A Hybrid Model of ARIMA and Multiple Polynomial Regression for Uncertainties Modeling of a Serial Production Line
Uncertainties of a serial production line affect on the
production throughput. The uncertainties cannot be prevented in a
real production line. However the uncertain conditions can be
controlled by a robust prediction model. Thus, a hybrid model
including autoregressive integrated moving average (ARIMA) and
multiple polynomial regression, is proposed to model the nonlinear
relationship of production uncertainties with throughput. The
uncertainties under consideration of this study are demand, breaktime,
scrap, and lead-time. The nonlinear relationship of production
uncertainties with throughput are examined in the form of quadratic
and cubic regression models, where the adjusted R-squared for
quadratic and cubic regressions was 98.3% and 98.2%. We optimized
the multiple quadratic regression (MQR) by considering the time
series trend of the uncertainties using ARIMA model. Finally the
hybrid model of ARIMA and MQR is formulated by better adjusted
R-squared, which is 98.9%.
[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. h. Boon, Business & economic forecasting techniques and
applications: University Putra Malaysia press, serdang, Selangor darul
ehsan, 2006.
[11] 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.
[12] L. Aburto and R. Weber, "Improved supply chain management based on
hybrid demand forecasts," Applied Soft Computing, vol. 7, pp. 136-144,
2007.
[13] M. Khashei and M. Bijari, "A New Hybrid Methodology for Nonlinear
Time Series Forecasting," Modelling and Simulation in Engineering,
2011.
[14] 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.
[15] 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.
[16] 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.
[17] J. Li, et al., "Comparisons of two-machine line models in throughput
analysis," International Journal of Production Research, vol. 44, pp.
1375-1398, 2006.
[18] 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.
[19] 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.
[20] J. Mula, et al., "Models for production planning under uncertainty: A
review," International Journal of Production Economics, vol. 103, pp.
271-285, 2006.
[21] S. Koh, et al., "A business model for uncertainty management,"
Benchmarking: An International Journal, vol. 12, pp. 383-400, 2005.
[22] M. A. Wazed, et al., "Uncertainty factors in real manufacturing
environment," Australian Journal of Basic and Applied Sciences, vol. 3,
pp. 342-351, 2009.
[23] 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.
[24] H. Tempelmeier, "Practical considerations in the optimization of flow
production systems," International Journal of Production Research, vol.
41, pp. 149-170, 2003.
[25] 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.
[26] 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.
[27] 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.
[28] C. M. Lee and C. N. Ko, "Short-term load forecasting using lifting
scheme and ARIMA models," Expert Systems With Applications, 2011.
[29] 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.
[30] R. I. D. Harris and R. Sollis, Applied time series modeling and
forecasting: J. Wiley, 2003.
[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. h. Boon, Business & economic forecasting techniques and
applications: University Putra Malaysia press, serdang, Selangor darul
ehsan, 2006.
[11] 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.
[12] L. Aburto and R. Weber, "Improved supply chain management based on
hybrid demand forecasts," Applied Soft Computing, vol. 7, pp. 136-144,
2007.
[13] M. Khashei and M. Bijari, "A New Hybrid Methodology for Nonlinear
Time Series Forecasting," Modelling and Simulation in Engineering,
2011.
[14] 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.
[15] 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.
[16] 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.
[17] J. Li, et al., "Comparisons of two-machine line models in throughput
analysis," International Journal of Production Research, vol. 44, pp.
1375-1398, 2006.
[18] 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.
[19] 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.
[20] J. Mula, et al., "Models for production planning under uncertainty: A
review," International Journal of Production Economics, vol. 103, pp.
271-285, 2006.
[21] S. Koh, et al., "A business model for uncertainty management,"
Benchmarking: An International Journal, vol. 12, pp. 383-400, 2005.
[22] M. A. Wazed, et al., "Uncertainty factors in real manufacturing
environment," Australian Journal of Basic and Applied Sciences, vol. 3,
pp. 342-351, 2009.
[23] 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.
[24] H. Tempelmeier, "Practical considerations in the optimization of flow
production systems," International Journal of Production Research, vol.
41, pp. 149-170, 2003.
[25] 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.
[26] 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.
[27] 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.
[28] C. M. Lee and C. N. Ko, "Short-term load forecasting using lifting
scheme and ARIMA models," Expert Systems With Applications, 2011.
[29] 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.
[30] R. I. D. Harris and R. Sollis, Applied time series modeling and
forecasting: J. Wiley, 2003.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:56982", author = "Amir Azizi and Amir Yazid b. Ali and Loh Wei Ping and Mohsen Mohammadzadeh", title = "A Hybrid Model of ARIMA and Multiple Polynomial Regression for Uncertainties Modeling of a Serial Production Line", abstract = "Uncertainties of a serial production line affect on the
production throughput. The uncertainties cannot be prevented in a
real production line. However the uncertain conditions can be
controlled by a robust prediction model. Thus, a hybrid model
including autoregressive integrated moving average (ARIMA) and
multiple polynomial regression, is proposed to model the nonlinear
relationship of production uncertainties with throughput. The
uncertainties under consideration of this study are demand, breaktime,
scrap, and lead-time. The nonlinear relationship of production
uncertainties with throughput are examined in the form of quadratic
and cubic regression models, where the adjusted R-squared for
quadratic and cubic regressions was 98.3% and 98.2%. We optimized
the multiple quadratic regression (MQR) by considering the time
series trend of the uncertainties using ARIMA model. Finally the
hybrid model of ARIMA and MQR is formulated by better adjusted
R-squared, which is 98.9%.", keywords = "ARIMA, multiple polynomial regression, production
throughput, uncertainties", volume = "6", number = "2", pages = "470-6", }
