Fuzzy Multi-objective Permutation Flow Shop Scheduling Problem with Fuzzy Processing Times under Learning and Aging Effects

Document Type : Research Paper

Authors

Kharazmi University

Abstract

In industries machine maintenance is used in order to avoid untimely machine fails as well as to improve production effectiveness. This research regards a permutation flow shop scheduling problem with aging and learning effects considering maintenance process. In this study, it is assumed that each machine may be subject to at most one maintenance activity during the planning horizon. The objectives aim to minimize the makespan, tardiness of jobs, tardiness cost while maximizing net present value, simultaneously. Due to complexity and Np-hardness of the problem, two Pareto-based multi-objective evolutionary algorithms including non-dominated ranked genetic algorithm (NRGA) and non-dominated sorting genetic algorithm (NSGA-II) are proposed to attain Pareto solutions. In order to demonstrate applicability of the proposed methodology, a real-world application in polymer manufacturing industry is considered.

Keywords


Aiello.,G,  La Scalia,G., Enea, M. (2013). A nondominated ranking Multi Objective Genetic Algorithm and electre method for unequal area facility layout problems. Expert Systems with Applications, 40, 4812–4819.
Alaghebandha, M., Hajipour, V. (2013). A soft computing-based approach to optimise queuing inventory control problem. International Journal of Systems Science. doi.org/10.1080/00207721.2013.809614.
Chang  PC.,  Chen  SH.,  Mani  V.  (2009).  A note on due-date assignment and single machine scheduling with a learning/aging effect. International Journal of Production Economics 117:142–149.
Cheng TCE, Lee WC, Wu CC. (2010). Single-machine scheduling with deteriorating functions for job processing times, 34:4171–4178.
Chinyao Low, Wen-Yi Lin. (2011). Minimizing the total completion time in a single-machine scheduling problem with a learning effect. Applied Mathematical Modelling, 35, 1946–1951.
Dirk Biskup. (2008). A state-of-the-art review on scheduling with learning effects. European Journal of Operational Research, 188, 315–329.
Dirk Biskup. (1999). Single-machine scheduling with learning considerations. European Journal of Operational Research, 115, 173-178.
Eren,  T,  Guner,  E.  (2008)  A  bicriteria  flow  shop  scheduling  with  a  learning  effect.  Applied Mathematical Modelling, 32, 1719-1733.
Ghemawat P (1985) Building strategy on the experience curve – a venerable management tool remains valuable – in the right circumstances. HarvBus Rev, 63:143–149.
GawiejnowiczS. (1996). A note on scheduling on a single processorwith speed dependent on a number of executed jobs. Information Processing Letters 57, 297-300.
Hyun, C. J., Kim, Y., & Kin, Y. K. (1998). A genetic algorithm for multiple objective sequencing problems in mixed model assembly. Computers & Operations Research, 25, 675–690.
Jian-Jun Wang., Bing-Hang Zhang. (2015). Permutation flowshop problems with bi-criterion makespan and total completion time objective and position-weighted learning effects. Computers & Operations Research,  58, Pages 24–31
Jian-Jun Wang., Ya-Jing Liu. (2014). Single-machine bicriterion group scheduling with deteriorating setup times and job processing times. Applied Mathematics and Computation, 242, 309–314.
Kalyanmoy, Deb., Pratap, A., Agarwal, S., Meyarivan, T. (2002). A Fast Elitist Multi objective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2):182 – 197.
Karimi, N., Zandieh, M., Karamooz, HR. (2010). Bi-objective group scheduling in hybrid flexible flowshop: a multi-phase approach, 37:4024–4032.
Kuo WH,. Yang DL. (2006a). Minimizing the makespan in a single machine scheduling problem with a time-based learning effect. Inf Process Lett, 97:64–67.
Kuo  WH,.  Yang  DL.  (2006b).  Minimizing  the  total  completion  time  in  a  single-machine scheduling problem with a time dependent learning effect. European Journal of Operational Research, 174:1184–1190.
Lai PJ, Lee WC. (2011). Single-machine scheduling with general sum-of-processing-time-based and position-based learning effects. OMEGA The International Journal Manage S, 39:467–471.
L.A. Zadeh. (1965). Fuzzy Sets, Information and control, 8, 3, 338–353.
Lee WC,. Wu CC. (2004). Minimizing total completion time in a two-machine flow shop with a learning effect. International Journal of Production Economics, 88:85–93.
Lee, W-C.,  Yeh, W-C., Chung Y-H. (2014). Total tardiness minimization in permutation flowshop with deterioration consideration, Applied Mathematical Modelling,  38, 13.
Liu  P.,  Zhou  X.,  Tang  L,  (2010).  Two-agent  single-machine  scheduling  with  position-dependent processing times. The International Journal of Advanced Manufacturing Technology, 48:325–331.
Moradi, H., Zandieh, M., Mahdavi, I. (2011). Non-dominated ranked genetic algorithm for a multi-objective mixed-model assembly line sequencing problem. International Journal of Production Research, 49, 12, 3479–3499.
Murata, T., Ishibuchi, H., & Tanaka, H. (1996) Multi-objective genetic algorithm and its application to flow shop scheduling. Computers & Industrial Engineering, 30, 957–968.
Pei-Chann Chang, Shih-Hsin Chen, V. Mani (2009) A note on due-date assignment and single machine scheduling with a learning/aging effect. The International Journal Production Economics 117, 142–149.
Peng-Jen Lai, Wen-Chiung Lee. (2011). Single- machine scheduling with general sum-of-processing-time-based and position-based learning effects. Omega, 39, 467–471.
Rahmati, S.H.A. (2012). Proposing a Pareto-based Multi-Objective Evolutionary Algorithm to Flexible Job Shop Scheduling Problem. World Academy of Science, Engineering and Technology, 61: 1160-1165.
Reddy, V., & Narendran, T. T. (2003) Heuristics for scheduling sequence dependent set-up jobs in flow line cells. International Journal of Production Research, 41(1), 193–206.
Rostami, M., Ebrahimzadeh Pilerood, A.,   Mahdavi Mazdeh, M. (2015). Multi-objective parallel machine scheduling problem with job deterioration and learning effect under fuzzy environment. Computers & Industrial Engineering,  85, Pages 206–215.
Rostami, M.,  Kheirandish, O., Ansari, N. (2015). Minimizing maximum  tardiness and delivery costs with batch delivery and job release times. Appl. Math. Modelling, http://dx.doi.org/10.1016/j.apm.2015.03.052.
Rudek, A., Rudek, R. (2012). On flow shop scheduling problems with aging effect and resource allocation. International Journal of Advanced Manufacturing Technology, 62, 135-145.
Safari., J. (2011) A NSGA II for a Multi-objectives Redundancy Allocation Problem. World Academy of Science, Engineering and Technology, 78: 1319-1325.
Schott JR. (1995). Fault tolerant design using single and multi-criteria genetic algorithms optimization. Master's thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA.
Suh-Jenq Yang, Dar-Li Yang. (2010). Minimizing the makespan on single machine scheduling with aging effect and variable maintenance activities. Omega, 38, 528–533.
T.C.E. Cheng, Wen-Hung Kuo, Dar-Li Yang. (2013). Scheduling with a position-weighted learning effect based on sum-of-logarithm-processing-times and job position. Information Sciences, 221, 490–500.
Janiak, A., Rudek, R. (2010). Scheduling jobs under an agingeffect. Journal of the Operational Research Society, 61:1041–1048.
Vahedi-Nouri, B., Fattahi, P., Ramezanian, R. (2013). Minimizing total flow time for the non-permutation flow shop scheduling problem with learning effects and availability constraints, Journal of Manufacturing Systems, 32(1), Pages 167–173.
Wang  JB.,  Wang  LY.,  Wang  D.,  Huang  X.,  Wang  XR . (2009a).  A  note  on  single-machine  total completion time problem with general deteriorating function. The International Journal of Advanced Manufacturing Technology, 44:1213–1218.
Wang  JB.,  Wang  LY.,  Wang  D.,  Wang  XY.  (2009b).  Single machine  scheduling  with  a  time dependent deterioration. The International Journal of Advanced Manufacturing Technology, 43:805–809.
Webb GK. (1994). Integrated circuit (IC) pricing. Journal High Technol Manag, Res, 5:247–260.
Wen-Chiung Lee., Wei-Chang Yeh., Yu-Hsiang Chung. (2014). Total tardiness minimization in permutation flowshop with deterioration consideration. Applied Mathematical Modelling, 38, 3081–3092.
Wen-Hung Kuo, Dar-Li Yang. (2006). Minimizing the makespan in a single machine scheduling problem with a time-based learning effect. Information Processing Letters, 97, 64–67.
Wu,  C.  C.,  Lee,  W.  C.,  Wang,  W.  C.  (2007).  A  two-machine  flow  shop  maximum  tardiness scheduling problem with a learning effect. International Journal of Advanced Manufacturing and Technology, 31, 743-750.
Wu, C. C., Lee, W.C. (2009) A note on the total completion time problem in a permutation flow shop with a learning effect. European Journal of Operational Research, 192, 343-347.
Wilson, A. D., King, R. E., & Hodgson, T. J. (2004). Scheduling non-similar groups on a flow line: Multiple group setups. Robotics and Computer-Integrated Manufacturing, 20, 505–515.
Yeh, W-C., Lai, P-J., Lee W-C., Chuang, M-C. (2014). Parallel-machine scheduling to minimize makespan with fuzzy processing times and learning effects, Information Sciences, 269, 142–158.
Zitzler, E. (1999). Evolutionary Algorithms for Multi-objective Optimization: Methods and Applications. PhD. Thesis, Dissertation ETH No. 13398, Swiss Federal Institute of Technology (ETH), Zürich, Switzerland.