Abstract
In this paper, we consider a serial production line consisting of \(n\) unreliable machines with \(n-1\) buffers. The objective is to determine the optimal preventive maintenance policy and the optimal buffer allocation that will minimize the total system cost subject to a given system throughput level. We assume that the mean time between failure of all machines will be increased after performing periodic preventive maintenance. An analytical decomposition-type approximation is used to estimate the production line throughput. The optimal design problem is formulated as a combinatorial optimization one where the decision variables are buffer levels and times between preventive maintenance. To solve this problem, the extended great deluge algorithm is proposed. Illustrative numerical examples are presented to illustrate the model.
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Ajorlou, S., & Shams, I. (2013). Artificial bee colony algorithm for CONWIP production control system in a multi-product multi-machine manufacturing environment. Journal of Intelligent Manufacturing, 24, 1145–1156.
Amiri, M., & Mohtashami, A. (2011). Buffer allocation in unreliable production lines based on design of experiments, simulation, and genetic algorithm. International Journal of Advanced Manufacturing, 62(1–4), 371–383.
Burke, E., Bykov, Y., Newall, J., & Petrovic, S. (2004). A time-predetermined local search approach to exam timetabling problems. IIE Transactions, 36(6), 509–528.
Buzzocott, J. A. (1967). Automatic transfer lines with buffer stocks. International Journal of Production Research, 6, 183–200.
Can, B., & Heavey, C. (2009). Sequential metamodelling with genetic programming and particle swarms. In Proceedings of the 2009 winter simulation conference (pp. 3150–3157).
Can, B., & Heavey, C. (2011). Comparison of experimental designs for simulation-based symbolic regression of manufacturing systems. Computers, Industrial Engineering, 61(3), 447–462.
Can, B., & Heavey, C. (2012). A comparison of genetic programming and artificial neural networks in metamodeling of discrete-event simulation models. Computers, Operations Research, 39(2), 424–436.
Chang, Q., Ni, J., Bandyopadhyay, P., Biller, S., & Xiao, G. (2007). Maintenance staffing management. Journal of Intelligent Manufacturing, 18(3), 351–360.
Cruz, F. R. B., Kendall, G., While, L., Duarte, A. R., & Brito, N. L. C. (2012). Throughput maximization of queueing networks with simultaneous minimization of service rates and buffers. Mathematical Problems in Engineering Engineering. doi:10.1155/2012/692593.
Dallery, Y., David, R., & Xie, X. L. (1989). Approximate analysis of transfer lines with unreliable machines and finite buffers. IEEE Transactions on Automatic Control, 34, 943–953.
Demir, L., Tunali, S., & Eliiyi, D. T. (2014). The state of the art on buffer allocation problem: a comprehensive survey. Journal of Intelligent Manufacturing, 25(3), 1–22.
Dimitrakos, T. D., & Kyriakidis, E. G. (2008). A semi-Markov decision algorithm for the maintenance of a production system with buffer capacity and continuous repair times. International Journal of Production Economics, 111(2), 752–762.
Dolgui, A., Eremeev, A., & Sigaev, V. (2007). HBBA: Hybrid algorithm for buffer allocation in tandem production lines. Journal of Intelligent Manufacturing, 18, 411–420.
Dubois, D., & Forestier, J. P. (1982). Productivité et en-cours moyens d’un ensemble de deux machines séparées par une zone de stockage. RAIRO Automatique, 16(2), 105–132.
Gento, A. M., & Redondo, A. (2003). Rough sets and maintenance in a production line. Expert Systems, 20(5), 271–279.
Groenevelt, H., Pintelon, L., & Seidmann, A. (1992). Production batching with machine breakdowns and safety stocks. Operations Research, 40(5), 959–971.
Hadidi, L. A., Al-Turki, U. M., & Rahim, A. (2012). Integrated models in production planning and scheduling, maintenance and quality: a review. International Journal of Industrial and Systems Engineering, 10(1), 21–50.
Hillier, F. S., & So, K. C. (1991). The effect of the coefficient of variation of operation times on the allocation of storage space in production line system. IIE Transactions, 23, 198–206.
Hillier, F. S., So, K. C., & Boling, R. W. (1993). Notes: Toward characterizing the optimal allocation of storage space in production line systems with variable processing times. Management Science, 39, 126–133.
Iravani, M. R., & Duenyas, I. (2002). Integrated maintenance and production control of a deteriorating production system. IIE Transactions, 34(5), 423–435.
Karamatsoukis, C. C., & Kyriakidis, E. G. (2009). Optimal maintenance of a production–inventory system with idle periods. European Journal of Operational Research, 196(2), 744–751.
Karamatsoukis, C. C., & Kyriakidis, E. G. (2012). Optimal maintenance of a production system with intermediate buffers. Mathematical Problems in Engineering. doi:10.1155/2012/673864.
Massim, Y., Yalaoui, F., Chatelet, E., Yalaoui, A., & Zeblah, A. (2012). Efficient immune algorithm for optimal allocations in series-parallel continuous manufacturing systems. Journal of Intelligent Manufacturing, 23(5), 1603–1619.
Matta, A., Pezzoni, M., & Semeraro, Q. (2012). A Kriging-based algorithm to optimize production systems approximated by analytical models. Journal of Intelligent Manufacturing, 23(3), 587–597.
Meller, R. D., & Kim, D. S. (1996). The impact of preventive maintenance on system cost and buffer size. European Journal of Operational Research, 95(3), 577–591.
McNamara, T., Shaaban, S., & Hudson, S. (2011). Unpaced production lines with three simultaneous imbalance sources. Industrial Management, Data Systems, 111(9), 1356–1380.
Nahas, N., Nourelfath, M., & Ait-Kadi, D. (2006). A new approach for buffer allocation in unreliable production lines. International Journal of Production Economics, 103(2), 873–881.
Nahas, N., Nourelfath, M., & Ait-Kadi, D. (2009). Selecting machines and buffers in unreliable series-parallel production lines. International Journal of Production Research, 47, 3741–3774.
Nahas, N., Khatab, A., Ait-Kadi, D., & Nourelfath, M. (2008). Extended great deluge algorithm for the imperfect preventive maintenance optimization of multi-state systems. Reliability Engineering and System Safety, 93(11), 1658–1672.
Northworthy, S., & Abdul-Kader, W. (2004). Impact of preventive maintenance on serial production line performance: a simulation approach. In ASAC 2004, Quebec city, Quebec.
Papadopoulos, H. T., Heavey, C., & Browne, J. (1993). Queueing theory in manufacturing systems analysis and design. London: Chapman and Hall.
Patchong, A., & Willaeys, D. (2001). Modeling and analysis of an unreliable flow, line composed of parallel-machine stages. IIE Transactions, 33, 559–568.
Raman, N. A., & Jamaludin, E. K. R. (2008). Implementation of Toyota Production System (TPS) in the production line of a local automotive parts manufacturer. In Proceedings of international conferenceon mechanical, manufacturing engineering.
Rezg, N., Chelbi, A., & Xie, X. (2005). Modeling and optimizing a joint inventory control and preventive maintenance strategy for a randomly failing production unit: analytical and simulation approaches. International Journal of Computer Integrated Manufacturing, 18(2–3), 225–235.
Sabuncuoglu, I., Erel, E., & Kok, A. G. (2002). Analysis of assembly systems for interdeparture time variability and throughput. IIE Transactions, 34, 23–40.
Sloan, T. W. (2004). A periodic review production and maintenance model with random demand, deteriorating equipment, and binomial yield. Journal of the Operational Research Society, 55(6), 647–656.
So, K. C. (1997). Optimal buffer allocation strategy for minimizing work-in-process inventory in unpaced production lines. IIE Transactions, 29, 81–88.
Singh, A., & Smith, J. M. G. (1997). Buffer allocation for an integer nonlinear network design problem. Computers & Operations Research, 24, 453–472.
Spinellis, D., & Papadopoulos, C. T. (2000a). A simulated annealing approach for buffer allocation in reliable production lines. Annals of Operations Research, 93, 373–384.
Spinellis, D., & Papadopoulos, C. T. (2000b). Stochastic algorithms for buffer allocation in reliable production lines. Mathematical Problems in Engineering, 5, 441–458.
Spinellis, D., Papadopoulos, C., & Macgregor Smith, J. (2000). Large production line optimization using simulated annealing. International Journal of Production Research, 38, 509–541.
Van der Duyn Schouten, F. A., & Vanneste, S. G. (1995). Maintenance optimization of a production system with buffer capacity. European Journal of Operational Research, 82(2), 323–338.
Yao, X., Xie, X., Fu, M. C., & Marcus, S. I. (2005). Optimal joint preventive maintenance and production policies. Naval Research Logistics, 52(7), 668–681.
Acknowledgments
The author would like to knowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through project No. FT-131006.
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Appendix
Appendix
Additional notations
- \(p_{s}(i)\) :
-
Probability of machine \(M_{d}(i)\) being starved in line \(i\).
- \(p_{b}(i)\) :
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Probability of machine \(M_{u}(i)\) being blocked in line \(i\).
- \(E(i) \) :
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Efficiency of line \(i\)
- \(e_{i }\) :
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The isolated efficiency of machine \(M_{i}\)
DDX Algorithm
Step 1: Initialize
Step 2: For \(\hbox {i} = 2, 3, \ldots , n -1\), calculate \(I_u (i), \mu _{u}(i) \,{and} \lambda _{u}(i)\) using the following equations:
where
Step 3: For \(\hbox {i} = \hbox {n}- 2,\hbox {n}-3,\ldots ,1\), calculate \(I_d (i), \mu _{d}(i) \,{ and } \lambda _{d}(i)\) using the following equations:
where
Go to step 2 until convergence of the unknown parameters.
For given values of \(\lambda _{u}(i), \mu _{u}(i),\lambda _{d}(i)\) and \(\mu _{d}(i)\), the performance parameters \(E(i)\), \(p_{s}(i)\) and \(p_{b}(i)\) and the average buffer level \(Q(i)\) can be obtained from Dubois and Forestier (1982).
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Nahas, N. Buffer allocation and preventive maintenance optimization in unreliable production lines. J Intell Manuf 28, 85–93 (2017). https://doi.org/10.1007/s10845-014-0963-y
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DOI: https://doi.org/10.1007/s10845-014-0963-y