Optimal control model for finite capacity continuous MRP with deteriorating items
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A general model for continuous material requirements planning problem is proposed which contains of reworking of returned items along with deterioration of items. In the proposed model there are separated stocks for manufactured, returned and reworked items and also it is possible to consider returned items from both inventories of manufactured and reworked items. A general finite time linear quadratic optimal control problem is presented to attain the goal values for inventories, demands and productions. The goal values for inventories, demands and production can be considered as the capacity of stocks, scheduled demand and capacity of transportation respectively. Since the time is considered as a continuous parameter, the carrying cost of production process is more real than the periodic approach wherein time is considered as a discrete parameter. Finally a solution method is presented and numerical simulations are provided to validate the approach.
KeywordsContinuous material requirements planning (CMRP) Finite capacity MRP Deterioration Linear quadratic optimal control Pontryagin minimum principle
The authors would like to thank the editor and anonymous referees for their constructive comments. This work was supported in part by: Research Deputy of Ferdowsi University of Mashhad, under Grant No. 39098 (dated Feb. 28, 2016).
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Conflicts of interest
The authors declare that they have no conflict of interest.
- Foul, A., Djemili, S., & Tadj, L. (2007). Optimal and self-tuning optimal control of a periodic-review hybrid production inventory system. Nonlinear Analysis: Hybrid Systems, 1(1), 68–80.Google Scholar
- Hedjar, R., Garg, A. K., & Tadj, L. (2015). Model predictive production planning in a three-stock reverse-logistics system with deteriorating items. International Journal of Systems Science: Operations & Logistics, 2, 187–198.Google Scholar
- Hedjar, R., Tadj, L., & Abid, C. (2012). Optimal control of integrated production-forecasting system. In: Jao, C. (ed.), Decision support systems. In-tech series in numerical analysis and scientific computing, 2012. ISBN: 978-953-51-0799-6.Google Scholar
- Mishra, U. (2016). An EOQ model with time dependent Weibull deterioration, quadratic demand and partial backlogging. International Journal of Applied and Computational Mathematics. https://doi.org/10.1007/s40819-015-0077-z.
- Pooya, A., & Pakdaman, M. (2017a). A delayed optimal control model for multi-stage production-inventory system with production lead times. The International Journal of Advanced Manufacturing Technology. https://doi.org/10.1007/s00170-017-0942-5.
- Pooya, A., Pakdaman, M., & Tadj, L. (2017). Exact and approximate solution for optimal inventory control of two-stock with reworking and forecasting of demand. Operational Research. https://doi.org/10.1007/s12351-017-0297-6.
- Rossi, T., Pozzi, R., Pero, M., & Cigolini, R. (2017). Improving production planning through finite capacity MRP. International Journal of Production Research. https://doi.org/10.1080/00207543.2016.1177235.
- Subbaram Naidu, D. (2002). Optimal control systems. Boca Raton: CRC Press.Google Scholar
- Sun, Y., & Zhu, Y. (2017). Bangbang property for an uncertain saddle point problem. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-014-1003-7.