Journal of Intelligent Manufacturing

, Volume 30, Issue 5, pp 2203–2215 | Cite as

Optimal control model for finite capacity continuous MRP with deteriorating items

  • Alireza PooyaEmail author
  • Morteza Pakdaman


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.


Continuous 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).

Compliance with Ethical Standards

Conflicts of interest

The authors declare that they have no conflict of interest.


  1. Benkherouf, L., Skouri, K., & Konstantaras, I. (2016). Optimal control of production, remanufacturing and refurbishing activities in a finite planning horizon inventory system. Journal of Optimization Theory and Applications, 168, 677–698.CrossRefGoogle Scholar
  2. Daz-Madroero, M., Mula, J., Jimnez, M., & Peidro, D. (2017). A rolling horizon approach for material requirement planning under fuzzy lead times. International Journal of Production Research, 55(8), 2197–2211.CrossRefGoogle Scholar
  3. Dong, Mi, Heb, F., & Wu, Z. (2011). Optimal control of a continuum model for single-product re-entrant manufacturing systems. International Journal of Production Research, 49, 6363–6385.CrossRefGoogle Scholar
  4. Effati, S., & Pakdaman, M. (2013). Optimal control problem via neural networks. Neural Computing and Applications, 23(7–8), 2093–2100.CrossRefGoogle Scholar
  5. 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
  6. Foul, A., & Tadj, L. (2006). Optimal control of a hybrid periodic-review production inventory system with disposal. International Journal of Operational Research, 2(4), 481–494.CrossRefGoogle Scholar
  7. Foul, A., Tadj, L., & Hedjar, R. (2012). Adaptive control of inventory systems with unknown deterioration rate. Journal of King Saud University Science, 24, 215–220.CrossRefGoogle Scholar
  8. Geetha, K. V., & Uthayakumar, R. (2009). Optimal inventory control policy for items with time-dependent demand. American Journal of Mathematical and Management Sciences, 29, 457–476.CrossRefGoogle Scholar
  9. Grubbstrom, R. W., Bogataj, M., & Bogataj, L. (2010). Optimal lotsizing within MRP theory. Annual Reviews in Control, 34, 89–100.CrossRefGoogle Scholar
  10. Grubbstrom, R. W., & Tang, O. (2012). The space of solution alternatives in the optimal lotsizing problem for general assembly systems applying MRP theory. International Journal of Production Economics, 140, 765–777.CrossRefGoogle Scholar
  11. Guchhait, P., Maiti, M. K., & Maiti, M. (2014). Inventory policy of a deteriorating item with variable demand under trade credit period. Computers & Industrial Engineering, 76, 75–88.CrossRefGoogle Scholar
  12. Hedjara, R., Bounkhel, M., & Tadj, L. (2005). Receding horizon control of a hybrid production system with deteriorating items. Nonlinear Analysis, 63, 405–422.CrossRefGoogle Scholar
  13. 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
  14. 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
  15. Hosseini, S., & Al Khaled, A. (2014). A survey on the imperialist competitive algorithm metaheuristic: Implementation in engineering domain and directions for future research. Applied Soft Computing, 24, 1078–1094.CrossRefGoogle Scholar
  16. Hosseini, S., & Barker, K. (2016). A Bayesian network model for resilience-based supplier selection. International Journal of Production Economics, 180, 68–87.CrossRefGoogle Scholar
  17. Ignaciuk, P., & Bartoszewicz, A. (2010). Linearquadratic optimal control strategy for periodic-review inventory systems. Automatica, 46, 1982–1993.CrossRefGoogle Scholar
  18. Jodlbauer, H., & Reitner, S. (2012). Material and capacity requirements planning with dynamic lead times. International Journal of Production Research, 50(16), 4477–4492.CrossRefGoogle Scholar
  19. Louly, M.-A., Dolgui, A., & Al-Ahmari, A. (2012). Optimal MRP offsetting for assembly systems with stochastic lead times: POQ policy and service level constraint. Journal of Intelligent Manufacturing, 23, 2485–2495.CrossRefGoogle Scholar
  20. Mezghiche, A., Moulai, M., & Tadj, L. (2015). Model predictive control of a forecasting production system with deteriorating items. International Journal of Operations Research and Information Systems, 6(4), 19–37.CrossRefGoogle Scholar
  21. Milne, R. J., Mahapatra, S., & Wang, C.-T. (2015). Optimizing planned lead times for enhancing performance of MRP systems. International Journal of Production Economics, 167, 220–231.CrossRefGoogle Scholar
  22. Minner, S., & Kleber, R. (2001). Optimal control of production and remanufacturing in a simple recovery model with linear cost functions. OR Spektrum, 23, 3–24.CrossRefGoogle Scholar
  23. Mishra, U. (2016). An EOQ model with time dependent Weibull deterioration, quadratic demand and partial backlogging. International Journal of Applied and Computational Mathematics.
  24. Mula, J., Lyons, A. C., Hernndez, J. E., & Poler, R. (2014). An integer linear programming model to support customer-driven material planning in synchronised, multi-tier supply chains. International Journal of Production Research, 52(14), 4267–4278.CrossRefGoogle Scholar
  25. Mula, J., Poler, R., & Garcia-Sabater, J. P. (2007). Material requirement planning with fuzzy constraints and fuzzy coefficients. Fuzzy Sets and Systems, 158(7), 783–793.CrossRefGoogle Scholar
  26. Pakdaman, M., & Effati, S. (2016). Approximating the solution of optimal control problems by fuzzy systems. Neural Processing Letters, 43(3), 667–686.CrossRefGoogle Scholar
  27. Paopongchuang, B., & Yenradee, P. (2014). Finite capacity material requirement planning with supplier constraints. International Journal of Industrial and Systems Engineering, 17(3), 350–375.CrossRefGoogle Scholar
  28. Pooya, A., & Faezirad, M. (2017). A taxonomy of manufacturing strategies and production systems using self-organizing map. Journal of Industrial and Production Engineering, 34, 300–311.CrossRefGoogle Scholar
  29. Pooya, A., & Pakdaman, M. (2017a). Analysing the solution of production-inventory optimal control systems by neural networks. RAIRO-Operations Research, 51, 577–590.CrossRefGoogle Scholar
  30. 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.
  31. 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.
  32. Ram, B., Naghshineh-Pour, M. R., & Yu, X. (2006). Material requirements planning with flexible bills-of-material. International Journal of Production Research, 44(2), 399–415.CrossRefGoogle Scholar
  33. Riezebos, J., & Zhu, X. (2015). MRP planned orders in a multiple-supplier environment with differing lead times. Production and Operations Management, 24, 883–895.CrossRefGoogle Scholar
  34. Rossi, T., Pozzi, R., Pero, M., & Cigolini, R. (2017). Improving production planning through finite capacity MRP. International Journal of Production Research.
  35. Sadeghian, R. (2011). Continuous materials requirements planning (CMRP) approach when order type is lot for lot and safety stock is zero and its applications. Applied Soft Computing, 11, 5621–5629.CrossRefGoogle Scholar
  36. Segerstedt, A. (2017). Cover-time planning/takt planning: A technique for materials requirement and production planning. International Journal of Production Economics, 194, 25–31.CrossRefGoogle Scholar
  37. Subbaram Naidu, D. (2002). Optimal control systems. Boca Raton: CRC Press.Google Scholar
  38. Sukkerd, W., & Wuttipornpun, T. (2016). Hybrid genetic algorithm and tabu search for finite capacity material requirement planning system in flexible flow shop with assembly operations. Computers and Industrial Engineering, 97, 157–169.CrossRefGoogle Scholar
  39. Sun, Y., & Zhu, Y. (2017). Bangbang property for an uncertain saddle point problem. Journal of Intelligent Manufacturing.
  40. Swamidass, P. M. (2000). Encyclopedia of production and manufacturing management. Berlin: Springer.CrossRefGoogle Scholar
  41. Vercraene, S., & Gayon, J.-P. (2013). Optimal control of a production-inventory system with product returns. International Journal of Production Economics, 142, 302–310.CrossRefGoogle Scholar
  42. Wuttipornpun, T., & Yenradee, P. (2004). Development of finite capacity material requirement planning system for assembly operations. Production Planning & Control, 15(5), 534–549.CrossRefGoogle Scholar
  43. Wuttipornpun, T., & Yenradee, P. (2007). Performance of TOC based finite capacity material requirement planning system for a multi-stage assembly factory. Production Planning and Control, 18(8), 703–715.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of ManagementFerdowsi University of MashhadMashhadIran
  2. 2.Climatological Research InstituteMashhadIran

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