uzsoy R (1994) Scheduling a single batch processing machine with non-identical job sizes. Int J Prod Res 32(7):1615–1635. https://doi.org/10.1080/00207549408957026
Wang HM, Chou FD (2010) Solving the parallel batch-processing machines with different release times, job sizes, and capacity limits by metaheuristics. Expert Syst Appl 37(2):1510–1521. https://doi.org/10.1016/j.eswa.2009.06.070
Xu SB, Bean JC (2007). A genetic algorithm for scheduling parallel non-identical batch processing machines. Paper presented at the 2007 In: IEEE Symposium on Computational Intelligence in Scheduling
Zehra F, Javed M, Khan D, Pasha M (2020) Comparative analysis of C++ and Python in terms of memory and time. doi:https://doi.org/10.20944/preprints202012.0516.v1
Acknowledgements
This work was supported by National Natural Science Foundation of China under Grant No. 72001216, Natural Science Foundation of Hunan Province, China under Grant No. 2020JJ5780, Central South University under Grant No. 202045007.
Funding
National Natural Science Foundation of China, 72001216, Bin Ji, Natural Science Foundation of Hunan Province, 2020JJ5780, Bin Ji, Central South University, 202045007, Bin Ji
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Xiao, X., Ji, B., Yu, S.S. et al. A tabu-based adaptive large neighborhood search for scheduling unrelated parallel batch processing machines with non-identical job sizes and dynamic job arrivals. Flex Serv Manuf J (2023). https://doi.org/10.1007/s10696-023-09488-9
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DOI: https://doi.org/10.1007/s10696-023-09488-9