Abstract
This study strives to schedule a just-in-time hybrid flowshop with sequence-dependent setup times by considering two performance measures, namely makespan and sum of the earliness and tardiness, simultaneously. The paper proposes a mixed integer programming model. However, since the simpler case with a single stage and with a single machine per stage is NP-hard, the utilization of the exact algorithms for the real-life problems is limited. Thus, this paper proposes a novel solving algorithm with a weighted L p -metric-based framework. Since the particle swarm optimization is originally designed for continuous solution space, in this study, we modify the particle position based on our representation so that a particle position is decoded into a schedule using the largest processing time algorithm, Hadamard product, and swap operator. Furthermore, we apply a variable neighborhood search and a tabu search to improve the solution quality. This hybridization which combines the advantages of the individual components is the key innovative aspect of the approach. We investigate the performance of our algorithm in the comparison with several algorithms and show that it has a good performance.
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References
Adenso-Diaz B (1996) An SA/TS mixture algorithm for the scheduling tardiness problem. Eur J Oper Res 88:516–524
Ahmed MU, Sundararaghavan PS (1990) Minimizing the weighted sum of late and early completion penalties in a single machine. IIE Trans 22(3):288–290
Ai TJ, Kachitvichyanukul V (2009) Particle swarm optimization and two solution representations for solving the capacitated vehicle routing problem. Comput Ind Eng 56(1):380–387
Allahverdi A, Ng CT, Cheng TCE, Kovalyov MY (2008) A survey of scheduling problems with setup times or costs. Eur J Oper Res 187:985–1032
Allaoui H, Artiba A (2004) Integrating simulation and optimization to schedule a hybrid flow shop with maintenance constraints. Comput Ind Eng 47:431–450
Baker KR, Scudder DG (1989) Sequencing with earliness and tardiness penalties: a review. Oper Res 38(1):22–36
Behnamian J, Fatemi Ghomi SMT, Zandieh M (2009) A multi-phase covering Pareto-optimal front method to multi-objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic. Expert Syst Appl 36(8):11057–11069
Bertel S, Billaut JC (2004) A genetic algorithm for an industrial multiprocessor flow shop scheduling problem with recirculation. Eur J Oper Res 159(3):651–662
Brah SA (1996) A comparative analysis of due date based job sequencing rules in a flow shop with multiple processors. Prod Plan Control 7(4):362–373
Chankong V, Haimes YY (1983) Multi objective decision making theory and methodology. Elsevier Science, New York
Choi H-S, Lee D-H (2007) A branch and bound algorithm for two-stage hybrid flow shops: minimizing the number of tardy jobs. J Korean Inst Ind Eng 33:213–220
Figielska E (2009) A genetic algorithm and a simulated annealing algorithm combined with column generation technique for solving the problem of scheduling in the hybrid flowshop with additional resources. Comput Ind Eng 56(1):142–151
Figielska E (2010) Heuristic algorithms for preemptive scheduling in a two-stage hybrid flowshop with additional renewable resources at each stage. Comput Ind Eng 59(4):509–519
Glover F, McMillan C (1986) The general employee scheduling problem: an integration of MS and AI. Comput Oper Res 13(5):563–573
Hu X, Eberhart RC, Shi Y (2003) Swarm intelligence for permutation optimization: a case study on n-queens problem. Proceedings of the IEEE Swarm Intelligence Symposium, Indianapolis, Indiana, USA, pp. 243–246
Janiak A, Kozan E, Lichtenstein M, Oguz C (2007) Metaheuristic approaches to the hybrid flowshop scheduling problem with a cost-related criterion. Int J Prod Econ 105:407–424
Jungwattanakit J, Reodecha M, Chaovalitwongse P, Werner F (2008) Algorithms for flexible flowshop problems with unrelated parallel machines, setup times, and dual criteria. Int J Adv Manuf Technol 37:354–370
Jungwattanakit J, Reodecha M, Chaovalitwongse P, Werner F (2005) An evaluation of sequencing heuristics for flexible flowshop scheduling problems with unrelated parallel machines and dual criteria. Otto-von-Guericke-Universitat Magdeburg, Preprint 28/05, 1–23
Kashan AH, Karimi B (2009) A discrete particle swarm optimization algorithm for scheduling parallel machines. Comput Ind Eng 56(1):216–223
Kennedy J, Eberhart RC (1995) Particle swarm optimization. In Proceedings of the IEEE international conference on neural networks, Perth, Australia, pp. 1942–1948
Król D, Drożdżowski M (2010) Use of MaSE methodology for designing a swarm-based multi-agent system. J Intell Fuzzy Syst 21(3):221–231
Kurz ME, Askin RG (2003) Comparing scheduling rules for flexible flow lines. Int J Prod Econ 85:371–388
Lee GC, Kim YD, Choi SW (2004) Bottleneck-focused scheduling for a hybrid flowshop. Int J Prod Res 42(1):165–181
Liu B, Wang L, Jin Y-J (2007) An effective hybrid particle swarm optimization for no-wait flow shop scheduling. Int J Adv Manuf Technol 31:1001–1011
M’Hallah R (2007) Minimizing total earliness and tardiness on a single machine using a hybrid heuristic. Comput Oper Res 34:3126–3142
Mladenovic N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24:1097–1100
Naderi B, Zandieh M, Aminnayeri M (2011) Incorporating periodic preventive maintenance into flexible flowshop scheduling problems. Appl Soft Comput 11(2):2094–2101
Naderi B, Zandieh M, Roshanaei V (2009) Scheduling hybrid flow shops with sequence dependent setup times to minimize makespan and maximum tardiness. Int J Adv Manuf Technol 41(11–12):1186–1198
Nishi T, Hiranaka Y, Inuiguchi M (2010) Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness. Comput Oper Res 37(1):189–198
Rios-Mercado RZ, Bard JF (1998) Computational experience with a branch-and-cut algorithm for flowshop scheduling with setups. Comput Oper Res 25(5):351–366
Ruiz R, Rodriguez JA (2010) The hybrid flow shop scheduling problem. Eur J Oper Res 205(1):1–18
Sha DY, Hsu C-Y (2006) A hybrid particle swarm optimization for job shop scheduling problem. Comput Ind Eng 51:791–808
Shiau D-F, Huang Y-M (2012) A hybrid two-phase encoding particle swarm optimization for total weighted completion time minimization in proportionate flexible flow shop scheduling. Int J Adv Manuf Technol 58(1–4):339–357
Tasgetiren MF, Liang Y-C, Sevkli M, Gencyilmaz G (2007) A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem. Eur J Oper Res 177:1930–1947
Wang X, Tang L (2009) A tabu search heuristic for the hybrid flowshop scheduling with finite intermediate buffers. Comput Oper Res 36:907–918
Yaurima V, Burtseva L, Tchernykh A (2009) Hybrid flowshop with unrelated machines, sequence-dependent setup time, availability constraints and limited buffers. Comput Ind Eng 56(4):1452–1463
Yin P-Y (2004) A discrete particle swarm algorithm for optimal polygonal approximation of digital curves. J Vis Commun Image Represent 15(2):241–260
Ying K-C (2009) An iterated greedy heuristic for multistage hybrid flowshop scheduling problems with multiprocessor tasks. J Oper Res Soc 60(6):810–817
Zhang H, Li H, Tam CM (2007) Particle swarm optimization for resource-constrained project scheduling. Int J Proj Manag 24:83–92
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Behnamian, J., Fatemi Ghomi, S.M.T. & Zandieh, M. Realistic variant of just-in-time flowshop scheduling: integration of L p -metric method in PSO-like algorithm. Int J Adv Manuf Technol 75, 1787–1797 (2014). https://doi.org/10.1007/s00170-014-6219-3
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DOI: https://doi.org/10.1007/s00170-014-6219-3