# American Institute of Mathematical Sciences

January  2020, 16(1): 189-205. 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, 2020, 16 (1) : 189-205. doi: 10.3934/jimo.2018146
##### References:

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##### References:
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%