# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2018146

## Application of the preventive maintenance scheduling to increase the equipment reliability: Case study- bag filters in cement factory

 Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Avenue, 15916-34311, Tehran, Iran

* S. M. T. Fatemi Ghomi: Fatemi@aut.ac.ir

Received  June 2017 Revised  May 2018 Published  September 2018

This paper solves a new model of preventive maintenance scheduling with novel methodology. The aim of solving this problem is to determine the period for which bag filter should be taken off line for planned preventive maintenance over a specific time horizon and maintain a certain level of reliability with minimal maintenance cost. A mathematical programming method (Benders' decomposition) and a metaheuristic algorithm are presented to provide solutions. The obtained objective value from Benders' decomposition method is considered as the stopping criterion in the metaheuristic algorithm. To demonstrate the significance and originality of the proposed model and the efficiency of the algorithms, computational analysis is provided to realistic bag filters system in the cement factory. The obtained result is a schedule that allows the cement factory to consider the preventive maintenance for bag filters over the time horizon.

Citation: Masoud Ebrahimi, Seyyed Mohammad Taghi Fatemi Ghomi, Behrooz Karimi. Application of the preventive maintenance scheduling to increase the equipment reliability: Case study- bag filters in cement factory. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018146
##### References:
 [1] H. Allaoui, Simultaneously scheduling n jobs and the preventive maintenance on the two-machine flow shop to minimize the makespan, International Journal of Production Economics, 112 (2008), 161-167. doi: 10.1016/j.ijpe.2006.08.017. [2] J. F. Benders, Partitioning procedures for solving mixed-variables programming problems, Numerische Mathematik, 4 (1962), 238-252. doi: 10.1007/BF01386316. [3] S. P. Canto, Application of Benders' decomposition to power plant preventive maintenance scheduling, European Journal of Operational Research, 184 (2008), 759-777. doi: 10.1016/j.ejor.2006.11.018. [4] J. X. Cao, The integrated yard truck and yard crane scheduling problem: Benders' decomposition-based methods, Transportation Research Part E: Logistics and Transportation Review, 46 (2010), 344-353. [5] T. Chen, Reusable rocket engine preventive maintenance scheduling using genetic algorithm, Reliability Engineering and System Safety, 114 (2013), 52-60. [6] M. Doostparast, F. Kolahan and M. Doostparast, A reliability-based approach to optimize preventive maintenance scheduling for coherent systems, Reliability Engineering and System Safety, 126 (2014), 98-106. [7] M. Ebrahimi, S. M. T. Fatemi Ghomi and B. Karimi, Hybrid flow shop scheduling with sequence dependent family setup time and uncertain due dates, Applied Mathematical Modelling, 38 (2014), 2490-2504. doi: 10.1016/j.apm.2013.10.061. [8] M.-C. Fitouhi and M. Nourelfath, Integrating noncyclical preventive maintenance scheduling and production planning for multi-state systems, Reliability Engineering and System Safety, 121 (2014), 175-186. [9] H. Go, J.-S. Kim and D.-H. Lee, Operation and preventive maintenance scheduling for containerships: Mathematical model and solution algorithm, European Journal of Operational Research, 229 (2013), 626-636. doi: 10.1016/j.ejor.2013.04.005. [10] M. Graisa and A. Al-Habaibeh, An investigation into current production challenges facing the Libyan cement industry and the need for innovative total productive maintenance (TPM) strategy, Journal of Manufacturing Technology Management, 22 (2011), 541-558. doi: 10.1108/17410381111126445. [11] E. Gustavsson, M. Patriksson, A. B. Strömberg, A. Wojciechowski and M. Önnheim, Preventive maintenance scheduling of multi-component systems with interval costs, Computers and Industrial Engineering, 76 (2014), 390-400. [12] M. Khatami, M. Mahootchi and R. Z. Farahani, Benders' decomposition for concurrent redesign of forward and closed-loop supply chain network with demand and return uncertainties, Transportation Research Part E: Logistics and Transportation Review, 79 (2015), 1-21. [13] Z. Lu, W. Cui and X. Han, Integrated production and preventive maintenance scheduling for a single machine with failure uncertainty, Computers and Industrial Engineering, 80 (2015), 236-244. [14] E. A. M. Miema and A. M. Mweta, An analysis of economics of investing in IT in the maintenance department: An empirical study in a cement factory in Tanzania, Journal of Quality in Maintenance Engineering, 9 (2003), 411-435. [15] Moghaddam and S. Kamran, Multi-objective preventive maintenance and replacement scheduling in a manufacturing system using goal programming, International Journal of Production Economics, 146 (2013), 704-716. [16] M. Mollahassani-Pour, A. Abdollahi and M. Rashidinejad, Application of a novel cost reduction index to preventive maintenance scheduling, International Journal of Electrical Power and Energy Systems, 56 (2014), 235-240. [17] B. Naderi, M. Zandieh and M. Aminnayeri, Incorporating periodic preventive maintenance into flexible flowshop scheduling problems, Applied Soft Computing, 11 (2011), 2094-2101. doi: 10.1016/j.asoc.2010.07.008. [18] M. Pandey, M. J. Zuo and R. Moghaddass, Selective maintenance scheduling over a finite planning horizon, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 230 (2016), 162-177. [19] M. Parastegari, AC constrained hydro-thermal generation scheduling problem: Application of Benders decomposition method improved by BFPSO, International Journal of Electrical Power and Energy Systems, 49 (2013), 199-212. [20] Pereira and C. MNA, A particle swarm optimization (PSO) approach for non-periodic preventive maintenance scheduling programming, Progress in Nuclear Energy, 52 (2010), 710-714. [21] S. Perez-Canto and J. C. Rubio-Romero, A model for the preventive maintenance scheduling of power plants including wind farms, Reliability Engineering and System Safety, 119 (2013), 67-75. [22] H. Shafeek, Continuous improvement of maintenance process for the cement industry — a case study, Journal of Quality in Maintenance Engineering, 20 (2014), 333-376. doi: 10.1108/JQME-07-2013-0047. [23] W. Zhu, M. Fouladirad and C. Berenguer, Bi-criteria maintenance policies for a system subject to competing wear and shock failures, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 229 (2015), 485-500.

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##### References:
 [1] H. Allaoui, Simultaneously scheduling n jobs and the preventive maintenance on the two-machine flow shop to minimize the makespan, International Journal of Production Economics, 112 (2008), 161-167. doi: 10.1016/j.ijpe.2006.08.017. [2] J. F. Benders, Partitioning procedures for solving mixed-variables programming problems, Numerische Mathematik, 4 (1962), 238-252. doi: 10.1007/BF01386316. [3] S. P. Canto, Application of Benders' decomposition to power plant preventive maintenance scheduling, European Journal of Operational Research, 184 (2008), 759-777. doi: 10.1016/j.ejor.2006.11.018. [4] J. X. Cao, The integrated yard truck and yard crane scheduling problem: Benders' decomposition-based methods, Transportation Research Part E: Logistics and Transportation Review, 46 (2010), 344-353. [5] T. Chen, Reusable rocket engine preventive maintenance scheduling using genetic algorithm, Reliability Engineering and System Safety, 114 (2013), 52-60. [6] M. Doostparast, F. Kolahan and M. Doostparast, A reliability-based approach to optimize preventive maintenance scheduling for coherent systems, Reliability Engineering and System Safety, 126 (2014), 98-106. [7] M. Ebrahimi, S. M. T. Fatemi Ghomi and B. Karimi, Hybrid flow shop scheduling with sequence dependent family setup time and uncertain due dates, Applied Mathematical Modelling, 38 (2014), 2490-2504. doi: 10.1016/j.apm.2013.10.061. [8] M.-C. Fitouhi and M. Nourelfath, Integrating noncyclical preventive maintenance scheduling and production planning for multi-state systems, Reliability Engineering and System Safety, 121 (2014), 175-186. [9] H. Go, J.-S. Kim and D.-H. Lee, Operation and preventive maintenance scheduling for containerships: Mathematical model and solution algorithm, European Journal of Operational Research, 229 (2013), 626-636. doi: 10.1016/j.ejor.2013.04.005. [10] M. Graisa and A. Al-Habaibeh, An investigation into current production challenges facing the Libyan cement industry and the need for innovative total productive maintenance (TPM) strategy, Journal of Manufacturing Technology Management, 22 (2011), 541-558. doi: 10.1108/17410381111126445. [11] E. Gustavsson, M. Patriksson, A. B. Strömberg, A. Wojciechowski and M. Önnheim, Preventive maintenance scheduling of multi-component systems with interval costs, Computers and Industrial Engineering, 76 (2014), 390-400. [12] M. Khatami, M. Mahootchi and R. Z. Farahani, Benders' decomposition for concurrent redesign of forward and closed-loop supply chain network with demand and return uncertainties, Transportation Research Part E: Logistics and Transportation Review, 79 (2015), 1-21. [13] Z. Lu, W. Cui and X. Han, Integrated production and preventive maintenance scheduling for a single machine with failure uncertainty, Computers and Industrial Engineering, 80 (2015), 236-244. [14] E. A. M. Miema and A. M. Mweta, An analysis of economics of investing in IT in the maintenance department: An empirical study in a cement factory in Tanzania, Journal of Quality in Maintenance Engineering, 9 (2003), 411-435. [15] Moghaddam and S. Kamran, Multi-objective preventive maintenance and replacement scheduling in a manufacturing system using goal programming, International Journal of Production Economics, 146 (2013), 704-716. [16] M. Mollahassani-Pour, A. Abdollahi and M. Rashidinejad, Application of a novel cost reduction index to preventive maintenance scheduling, International Journal of Electrical Power and Energy Systems, 56 (2014), 235-240. [17] B. Naderi, M. Zandieh and M. Aminnayeri, Incorporating periodic preventive maintenance into flexible flowshop scheduling problems, Applied Soft Computing, 11 (2011), 2094-2101. doi: 10.1016/j.asoc.2010.07.008. [18] M. Pandey, M. J. Zuo and R. Moghaddass, Selective maintenance scheduling over a finite planning horizon, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 230 (2016), 162-177. [19] M. Parastegari, AC constrained hydro-thermal generation scheduling problem: Application of Benders decomposition method improved by BFPSO, International Journal of Electrical Power and Energy Systems, 49 (2013), 199-212. [20] Pereira and C. MNA, A particle swarm optimization (PSO) approach for non-periodic preventive maintenance scheduling programming, Progress in Nuclear Energy, 52 (2010), 710-714. [21] S. Perez-Canto and J. C. Rubio-Romero, A model for the preventive maintenance scheduling of power plants including wind farms, Reliability Engineering and System Safety, 119 (2013), 67-75. [22] H. Shafeek, Continuous improvement of maintenance process for the cement industry — a case study, Journal of Quality in Maintenance Engineering, 20 (2014), 333-376. doi: 10.1108/JQME-07-2013-0047. [23] W. Zhu, M. Fouladirad and C. Berenguer, Bi-criteria maintenance policies for a system subject to competing wear and shock failures, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 229 (2015), 485-500.
Benders decomposition flow chart
Solution representation
A crossover example
Solution procedures of NSGAII algorithm
Converges of the lower and upper bounds versus iterations
The progress of NSGAII for obtaining the optimal solution
The input parameters for model
 Bag filter.No Bag filter size Scale parameter Shape parameter Repair time (hr) Replacement time (hr) Repair cost (＄) Replacement cost(＄) 1 Small 2500 2.5 50 120 20 40 2 Small 2500 2.5 50 120 20 40 3 Small 2500 2.5 50 120 20 40 4 Small 2500 2.5 50 120 20 40 5 Small 2500 2.5 50 120 20 40 6 Small 2500 2.5 50 120 20 40 7 Small 2500 2.5 50 120 20 40 8 Small 2500 2.5 50 120 20 40 9 Small 2500 2.5 50 120 20 40 10 Small 2500 2.5 50 120 20 40 11 Small 2500 2.5 50 120 20 40 12 Medium 2400 2.6 50 120 50 100 13 Medium 2400 2.6 50 120 50 100 14 Medium 2400 2.6 50 120 50 100 15 Small 2500 2.5 50 120 20 40 16 Small 2500 2.5 50 120 20 40 17 Small 2500 2.5 50 120 20 40 18 Large 2400 2.4 50 120 120 240 19 Small 2500 2.5 50 120 20 40 20 Small 2500 2.5 50 120 20 40 21 Small 2500 2.5 50 120 20 40 22 Small 2500 2.5 50 120 20 40 23 Large 2400 2.4 50 120 120 240 24 Small 2500 2.5 50 120 20 40 25 Small 2500 2.5 50 120 20 40 26 Small 2500 2.5 50 120 20 40 27 Small 2500 2.5 50 120 20 40 28 Small 2500 2.5 50 120 20 40 29 Small 2500 2.5 50 120 20 40 30 Large 2400 2.4 50 120 120 240 31 Small 2500 2.5 50 120 20 40 32 Small 2500 2.5 50 120 20 40 33 Large 2400 2.4 50 120 120 240 34 Small 2500 2.5 50 120 20 40 35 Small 2500 2.5 50 120 20 40
 Bag filter.No Bag filter size Scale parameter Shape parameter Repair time (hr) Replacement time (hr) Repair cost (＄) Replacement cost(＄) 1 Small 2500 2.5 50 120 20 40 2 Small 2500 2.5 50 120 20 40 3 Small 2500 2.5 50 120 20 40 4 Small 2500 2.5 50 120 20 40 5 Small 2500 2.5 50 120 20 40 6 Small 2500 2.5 50 120 20 40 7 Small 2500 2.5 50 120 20 40 8 Small 2500 2.5 50 120 20 40 9 Small 2500 2.5 50 120 20 40 10 Small 2500 2.5 50 120 20 40 11 Small 2500 2.5 50 120 20 40 12 Medium 2400 2.6 50 120 50 100 13 Medium 2400 2.6 50 120 50 100 14 Medium 2400 2.6 50 120 50 100 15 Small 2500 2.5 50 120 20 40 16 Small 2500 2.5 50 120 20 40 17 Small 2500 2.5 50 120 20 40 18 Large 2400 2.4 50 120 120 240 19 Small 2500 2.5 50 120 20 40 20 Small 2500 2.5 50 120 20 40 21 Small 2500 2.5 50 120 20 40 22 Small 2500 2.5 50 120 20 40 23 Large 2400 2.4 50 120 120 240 24 Small 2500 2.5 50 120 20 40 25 Small 2500 2.5 50 120 20 40 26 Small 2500 2.5 50 120 20 40 27 Small 2500 2.5 50 120 20 40 28 Small 2500 2.5 50 120 20 40 29 Small 2500 2.5 50 120 20 40 30 Large 2400 2.4 50 120 120 240 31 Small 2500 2.5 50 120 20 40 32 Small 2500 2.5 50 120 20 40 33 Large 2400 2.4 50 120 120 240 34 Small 2500 2.5 50 120 20 40 35 Small 2500 2.5 50 120 20 40
Maintenance scheduling for bag filters
 B/p 1 2 3 4 5 6 7 8 9 10 11 12 13 1 $\surd$ 2 $\surd$ 3 $\surd$ 4 $\surd$ 5 $\surd$ 6 $\surd$ 7 $\surd$ 8 $\surd$ 9 $\surd$ 10 $\surd$ 11 $\surd$ 12 $\surd$ 13 $\surd$ 14 $\surd$ 15 $\surd$ 16 $\surd$ 17 $\surd$ 18 $\surd$ 19 $\surd$ 20 $\surd$ 21 $\surd$ 22 $\surd$ 23 $\surd$ 24 $\surd$ 25 $\surd$ 26 $\surd$ 27 $\surd$ 28 $\surd$ 29 $\surd$ 30 $\surd$ 31 $\surd$ 32 $\surd$ 33 $\surd$ 34 $\surd$ 35 $\surd$
 B/p 1 2 3 4 5 6 7 8 9 10 11 12 13 1 $\surd$ 2 $\surd$ 3 $\surd$ 4 $\surd$ 5 $\surd$ 6 $\surd$ 7 $\surd$ 8 $\surd$ 9 $\surd$ 10 $\surd$ 11 $\surd$ 12 $\surd$ 13 $\surd$ 14 $\surd$ 15 $\surd$ 16 $\surd$ 17 $\surd$ 18 $\surd$ 19 $\surd$ 20 $\surd$ 21 $\surd$ 22 $\surd$ 23 $\surd$ 24 $\surd$ 25 $\surd$ 26 $\surd$ 27 $\surd$ 28 $\surd$ 29 $\surd$ 30 $\surd$ 31 $\surd$ 32 $\surd$ 33 $\surd$ 34 $\surd$ 35 $\surd$
Maintenance scheduling based on 52 weeks and type of bag filters, system reliability
 Week Small bag filter Medium bag filter Large bag filter Reliability at the end of week 1 97.2% 2 3 93.6% 3 97.6% 4 23, 30 91.3% 5 9 92.4% 6 26 92.0% 7 95.7% 8 95.4% 9 15 93.6% 10 96.0% 11 21, 28, 29 90.8% 12 1, 5, 35 91.1% 13 95.5% 14 94.8% 15 l 96.2% 16 93.9% 17 6 92.4% 18 94.6% 19 7, 20 90.4% 20 95.0% 21 96.2% 22 15 93.9% 23 24 93.4% 24 91.1% 25 92.2% 26 94.6% 27 2 90.4% 28 34 90.0% 29 91.7% 30 90.0% 31 16, 19 91.6% 32 2.5 93.2% 33 8 90.7% 34 25 91.3% 35 91.8% 36 33 90.7% 37 12, 13 90.0% 38 22 90.8% 39 14 91.2% 40 92.1% 41 92.0% 42 32 90.3% 43 93.0% 44 11 2500 2.5 91.0% 45 92.1% 46 91.9% 47 17, 31 90.2% 48 91.7% 49 3, 27 90.0% 50 93.4% 51 17 91.6% 52 95.7%
 Week Small bag filter Medium bag filter Large bag filter Reliability at the end of week 1 97.2% 2 3 93.6% 3 97.6% 4 23, 30 91.3% 5 9 92.4% 6 26 92.0% 7 95.7% 8 95.4% 9 15 93.6% 10 96.0% 11 21, 28, 29 90.8% 12 1, 5, 35 91.1% 13 95.5% 14 94.8% 15 l 96.2% 16 93.9% 17 6 92.4% 18 94.6% 19 7, 20 90.4% 20 95.0% 21 96.2% 22 15 93.9% 23 24 93.4% 24 91.1% 25 92.2% 26 94.6% 27 2 90.4% 28 34 90.0% 29 91.7% 30 90.0% 31 16, 19 91.6% 32 2.5 93.2% 33 8 90.7% 34 25 91.3% 35 91.8% 36 33 90.7% 37 12, 13 90.0% 38 22 90.8% 39 14 91.2% 40 92.1% 41 92.0% 42 32 90.3% 43 93.0% 44 11 2500 2.5 91.0% 45 92.1% 46 91.9% 47 17, 31 90.2% 48 91.7% 49 3, 27 90.0% 50 93.4% 51 17 91.6% 52 95.7%

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