Production Throughput Modeling under Five Uncertain Variables Using Bayesian Inference
Throughput is an important measure of performance of production system. Analyzing and modeling of production throughput is complex in today-s dynamic production systems due to uncertainties of production system. The main reasons are that uncertainties are materialized when the production line faces changes in setup time, machinery break down, lead time of manufacturing, and scraps. Besides, demand changes are fluctuating from time to time for each product type. These uncertainties affect the production performance. This paper proposes Bayesian inference for throughput modeling under five production uncertainties. Bayesian model utilized prior distributions related to previous information about the uncertainties where likelihood distributions are associated to the observed data. Gibbs sampling algorithm as the robust procedure of Monte Carlo Markov chain was employed for sampling unknown parameters and estimating the posterior mean of uncertainties. The Bayesian model was validated with respect to convergence and efficiency of its outputs. The results presented that the proposed Bayesian models were capable to predict the production throughput with accuracy of 98.3%.
[1] C. S. Tang, "The impact of uncertainty on a production line,"
Management Science, pp. 1518-1531, 1990.
[2] P. M. Swamidass and W. T. Newell, "Manufacturing strategy,
environmental uncertainty and performance: a path analytic model,"
Management Science, pp. 509-524, 1987.
[3] C. J. Ho, "Evaluating the impact of operating environments on MRP
system nervousness," International Journal of Production Research, vol.
27, pp. 1115-1135, 1989.
[4] R. Stratton, Robey, D., and Allison, I., "Utilising buffer management to
manage uncertainty and focus improvement," in Proceedings of the
International Annual Conference of EurOMA, Gronegen, the
Netherlands, 2008.
[5] P. Kouvelis and J. Li, "Flexible Backup Supply and the Management of
Lead Time Uncertainty," Production and Operations Management, vol.
17, pp. 184-199, 2008.
[6] S. C. Graves, "Uncertainty and Production Planning," Planning
Production and Inventories in the Extended Enterprise, pp. 83-101,
2011.
[7] Z. Hoque, "A contingency model of the association between strategy,
environmental uncertainty and performance measurement: impact on
organizational performance," International Business Review, vol. 13, pp.
485-502, 2004.
[8] X. Yan and X. Su, Linear regression analysis: theory and computing:
World Scientific Pub Co Inc, 2009.
[9] G. Kirchgässner and J. Wolters, Introduction to modern time series
analysis: Springer Verlag, 2007.
[10] T. Efendigil, Önüt, S., Kahraman, C., "A decision support system for
demand forecasting with artificial neural networks and neuro-fuzzy
models: A comparative analysis," Expert Systems With Applications,
vol. 36, pp. 6697-6707, 2009.
[11] L. Aburto and R. Weber, "Improved supply chain management based on
hybrid demand forecasts," Applied Soft Computing, vol. 7, pp. 136-144,
2007.
[12] M. Khashei and M. Bijari, "A New Hybrid Methodology for Nonlinear
Time Series Forecasting," Modelling and Simulation in Engineering,
2011.
[13] C. F. Chien, Hsiao, C.W., Meng, C., Hong, K.T. and S. T. Wang, "Cycle
time prediction and control based on production line status and
manufacturing data mining," 2005, pp. 327-330.
[14] K. R. Baker and S. G. Powell, "A predictive model for the throughput of
simple assembly systems," European journal of operational research,
vol. 81, pp. 336-345, 1995.
[15] D. E. Blumenfeld and J. Li, "An analytical formula for throughput of a
production line with identical stations and random failures,"
Mathematical Problems in Engineering, vol. 3, pp. 293-308, 2005.
[16] J. Li, et al., "Comparisons of two-machine line models in throughput
analysis," International Journal of Production Research, vol. 44, pp.
1375-1398, 2006.
[17] J. Li, et al., "Throughput analysis of production systems: recent
advances and future topics," International Journal of Production
Research, vol. 47, pp. 3823-3851, 2009.
[18] J. Alden, "Estimating performance of two workstations in series with
downtime and unequal speeds," General Motors Research &
Development Center, Report R&D-9434, Warren, MI, 2002.
[19] J. Mula, et al., "Models for production planning under uncertainty: A
review," International Journal of Production Economics, vol. 103, pp.
271-285, 2006.
[20] S. Koh, et al., "A business model for uncertainty management,"
Benchmarking: An International Journal, vol. 12, pp. 383-400, 2005.
[21] M. A. Wazed, et al., "Uncertainty factors in real manufacturing
environment," Australian Journal of Basic and Applied Sciences, vol. 3,
pp. 342-351, 2009.
[22] A. M. Deif and H. A. ElMaraghy, "Modelling and analysis of dynamic
capacity complexity in multi-stage production," Production Planning and
Control, vol. 20, pp. 737-749, 2009.
[23] H. Tempelmeier, "Practical considerations in the optimization of flow
production systems," International Journal of Production Research, vol.
41, pp. 149-170, 2003.
[24] M. S. Han and D. J. Park, "Optimal buffer allocation of serial production
lines with quality inspection machines," Computers & Industrial
Engineering, vol. 42, pp. 75-89, 2002.
[25] Y. C. Chou, et al., "Evaluating alternative capacity strategies in
semiconductor manufacturing under uncertain demand and price
scenarios," International Journal of Production Economics, vol. 105, pp.
591-606, 2007.
[26] L. Li, et al., "Throughput Bottleneck Prediction of Manufacturing
Systems Using Time Series Analysis," Journal of Manufacturing
Science and Engineering, vol. 133, p. 021015, 2011.
[27] C. M. Lee and C. N. Ko, "Short-term load forecasting using lifting
scheme and ARIMA models," Expert Systems With Applications, 2011.
[28] F. Z. a. S. Zhong, "Time series forecasting using a hybrid RBF neural
network and AR model based on binomial smoothing," World Academy
of Science, Engineering and Technology, vol. 75, pp. 1471-1475, 2011.
[29] D. J. Spiegelhalter, , K. R. Abrams, J. P. Myles, Bayesian approaches to
clinical trials and health-care evaluation, vol. 13: Wiley, Chichester,
2004.
[30] D. J. Spiegelhalter, N. G. Best, B. P. Carlin, A. Van Der Linde, Bayesian
measures of model complexity and fit, Journal of the Royal Statistical
Society. Series B, Statistical Methodology, 2002, pp. 583-639.
[31] S. P. Brooks and A. Gelman, Alternative methods for monitoring
convergence of iterative simulations, Journal of Computational and
Graphical Statistics, vol. 7, 1998, pp. 434-455.
[32] G. B. Hua, Residential construction demand forecasting using economic
indicators: a comparative study of artificial neural networks and multiple
regression, Construction Management and Economics, vol. 14, 1996, pp.
25-34.
[33] L. Aburto and R. Weber, Improved supply chain management based on
hybrid demand forecasts, Applied Soft Computing, vol. 7, 2007, pp.
136-144.
[34] F. Zheng and S. Zhong, Time series forecasting using a hybrid RBF
neural network and AR model based on binomial smoothing, World
Academy of Science, Engineering and Technology, vol. 75, 2011, pp.
1471-1475.
[35] C. F. Chien, C. Y. Hsu, C. W. Hsiao, Manufacturing intelligence to
forecast and reduce semiconductor cycle time, Journal of Intelligent
Manufacturing, 2011 pp. 1-14.
[36] S. F. Arnold, Mathematical Statistics, Prentice-Hall, 1990.
[37] R. E. Walpole, Mayers, R.H., Mayers, S.L, Probability and statistics for
engineers and scienticts, 6 ed., New Jersey, Prentice Hall Int. , 1998.
[38] Amir Azizi, Amir Yazid b. Ali, Loh Wei Ping and Mohammadzadeh, M.
(2012b). A Hybrid model of ARIMA and Multiple Polynomial
Regression for Uncertainties Modeling of a Serial Production Line.
International Conference on Engineering and Technology Management
(ICETM), P-ISSN 2010-376X and E-ISSN 2010-3778, Kuala Lumpur,
Malaysia, 62, 63-68.
[39] Amir Azizi, Amir Yazid b. Ali, Loh Wei Ping and Mohsen
Mohammadzadeh (2012c). Estimating and Modeling Uncertainties
Affecting Production Throughput using ARIMA-Multiple Linear
Regression International Proceedings of Computer Science and
Information Technology, ISSN 2010-460X, Singapore, Trans Tech
Publications, 1263-1268.
[40] Amir Azizi, Amir Yazid b. Ali and Loh Wei Ping (2011a). Prediction of
the Production Throughput under Uncertain Conditions Using ANFIS: A
Case Study. International Journal for Advances in Computer Science
(IJACS), ISSN 2218-6638, 2(4), 27-32.
[1] C. S. Tang, "The impact of uncertainty on a production line,"
Management Science, pp. 1518-1531, 1990.
[2] P. M. Swamidass and W. T. Newell, "Manufacturing strategy,
environmental uncertainty and performance: a path analytic model,"
Management Science, pp. 509-524, 1987.
[3] C. J. Ho, "Evaluating the impact of operating environments on MRP
system nervousness," International Journal of Production Research, vol.
27, pp. 1115-1135, 1989.
[4] R. Stratton, Robey, D., and Allison, I., "Utilising buffer management to
manage uncertainty and focus improvement," in Proceedings of the
International Annual Conference of EurOMA, Gronegen, the
Netherlands, 2008.
[5] P. Kouvelis and J. Li, "Flexible Backup Supply and the Management of
Lead Time Uncertainty," Production and Operations Management, vol.
17, pp. 184-199, 2008.
[6] S. C. Graves, "Uncertainty and Production Planning," Planning
Production and Inventories in the Extended Enterprise, pp. 83-101,
2011.
[7] Z. Hoque, "A contingency model of the association between strategy,
environmental uncertainty and performance measurement: impact on
organizational performance," International Business Review, vol. 13, pp.
485-502, 2004.
[8] X. Yan and X. Su, Linear regression analysis: theory and computing:
World Scientific Pub Co Inc, 2009.
[9] G. Kirchgässner and J. Wolters, Introduction to modern time series
analysis: Springer Verlag, 2007.
[10] T. Efendigil, Önüt, S., Kahraman, C., "A decision support system for
demand forecasting with artificial neural networks and neuro-fuzzy
models: A comparative analysis," Expert Systems With Applications,
vol. 36, pp. 6697-6707, 2009.
[11] L. Aburto and R. Weber, "Improved supply chain management based on
hybrid demand forecasts," Applied Soft Computing, vol. 7, pp. 136-144,
2007.
[12] M. Khashei and M. Bijari, "A New Hybrid Methodology for Nonlinear
Time Series Forecasting," Modelling and Simulation in Engineering,
2011.
[13] C. F. Chien, Hsiao, C.W., Meng, C., Hong, K.T. and S. T. Wang, "Cycle
time prediction and control based on production line status and
manufacturing data mining," 2005, pp. 327-330.
[14] K. R. Baker and S. G. Powell, "A predictive model for the throughput of
simple assembly systems," European journal of operational research,
vol. 81, pp. 336-345, 1995.
[15] D. E. Blumenfeld and J. Li, "An analytical formula for throughput of a
production line with identical stations and random failures,"
Mathematical Problems in Engineering, vol. 3, pp. 293-308, 2005.
[16] J. Li, et al., "Comparisons of two-machine line models in throughput
analysis," International Journal of Production Research, vol. 44, pp.
1375-1398, 2006.
[17] J. Li, et al., "Throughput analysis of production systems: recent
advances and future topics," International Journal of Production
Research, vol. 47, pp. 3823-3851, 2009.
[18] J. Alden, "Estimating performance of two workstations in series with
downtime and unequal speeds," General Motors Research &
Development Center, Report R&D-9434, Warren, MI, 2002.
[19] J. Mula, et al., "Models for production planning under uncertainty: A
review," International Journal of Production Economics, vol. 103, pp.
271-285, 2006.
[20] S. Koh, et al., "A business model for uncertainty management,"
Benchmarking: An International Journal, vol. 12, pp. 383-400, 2005.
[21] M. A. Wazed, et al., "Uncertainty factors in real manufacturing
environment," Australian Journal of Basic and Applied Sciences, vol. 3,
pp. 342-351, 2009.
[22] A. M. Deif and H. A. ElMaraghy, "Modelling and analysis of dynamic
capacity complexity in multi-stage production," Production Planning and
Control, vol. 20, pp. 737-749, 2009.
[23] H. Tempelmeier, "Practical considerations in the optimization of flow
production systems," International Journal of Production Research, vol.
41, pp. 149-170, 2003.
[24] M. S. Han and D. J. Park, "Optimal buffer allocation of serial production
lines with quality inspection machines," Computers & Industrial
Engineering, vol. 42, pp. 75-89, 2002.
[25] Y. C. Chou, et al., "Evaluating alternative capacity strategies in
semiconductor manufacturing under uncertain demand and price
scenarios," International Journal of Production Economics, vol. 105, pp.
591-606, 2007.
[26] L. Li, et al., "Throughput Bottleneck Prediction of Manufacturing
Systems Using Time Series Analysis," Journal of Manufacturing
Science and Engineering, vol. 133, p. 021015, 2011.
[27] C. M. Lee and C. N. Ko, "Short-term load forecasting using lifting
scheme and ARIMA models," Expert Systems With Applications, 2011.
[28] F. Z. a. S. Zhong, "Time series forecasting using a hybrid RBF neural
network and AR model based on binomial smoothing," World Academy
of Science, Engineering and Technology, vol. 75, pp. 1471-1475, 2011.
[29] D. J. Spiegelhalter, , K. R. Abrams, J. P. Myles, Bayesian approaches to
clinical trials and health-care evaluation, vol. 13: Wiley, Chichester,
2004.
[30] D. J. Spiegelhalter, N. G. Best, B. P. Carlin, A. Van Der Linde, Bayesian
measures of model complexity and fit, Journal of the Royal Statistical
Society. Series B, Statistical Methodology, 2002, pp. 583-639.
[31] S. P. Brooks and A. Gelman, Alternative methods for monitoring
convergence of iterative simulations, Journal of Computational and
Graphical Statistics, vol. 7, 1998, pp. 434-455.
[32] G. B. Hua, Residential construction demand forecasting using economic
indicators: a comparative study of artificial neural networks and multiple
regression, Construction Management and Economics, vol. 14, 1996, pp.
25-34.
[33] L. Aburto and R. Weber, Improved supply chain management based on
hybrid demand forecasts, Applied Soft Computing, vol. 7, 2007, pp.
136-144.
[34] F. Zheng and S. Zhong, Time series forecasting using a hybrid RBF
neural network and AR model based on binomial smoothing, World
Academy of Science, Engineering and Technology, vol. 75, 2011, pp.
1471-1475.
[35] C. F. Chien, C. Y. Hsu, C. W. Hsiao, Manufacturing intelligence to
forecast and reduce semiconductor cycle time, Journal of Intelligent
Manufacturing, 2011 pp. 1-14.
[36] S. F. Arnold, Mathematical Statistics, Prentice-Hall, 1990.
[37] R. E. Walpole, Mayers, R.H., Mayers, S.L, Probability and statistics for
engineers and scienticts, 6 ed., New Jersey, Prentice Hall Int. , 1998.
[38] Amir Azizi, Amir Yazid b. Ali, Loh Wei Ping and Mohammadzadeh, M.
(2012b). A Hybrid model of ARIMA and Multiple Polynomial
Regression for Uncertainties Modeling of a Serial Production Line.
International Conference on Engineering and Technology Management
(ICETM), P-ISSN 2010-376X and E-ISSN 2010-3778, Kuala Lumpur,
Malaysia, 62, 63-68.
[39] Amir Azizi, Amir Yazid b. Ali, Loh Wei Ping and Mohsen
Mohammadzadeh (2012c). Estimating and Modeling Uncertainties
Affecting Production Throughput using ARIMA-Multiple Linear
Regression International Proceedings of Computer Science and
Information Technology, ISSN 2010-460X, Singapore, Trans Tech
Publications, 1263-1268.
[40] Amir Azizi, Amir Yazid b. Ali and Loh Wei Ping (2011a). Prediction of
the Production Throughput under Uncertain Conditions Using ANFIS: A
Case Study. International Journal for Advances in Computer Science
(IJACS), ISSN 2218-6638, 2(4), 27-32.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:56632", author = "Amir Azizi and Amir Yazid B. Ali and Loh Wei Ping", title = "Production Throughput Modeling under Five Uncertain Variables Using Bayesian Inference", abstract = "Throughput is an important measure of performance of production system. Analyzing and modeling of production throughput is complex in today-s dynamic production systems due to uncertainties of production system. The main reasons are that uncertainties are materialized when the production line faces changes in setup time, machinery break down, lead time of manufacturing, and scraps. Besides, demand changes are fluctuating from time to time for each product type. These uncertainties affect the production performance. This paper proposes Bayesian inference for throughput modeling under five production uncertainties. Bayesian model utilized prior distributions related to previous information about the uncertainties where likelihood distributions are associated to the observed data. Gibbs sampling algorithm as the robust procedure of Monte Carlo Markov chain was employed for sampling unknown parameters and estimating the posterior mean of uncertainties. The Bayesian model was validated with respect to convergence and efficiency of its outputs. The results presented that the proposed Bayesian models were capable to predict the production throughput with accuracy of 98.3%.
", keywords = "Bayesian inference, Uncertainty modeling, Monte
Carlo Markov chain, Gibbs sampling, Production throughput", volume = "6", number = "9", pages = "1946-8", }
