Abstract
This paper investigates a parallel-machine group scheduling problem where non-identical jobs with arbitrary sizes and inclusive processing set restrictions can be either processed on in-house parallel machines in the form of serial batch or outsourced with cost. The objective of our study is aimed at minimizing the weighted sum of the in-house makespan and the total outsourcing cost for a platform manufacturing enterprise. Some structural properties are identified for the optimal solution in some special cases of the studied problem, which contribute to the optimal solution for the studied problem. Further, based on these properties, a novel hybrid algorithm VNS–NKEA is proposed to solve the studied problem, which integrates neighborhood knowledge-based evolutionary algorithm (NKEA) and variable neighborhood search (VNS). To demonstrate the better performance including solution quality and the convergence speed of the proposed algorithm, computational experiments are conducted to evaluate its performance by comparing with other proposed algorithms. The experiment results show that the hybrid algorithm performs quite better than other compared algorithms for each instance, which reflect that the hybrid algorithm can solve the studied problem effectively.
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References
Ikura, Y., Gimple, M.: Efficient scheduling algorithms for a single batch processing machine. Oper. Res. Lett. 5(2), 61–65 (1986)
Uzsoy, R.: Scheduling a single batch processing machine with non-identical job sizes. Int. J. Prod. Res. 32(7), 1615–1635 (1994)
Dupont, L., Ghazvini, F.J.: Minimizing makespan on a single batch processing machine with non-identical job sizes. J. Eur. Syst. Autom. 32(4), 431–440 (1998)
Liu, P., Zhou, X., Tang, L.: Two-agent single-machine scheduling with position-dependent processing times. Int. J. Adv. Manuf. Technol. 48(1–4), 325–331 (2010)
Tang, L., Zhao, X., Liu, J., Leung, J.Y.T.: Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine. Eur. J. Oper. Res. 263(2), 401–411 (2017)
Ozturk, O., Espinousea, M.L., Mascolo, M.D., Gouin, A.: Makespan minimization on parallel batch processing machines with non-identical job sizes and release dates. Int. J. Prod. Res. 50(20), 6022–6035 (2012)
Wang, J.Q., Fan, G.Q., Zhang, Y., Zhang, C.W., Leung, J.Y.: Two-agent scheduling on a single parallel-batching machine with equal processing time and non-identical job sizes. Eur. J. Oper. Res. 258(2), 478–490 (2017)
Cheng, B., Yang, S., Hu, X., Chen, B.: Minimizing makespan and total completion time for parallel batch processing machines with non-identical job sizes. Appl. Math. Model. 36(7), 3161–3167 (2012)
Abedi, M., Seidgar, H., Fazlollahtabar, H., Bijani, R.: Bi-objective optimization for scheduling the identical parallel batch-processing machines with arbitrary job sizes, unequal job release times and capacity limits. Int. J. Prod. Res. 53(6), 1680–1711 (2015)
Damodaran, P., Manjeshwar, P.K., Srihari, K.: Minimizing makespan on a batch-processing machine with non-identical job sizes using genetic algorithms. Int. J. Prod. Econ. 103(2), 882–891 (2006)
Melouk, S., Damodaran, P., Chang, P.Y.: Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing. Int. J. Prod. Econ. 87(2), 141–147 (2004)
Ng, C.T., Cheng, T.C.E., Yuan, J.J., Liu, Z.H.: On the single machine serial batching scheduling problem to minimize total completion time with precedence constraints, release dates and identical processing times. Oper. Res. Lett. 31(4), 323–326 (2003)
Yuan, J.J., Lin, Y.X., Cheng, T.C.E., Ng, C.T.: Single machine serial-batching scheduling problem with a common batch size to minimize total weighted completion time. Int. J. Prod. Econ. 105(2), 402–406 (2007)
Shen, L., Buscher, U.: Solving the serial batching problem in job shop manufacturing systems. Eur. J. Oper. Res. 221(1), 14–26 (2012)
Browne, S., Yechiali, U.: Scheduling deteriorating jobs on a single processor. Oper. Res. 38, 495–498 (1990)
Mosheiov, G.: Scheduling jobs under simple linear deterioration. Comput. Oper. Res. 21, 653–659 (1994)
Cheng, T.C.E., Ding, Q.: Single machine scheduling with deadlines and increasing rate of processing times. Acta Inf. 36(9–10), 673–692 (2000)
Mosheiov, G.: Scheduling jobs with step-deterioration: minimizing makespan on a single and multi-machine. Comput. Ind. Eng. 28(4), 869–879 (1995)
Cheng, T.C.E., Ding, Q., Kovalyov, M.Y., Bachman, A., Janiak, A.: Scheduling jobs with piecewise linear decreasing processing times. Nav. Res. Logist. 50, 531–554 (2003)
Sundararaghavan, P.S., Kunnathur, A.S.: Single machine scheduling with start time dependent processing times: some solvable cases. Eur. J. Oper. Res. 79, 394–403 (1994)
Jeng, A.A.K., Lin, B.M.T.: Makespan minimization in single-machine scheduling with step-deterioration of processing times. J. Oper. Res. Soc. 55, 247–256 (2004)
Low, C., Hsu, C., Su, C.: Minimizing the makespan with an availability constraint on a single machine under simple linear deterioration. Comput. Math. Appl. 56, 257–265 (2008)
Layegh, J., Jolai, F., Amalnik, M.S.: A memetic algorithm for minimizing the total weighted completion time on a single machine under step-deterioration. Adv. Eng. Softw. 40, 1074–1077 (2009)
Li, S., Ng, C.T., Cheng, T.C.E., Yuan, J.J.: Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan. Eur. J. Oper. Res. 210, 482–488 (2011)
Pei, J., Liu, X., Pardalos, P.M., Fan, W., Yang, S.: Scheduling deteriorating jobs on a single serial-batching machine with multiple job types and sequence-dependent setup times. Ann. Oper. Res. 249, 175–195 (2017)
Liao, B., Pei, J., Yang, S., Pardalos, P.M., Lu, S.: Single-machine and parallel-machine parallel batching scheduling considering deteriorating jobs, various group, and time-dependent setup time. Informatica 29(2), 281–301 (2018)
Xu, Y.T., Zhang, Y., Huang, X.: Single-machine ready times scheduling with group technology and proportional linear deterioration. Appl. Math. Model. 38, 384–391 (2014)
Wu, C.C., Shiau, Y.R., Lee, W.C.L.: Single-machine group scheduling problems with deterioration consideration. Comput. Oper. Res. 35(5), 1652–1659 (2008)
Wang, J.B., Huang, X., Wu, Y.B., Ji, P.: Group scheduling with independent setup times, ready times, and deteriorating job processing times. Int. J. Adv. Manuf. Technol. 60, 643–649 (2012)
Wu, C.C., Lee, W.C.: Single-machine group-scheduling problems with deteriorating setup times and job-processing times. Int. J. Prod. Econ. 115, 128–133 (2008)
Wang, J.B., Gao, W.J., Wang, L.Y., Wang, D.: Single machine group scheduling with general linear deterioration to minimize the makespan. Int. J. Adv. Manuf. Technol. 43, 146–150 (2009)
Nomden, G., van der Zee, D.J.: Virtual cellular manufacturing: configuring routing flexibility. Int. J. Prod. Econ. 112, 439–451 (2008)
Rustogi, K., Strusevich, V.A.: Simple matching vs linear assignment in scheduling models with positional effects: a critical review. Eur. J. Oper. Res. 222, 393–407 (2012)
Hwang, H.C., Chang, S.Y., Lee, K.: Parallel machine scheduling under a grade of service provision. Comput. Oper. Res. 31(12), 2055–2061 (2004)
Li, C., Li, Q.: Scheduling jobs with release dates, equal processing times, and inclusive processing set restrictions. J. Oper. Res. Soc. 66(3), 516–523 (2015)
Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: Sequencing and scheduling: algorithms and complexity. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P.H. (eds.) Logistics of Production and Inventory, pp. 445–522. North Holland, Amsterdam (1993)
Li, C.L., Wang, X.: Scheduling parallel machines with inclusive processing set restrictions and job release times. Eur. J. Oper. Res. 200(3), 702–710 (2010)
Wu, J.Z., Chien, C.F., Gen, M.: Coordinating strategic outsourcing decisions for semiconductor assembly using a bi-objective genetic algorithm. Int. J. Prod. Res. 50(1), 235–260 (2012)
Yadav, V., Gupta, R.K.: A paradigmatic and methodological review of research in outsourcing. Inf. Resour. Manag. J. 21(1), 27–43 (2008)
Gonzalez, R., Gasco, J., Llopis, J.: Information systems outsourcing: a literature analysis. Inf. Manag. 43(7), 821–834 (2006)
Qi, X.: Coordinated logistics scheduling for in-house production and outsourcing. IEEE Trans. Autom. Sci. Eng. 5, 188–192 (2008)
Ruiz-Torres, A.J., Ho, J.C., López, F.J.: Generating Pareto schedules with outsource and internal parallel resources. Int. J. Prod. Econ. 103(2), 810–825 (2006)
Qi, X.: Two-stage production scheduling with an option of outsourcing from a remote supplier. J. Syst. Sci. Syst. Eng. 18(1), 1–15 (2009)
Neto, R.F.T., Filho, M.G., Silva, F.M.: An ant colony optimization approach for the parallel machine scheduling problem with outsourcing allowed. J. Intell. Manuf. 26(3), 527–538 (2015)
Pei, J., Liu, X., Pardalos, P.M., Athanasios, M., Shanlin, Y.: Serial-batching scheduling with time-dependent setup time and effects of deterioration and learning on a single-machine. J. Global Optim. 67(1–2), 251–262 (2017)
Fan, W., Pei, J., Liu, X., Pardalos, P.M., Kong, M.: Serial-batching group scheduling with release times and the combined effects of deterioration and truncated job-dependent learning. J. Global Optim. 71(1), 147–163 (2018)
Pei, J., Cheng, B., Liu, X., Pardalos, P.M., Kong, M.: Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time. Ann. Oper. Res. (2017). https://doi.org/10.1007/s10479-017-2481-8
Pei, J., Liu, X., Liao, B., Pardalos, P.M., Kong, M.: Single-machine scheduling with learning effect and resource-dependent processing times in the serial-batching production. Appl. Math. Model. 58, 245–253 (2017)
Pei, J., Liu, X., Fan, W., Pardalos, P.M., Lu, S.: A hybrid BA–VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers. Omega (2017). https://doi.org/10.1016/j.omega.2017.12.003
Liu, X., Lu, S., Pei, J., Pardalos, P.M.: A hybrid VNS–HS algorithm for a supply chain scheduling problem with deteriorating jobs. Int. J. Prod. Res. (2017). https://doi.org/10.1080/00207543.2017.1418986
Pei, J., Wang, X., Fan, W., Pardalos, P.M.: Scheduling step-deteriorating jobs on bounded parallel-batching machines to maximise the total net revenue. J. Oper. Res. Soc. (2018). https://doi.org/10.1080/01605682.2018.1464428
Ma, C., Kong, M., Pei, J., Pardalos, P.M.: BRKGA–VNS for parallel-batching scheduling on a single machine with step-deteriorating jobs and release times. In: International Workshop on Machine Learning, Optimization, and Big Data, pp. 414–425. Springer, Cham (2017)
Pei, J., Liu, X., Pardalos, P.M., Fan, W., Wang, L., Yang, S.: Solving a supply chain scheduling problem with non-identical job sizes and release times by applying a novel effective heuristic algorithm. Int. J. Syst. Sci. 47(4), 765–776 (2016)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 5, 287–326 (1979)
Lee, I.S., Sung, C.S.: Single machine scheduling with outsourcing allowed. Int. J. Prod. Econ. 111, 623–634 (2008)
Dupont, L., Dhaenens-Flipo, C.: Minimizing the makespan on a batch machine with non-identical job sizes: an exact procedure. Comput. Oper. Res. 29, 807–819 (2002)
Wen, Y., Xu, H., Yang, J.: A heuristic-based hybrid genetic-variable neighborhood search algorithm for task scheduling in heterogeneous multiprocessor system. Inf. Sci. 181(3), 567–581 (2011)
Duarte, A., Pantrigo, J.J., Pardo, E.G., Mladenović, N.: Multi-objective variable neighborhood search: an application to combinatorial optimization problems. J. Global Optim. 63(3), 515–536 (2015)
Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)
Hansen, P., Mladenović, N., Pérez, J.A.M.: Variable neighbourhood search: methods and applications. 4OR Q. J Oper. Res. 6(4), 319–360 (2008)
Mladenović, N., Urošević, D., Ilić, A.: A general variable neighborhood search for the one-commodity pickup-and-delivery travelling salesman problem. Eur. J. Oper. Res. 220(1), 270–285 (2012)
Jarboui, B., Derbel, H., Hanafi, S., Mladenović, N.: Variable neighborhood search for location routing. Comput. Oper. Res. 40(1), 47–57 (2013)
Yu, Z., Wong, H., Wang, D., Wei, M.: Neighborhood knowledge-based evolutionary algorithm for multiobjective optimization problems. IEEE Trans. Evol. Comput. 15(6), 812–830 (2011)
Lei, D.: Variable neighborhood search for two-agent flow shop scheduling problem. Comput. Ind. Eng. 80(C), 125–131 (2015)
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Nos. 71871080, 71601065, 71501058, 71690235, 71231004), and Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), and Base of Introducing Talents of Discipline to Universities for Optimization and Decision-making in the Manufacturing Process of Complex Product (111 Project). Panos M. Pardalos is partially supported by the Project of “Distinguished International Professor by the Chinese Ministry of Education” (MS2014HFGY026).
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Liao, B., Song, Q., Pei, J. et al. Parallel-machine group scheduling with inclusive processing set restrictions, outsourcing option and serial-batching under the effect of step-deterioration. J Glob Optim 78, 717–742 (2020). https://doi.org/10.1007/s10898-018-0707-1
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DOI: https://doi.org/10.1007/s10898-018-0707-1