Abstract
In this paper, flexible preventive maintenance (PM) activities are incorporated into two-stage assembly flow shop scheduling where m dedicated machines in the fabrication stage and one machine in the assembly stage. The operational status of each machine is described by a continuous variable, maintenance level. The maintenance level value is inversely proportional to the processing time. Once a PM activity is performed, this value will return to the initial value. Different from the PM at fixed predefined time intervals, flexible PM can be carried out at any time point, but the maintenance levels are not less than 0. Hence, a MILP model with maintenance level constraints is formulated to minimize the total completion time and maintenance time. Regarding the methods, a latest PM decision strategy is proposed to determine the execution time of PM activities. This new strategy is embedded into 15 constructive heuristics and 7 meta-heuristics (three variants of iterated local search, three variants of Q-learning-based ant colony system with local search and a Q-learning-based hyper-heuristics) to address this new problem. The final experimental analysis demonstrates the significance of the integrated model and the effectiveness of the proposed constructive heuristics and meta-heuristics.
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References
Al-Anzi FS, Allahverdi A (2006) A hybrid Tabu search heuristic for the two-stage assembly scheduling problem. Int J Oper Res 3: 109–119
Al-Anzi FS, Allahverdi A (2007) A self-adaptive differential evolution heuristic for two-stage assembly scheduling problem to minimize maximum lateness with setup times. Eur J Oper Res 182: 80–94
Al-Anzi FS, Allahverdi A (2013) An artificial immune system heuristic for two-stage multi-machine assembly scheduling problem to minimize total completion time. J Manuf Syst 32: 825–830
Allahverdi A, Al-Anzi FS (2009) The two-stage assembly scheduling problem to minimize total completion time with setup times. Comput Oper Res 36:2740–2747
Allahverdi A, Aydilek H (2013) The two stage assembly flowshop scheduling problem to minimize total tardiness. J Intell Manuf 26:225–237
Allahverdi A, Aydilek H, Aydilek A (2016) Two-stage assembly scheduling problem for minimizing total tardiness with setup times. Appl Math Model 40:7796–7815
Aydilek A, Aydilek H, Allahverdi A (2017) Minimising maximum tardiness in assembly flowshops with setup times. Int J Prod Res 55:7541–7565
Baykasoglu A, Dereli T (2008) Two-sided assembly line balancing using an ant-colony-based heuristic. Int J Adv Manuf Technol 36:582–588
Blocher JD, Chhajed D (2007) Minimizing customer order lead-time in a two-stage assembly supply chain. Ann Oper Res 161:25–52
Bock S, Briskorn D, Horbach A (2011) Scheduling flexible maintenance activities subject to job-dependent machine deterioration. J Sched 15:565–578
Burke EK, Bykov Y (2008) A late acceptance strategy in hill-climbing for examination timetabling problems. In: Conference on the practice & theory of automated timetabling
Chung TP, Chen F (2019) A complete immunoglobulin-based artificial immune system algorithm for two-stage assembly flowshop scheduling problem with part splitting and distinct due windows. Int J Prod Res 57:3219–3237
El Khoukhi F, Boukachour J, Alaoui AEH (2017) The "Dual-Ants Colony": a novel hybrid approach for the flexible job shop scheduling problem with preventive maintenance. Comput Ind Eng 106: 236–255.
Fattahi P, Hosseini SMH, Jolai F (2013) A mathematical model and extension algorithm for assembly flexible flow shop scheduling problem. Int J Adv Manuf Technol 65:787–802
Fernandez-Viagas V, Framinan JM (2014) A bounded-search iterated greedy algorithm for the distributed permutation flowshop scheduling problem. Int J Prod Res 53:1111–1123
Framinan JM, Perez-Gonzalez P (2017) The 2-stage assembly flowshop scheduling problem with total completion time: efficient constructive heuristic and metaheuristic. Comput Oper Res 88:237–246
Framinan JM, Perez-Gonzalez P, Fernandez-Viagas V (2019) Deterministic assembly scheduling problems: a review and classification of concurrent-type scheduling models and solution procedures. Eur J Oper Res 273:401–417
Jung S, Woo Y-B, Kim BS (2017) Two-stage assembly scheduling problem for processing products with dynamic component-sizes and a setup time. Comput Ind Eng 104:98–113
Kazemi H, Mazdeh MM, Rostami M (2017) The two stage assembly flow-shop scheduling problem with batching and delivery. Eng Appl Artif Intell 63: 98–107
Komaki GM, Teymourian E, Kayvanfar V (2015) Minimising makespan in the two-stage assembly hybrid flow shop scheduling problem using artificial immune systems. Int J Prod Res 54:963–983
Komaki GM, Sheikh S, Malakooti B (2019) Flow shop scheduling problems with assembly operations: a review and new trends. Int J Prod Res 57:2926–2955
Lee IS (2018) Minimizing total completion time in the assembly scheduling problem. Comput Ind Eng 122:211–218
Lee C-Y, Cheng TCE, Lin BMT (1993) Minimizing the makespan in the 3-machine assembly-type flowshop scheduling problem. Manag Sci 39:616–625
Li J-Q, Pan Q-K (2012) Chemical-reaction optimization for flexible job-shop scheduling problems with maintenance activity. Appl Soft Comput 12:2896–2912
Li J-Q, Pan Q-K, Tasgetiren MF (2014) A discrete artificial bee colony algorithm for the multi-objective flexible job-shop scheduling problem with maintenance activities. Appl Math Model 38:1111–1132
Liao C-J, Lee C-H, Lee H-C (2015) An efficient heuristic for a two-stage assembly scheduling problem with batch setup times to minimize makespan. Comput Ind Eng 88:317–325
Lin WC (2018) Minimizing the Makespan for a two-stage three-machine assembly flow shop problem with the sum-of-processing-time based learning effect, Discrete Dynamics in Nature and Society
Minella G, Ruiz R, Ciavotta M (2011) Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems. Comput Oper Res 38:1521–1533
Miyata HH, Nagano MS, Gupta JND (2019) Integrating preventive maintenance activities to the no-wait flow shop scheduling problem with dependent-sequence setup times and makespan minimization. Comput Ind Eng 135:79–104
Mosheiov G, Sarig A, Strusevich VA, Mosheiff J (2018) Two-machine flow shop and open shop scheduling problems with a single maintenance window. Eur J Oper Res 271:388–400
Naderi B, Zandieh M, Aminnayeri M (2011) Incorporating periodic preventive maintenance into flexible flowshop scheduling problems. Appl Soft Comput 11:2094–2101
Navaei J, Ghomi S, Jolai F, Shiraqai ME, Hidaji H (2013) Two-stage flow-shop scheduling problem with non-identical second stage assembly machines. Int J Adv Manuf Technol 69:2215–2226
Navaei J, Ghomi S, Jolai F, Mozdgir A (2014) Heuristics for an assembly flow-shop with non-identical assembly machines and sequence dependent setup times to minimize sum of holding and delay costs. Comput Oper Res 44:52–65
Potts CN, Sevast’janov SV, Strusevich VA, Van Wassenhove LN, Zwaneveld CM (1995) The two-stage assembly scheduling problem: complexity and approximation. Oper Res 43:346–355
Ruiz R, García-Díaz JC, Maroto C (2007) Considering scheduling and preventive maintenance in the flowshop sequencing problem. Comput Oper Res 34: 3314–3330.
Safari E, Jafar Sadjadi S, Shahanaghi K (2009) Scheduling flowshops with condition-based maintenance constraint to minimize expected makespan. Int J Adv Manuf Technol 46: 757–767
Seidgar H, Kiani M, Abedi M, Fazlollahtabar H (2013) An efficient imperialist competitive algorithm for scheduling in the two-stage assembly flow shop problem. Int J Prod Res 52:1240–1256
Seidgar H, Zandieh M, Fazlollahtabar H, Mahdavi I (2016a) Simulated imperialist competitive algorithm in two-stage assembly flow shop with machine breakdowns and preventive maintenance. Proc Inst Mech Eng Part B-J Eng Manuf 230:934–953
Seidgar H, Zandieh M, Mahdavi I (2016b) Bi-objective optimization for integrating production and preventive maintenance scheduling in two-stage assembly flow shop problem. J Ind Prod Eng 33:404–425
Seidgar H, Fazlollahtabar H, Zandieh M (2019) Scheduling two-stage assembly flow shop with random machines breakdowns: integrated new self-adapted differential evolutionary and simulation approach. Soft Computing
Seif J, Dehghanimohammadabadi M, Yu AJ (2019) Integrated preventive maintenance and flow shop scheduling under uncertainty, Flex Serv Manuf J
Shamsaei F, Van Vyve M (2016) Solving integrated production and condition-based maintenance planning problems by MIP modeling. Flex Serv Manuf J 29:184–202
Sheikhalishahi M, Eskandari N, Mashayekhi A, Azadeh A (2019) Multi-objective open shop scheduling by considering human error and preventive maintenance. Appl Math Model 67:573–587
Sung CS, Kim HA (2008) A two-stage multiple-machine assembly scheduling problem for minimizing sum of completion times. Int J Prod Econ 113:1038–1048
Talens C, Fernandez-Viagas V, Perez-Gonzalez P, Framinan JM (2020) New efficient constructive heuristics for the two-stage multi-machine assembly scheduling problem. Comput Ind Eng 140
Torabzadeh E, Zandieh M (2010) Cloud theory-based simulated annealing approach for scheduling in the two-stage assembly flowshop. Adv Eng Softw 41:1238–1243
Tozkapan A, Kırca Ö, Chung C-S (2003) A branch and bound algorithm to minimize the total weighted flowtime for the two-stage assembly scheduling problem. Comput Oper Res 30:309–320
Wang S, Liu M (2014) Two-stage hybrid flow shop scheduling with preventive maintenance using multi-objective tabu search method. Int J Prod Res 52:1495–1508
Wu CC, Wang DJ, Cheng SR, Chung IH, Lin WC (2018a) A two-stage three-machine assembly scheduling problem with a position-based learning effect. Int J Prod Res 56:3064–3079
Wu CC, Chen JY, Lin WC, Lai KJ, Liu SC, Yu PW (2018b) A two-stage three-machine assembly flow shop scheduling with learning consideration to minimize the flowtime by six hybrids of particle swarm optimization. Swarm Evolutionary Comput 41:97–110
Wu CC, Chen JY, Lin WC, Lai K, Bai D, Lai SY (2019) A two-stage three-machine assembly scheduling flowshop problem with both two-agent and learning phenomenon. Comput Ind Eng 130:485–499
Ye H, Wang X, Liu K (2020) Adaptive preventive maintenance for flow shop scheduling with resumable processing. IEEE Trans Autom Sci Eng 1–8
Yokoyama M (2001) Hybrid flow-shop scheduling with assembly operations. Int J Prod Econ 73:103–116
Yokoyama M (2004) Scheduling for two-stage production system with setup and assembly operations. Comput Oper Res 31:2063–2078
Yokoyama M, Santos DL (2005) Three-stage flow-shop scheduling with assembly operations to minimize the weighted sum of product completion times. Eur J Oper Res 161:754–770
Yu AJ, Seif J (2016) Minimizing tardiness and maintenance costs in flow shop scheduling by a lower-bound-based GA. Comput Ind Eng 97:26–40
Zandieh M, Khatami AR, Rahmati SHA (2017) Flexible job shop scheduling under condition-based maintenance: improved version of imperialist competitive algorithm. Appl Soft Comput 58:449–464
Zhang Y, Zhou Z, Liu J (2010) The production scheduling problem in a multi-page invoice printing system. Comput Oper Res 37:1814–1821
Zhang Z, Tang Q, Ruiz R, Zhang L (2020) Ergonomic risk and cycle time minimization for the U-shaped worker assignment assembly line balancing problem: a multi-objective approach. Comput Oper Res 118
Zhang Z, Tang Q, Chica M (2020) Multi-manned assembly line balancing with time and space constraints: a MILP model and memetic ant colony system. Comput Ind Eng
Zhou X, Lu Z, Xi L (2012) Preventive maintenance optimization for a multi-component system under changing job shop schedule. Reliab Eng Syst Saf 101:14–20
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This work is supported by National Natural Science Foundation of China (No. 51875421).
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Appendices
Appendices A: The flowchart of TCK1_PM
Appendix B: The flowcharts of S1_PM, S2_PM and S3_PM
Appendix C The flowcharts of A1_PM and A2_PM
Appendix D: The flowcharts of G1_PM, G2_PM, G3_PM and G4_PM
Appendix E: The flowchart of FAP_PM
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Zhang, Z., Tang, Q. Integrating preventive maintenance to two-stage assembly flow shop scheduling: MILP model, constructive heuristics and meta-heuristics. Flex Serv Manuf J 34, 156–203 (2022). https://doi.org/10.1007/s10696-021-09403-0
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DOI: https://doi.org/10.1007/s10696-021-09403-0