Delayed control model for multi-stage closed-loop continuous MRP with rework and recycle

Mahdi Miri; Kash Barker; Andrés D. González; Roberto Sacile; Mahdi Miri; Kash Barker; Andrés D. González; Roberto Sacile

doi:10.3934/jimo.2026019

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 1: 504-527. doi: 10.3934/jimo.2026019

Previous Article Next Article

Research article Special Issues

Delayed control model for multi-stage closed-loop continuous MRP with rework and recycle

1.
School of Industrial and Systems Engineering, University of Oklahoma, Norman, Oklahoma, USA
2.
Department of Informatics, Bio-Engineering, Robotics and Systems Engineering, University of Genoa, Genoa, Italy

Received: 23 June 2025 Revised: 11 November 2025 Accepted: 21 November 2025 Published: 15 December 2025
34H05, 90B05

Inventory accumulation is a natural consequence of material flow in manufacturing systems, particularly under dynamic conditions. Manufacturing companies must manage a diverse range of inventory types, including raw materials, semi-finished goods, and finished products. This article proposes a novel multi-stage continuous material requirements planning (MRP) system formulated as a linear–quadratic optimal control model that incorporates production lead times, returns, rework, and recycling. The delayed-control framework provides the foundation for a sustainable production-planning technology roadmap through delay-dependent feedback, dynamic flow relationships, and a multi-stage recovery operation. The roadmap emphasizes the ability to synchronize production and inventory decisions across interrelated stages of production and inventory levels, producing operational, efficiency, and stability improvements. Applied to a fertilizer production case study, the model reduced inventory deviations, enhanced coordination of ordering and production activities, and improved responsiveness to demand changes. The inclusion of perishability and delay mechanisms produced more realistic production planning and waste minimization.
- optimal control,
- continuous material requirements planning,
- multi-stage production systems,
- reworking,
- recycling,
- lead time
Citation: Mahdi Miri, Kash Barker, Andrés D. González, Roberto Sacile. Delayed control model for multi-stage closed-loop continuous MRP with rework and recycle[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 504-527. doi: 10.3934/jimo.2026019

Related Papers:

Abstract

Inventory accumulation is a natural consequence of material flow in manufacturing systems, particularly under dynamic conditions. Manufacturing companies must manage a diverse range of inventory types, including raw materials, semi-finished goods, and finished products. This article proposes a novel multi-stage continuous material requirements planning (MRP) system formulated as a linear–quadratic optimal control model that incorporates production lead times, returns, rework, and recycling. The delayed-control framework provides the foundation for a sustainable production-planning technology roadmap through delay-dependent feedback, dynamic flow relationships, and a multi-stage recovery operation. The roadmap emphasizes the ability to synchronize production and inventory decisions across interrelated stages of production and inventory levels, producing operational, efficiency, and stability improvements. Applied to a fertilizer production case study, the model reduced inventory deviations, enhanced coordination of ordering and production activities, and improved responsiveness to demand changes. The inclusion of perishability and delay mechanisms produced more realistic production planning and waste minimization.

References

[1]	Y. Guo, F. Liu, J. S. Song, S. Wang, Supply chain resilience: A review from the inventory management perspective, Available at SSRN, 4393061, 2023.
[2]	J. Browne, J. Harhen, J. Shivnan, Production Management Systems: An Integrated Perspective, Addison-Wesley Publishing Company, 1996.
[3]	R. Sadeghian, Continuous materials requirements planning (CMRP) approach when order type is lot for lot and safety stock is zero and its applications, Appl. Soft Comput., 11 (2011), 5621–5629. https://doi.org/10.1016/j.asoc.2011.04.002 doi: 10.1016/j.asoc.2011.04.002
[4]	M. A. Louly, A. Dolgui, A. Al-Ahmari, Optimal MRP offsetting for assembly systems with stochastic lead times: POQ policy and service level constraint, J. Intell. Manuf., 23 (2012), 2485–2495. https://doi.org/10.1007/s10845-011-0515-7 doi: 10.1007/s10845-011-0515-7
[5]	R. W. Grubbström, O. Tang, The space of solution alternatives in the optimal lotsizing problem for general assembly systems applying MRP theory, Int. J. Prod. Econ., 140 (2012), 765–777. https://doi.org/10.1016/j.ijpe.2011.01.012 doi: 10.1016/j.ijpe.2011.01.012
[6]	A. Pooya, M. Pakdaman, Optimal control model for finite capacity continuous MRP with deteriorating items, J. Intell. Manuf., 30 (2019), 2203–2215. https://doi.org/10.1007/s10845-017-1383-6 doi: 10.1007/s10845-017-1383-6
[7]	A. Pooya, M. Pakdaman, Analysing the solution of production-inventory optimal control systems by neural networks, RAIRO-Oper. Res., 51 (2017), 577–590. https://doi.org/10.1051/ro/2016044 doi: 10.1051/ro/2016044
[8]	A. Pooya, M. Pakdaman, A delayed optimal control model for multi-stage production-inventory system with production lead times, Int. J. Adv. Manuf. Technol., 94 (2018), 751–761. https://doi.org/10.1007/s00170-017-0942-5 doi: 10.1007/s00170-017-0942-5
[9]	M. Miri, Optimal control model for a continuous model of supply chain and its solution using genetic algorithm (in persian), In 14th International Conference of Iranian Operations Research Society. Sadjad University of Mashhad, Iran, 2021.
[10]	S. Sowmica, M. Suvinthra, Optimal control strategies for a two-item production-maintenance system with deterioration, Results Control Optim., 14 (2024), 100385. https://doi.org/10.1016/j.rico.2024.100385 doi: 10.1016/j.rico.2024.100385
[11]	H. Rachih, F. Mhada, R. Chiheb, Simulation optimization of an inventory control model for a reverse logistics system, Decis. Scie. Lett., 11 (2022), 43–54. https://doi.org/10.5267/j.dsl.2021.9.001 doi: 10.5267/j.dsl.2021.9.001
[12]	H. Öztürk, Optimal production run time for an imperfect production inventory system with rework, random breakdowns and inspection costs, Opera. Res. Int. J., 21 (2021), 167–204. https://doi.org/10.1007/s12351-018-0439-5 doi: 10.1007/s12351-018-0439-5
[13]	M. Eshaghnezhad, A. Mansoori, S. Effati, Optimal control problem: A case study on production planning in the reverse logistics system, J. Syst. Thinking Pract., 2 (2023). https://doi.org/10.22067/JSTINP.2023.81194.1037
[14]	G. Aiello, C. Muriana, S. Quaranta, I. A. S. Abusohyon, A sustainable inventory management model for closed loop supply chain involving waste reduction and treatment, Cleaner Logistics Supply Chain, 16 (2025), 100244. https://doi.org/10.1016/j.clscn.2025.100244 doi: 10.1016/j.clscn.2025.100244
[15]	N. Sharma, M. Jain, D. Sharma, Anfis and metaheuristics for green supply chain with inspection and rework, arXiv preprint arXiv: 2401.09154, 2024. https://doi.org/10.48550/arXiv.2401.09154
[16]	S. Mahata, B. K. Debnath, Impact of green technology and flexible production on multi-stage economic production rate (epr) inventory model with imperfect production and carbon emissions, J. Cleaner Prod., 504 (2025), 145187. https://doi.org/10.1016/j.jclepro.2025.145187 doi: 10.1016/j.jclepro.2025.145187
[17]	A. Hatami-Marbini, S. M. Sajadi, H. Malekpour, Optimal control and simulation for production planning of network failure-prone manufacturing systems with perishable goods, Comput. Ind. Eng., 146 (2020), 106614. https://doi.org/10.1016/j.cie.2020.106614 doi: 10.1016/j.cie.2020.106614
[18]	A. Foul, L. Tadj, R. Hedjar, Adaptive control of inventory systems with unknown deterioration rate, J. King Saud Univ. Sci., 24 (2012), 215–220. https://doi.org/10.1016/j.jksus.2011.02.001 doi: 10.1016/j.jksus.2011.02.001
[19]	J. Shen, Y. Jin, B. Liu, Z. Lu, X. Chen, An uncertain production-inventory problem with deteriorating items, Adv. Cont. Discr. Mod., 2022 (2022), 42. https://doi.org/10.1186/s13662-022-03714-8 doi: 10.1186/s13662-022-03714-8
[20]	P. Megoze Pongha, G. R. Kibouka, J. P. Kenné, L. A. Hof, Production, maintenance and quality inspection planning of a hybrid manufacturing/remanufacturing system under production rate-dependent deterioration, Int. J. Adv. Manuf. Technol., 121 (2022), 1289–1314. https://doi.org/10.1007/s00170-022-09078-3 doi: 10.1007/s00170-022-09078-3
[21]	P. Ignaciuk, Linear-quadratic optimal control of multi-modal distribution systems with imperfect channels, Int. J. Prod. Res., 60 (2022), 5523–5538. https://doi.org/10.1080/00207543.2021.1963876 doi: 10.1080/00207543.2021.1963876
[22]	D. P. Covei, Stochastic production planning with regime switching: Numerical and sensitivity analysis, optimal control, and python implementation, arXiv preprint arXiv: 2505.08057, 2025. https://doi.org/10.48550/arXiv.2505.08057
[23]	E. A. Attia, M. M. Miah, A. S. Arif, A. AlArjani, M.Hasan, M. S. Uddin, A novel model for economic recycle quantity with two-level piecewise constant demand and shortages, Computation, 12 (2024), 13. https://doi.org/10.3390/computation12010013 doi: 10.3390/computation12010013
[24]	R. J. Milne, S. Mahapatra, C. T. Wang, Optimizing planned lead times for enhancing performance of MRP systems, Int. J. Prod. Econ., 167 (2015), 220–231. https://doi.org/10.1016/j.ijpe.2015.05.013 doi: 10.1016/j.ijpe.2015.05.013
[25]	G. Rigatos, P. Siani, M. Al-Numay, M. Abbaszadeh, J. Liu, D. Sarno, Nonlinear optimal control for supply chain networks under time-delays, 2024. https://doi.org/10.21203/rs.3.rs-4145311/v1
[26]	R. Hedjar, L. Tadj, C. Abid, Optimal Control of Integrated Production–Forecasting System, Decision Support Systems, 2012.
[27]	N. M. Dizbin, B. Tan, Optimal control of production-inventory systems with correlated demand inter-arrival and processing times, Int. J. Prod. Econ., 228 (2020), 107692. https://doi.org/10.1016/j.ijpe.2020.107692 doi: 10.1016/j.ijpe.2020.107692
[28]	H. AL Khazraji, C. Cole, W. Guo, Optimization and simulation of dynamic performance of production–inventory systems with multivariable controls, Mathematics, 9 (2021), 568. https://doi.org/10.3390/math9050568 doi: 10.3390/math9050568
[29]	Z. L. Jin, M. Maasoumy, Y. Liu, Z. Zheng, Z. Ren, Stochastic optimization of inventory at large-scale supply chains, arXiv preprint arXiv: 2502.11213, 2025. https://arXiv.org/abs/2502.11213.
[30]	D. Marsetiya Utama, A. Bripka Putri, The production-inventory model with imperfect, rework, and scrap items under stochastic demand, Int. J. Adv. Appl. Sci., 2252 (2024), 8814. https://doi.org/10.11591/IJAAS.V13.I4.PP896-906 doi: 10.11591/IJAAS.V13.I4.PP896-906
[31]	C. Hake, J. Weigele, F. Reichert, C. Friedrich, Evaluation of artificial intelligence methods for lead time prediction in non-cycled areas of automotive production, arXiv preprint arXiv: 2501.07317, 2025. https://arXiv.org/abs/2501.07317.
[32]	T. Rossi, R. Pozzi, M. Pero, R. Cigolini, Improving production planning through finite-capacity MRP, Int. J. Prod. Res., 55 (2017), 377–391. https://doi.org/10.1080/00207543.2016.1177235 doi: 10.1080/00207543.2016.1177235
[33]	H. A. Le Thi, D. Q. Tran, Optimizing a multi-stage production/inventory system by DC programming based approaches, Comput. Optim. Appl., 57 (2014), 441–468. https://doi.org/10.1007/s10589-013-9600-5 doi: 10.1007/s10589-013-9600-5
[34]	A. Mezghiche, M. Moulaï, L. Tadj, Model predictive control of a forecasting production system with deteriorating items, International Journal of Operations Research and Information Systems (IJORIS), 6 (2015), 19–37. https://doi.org/10.4018/IJORIS.2015100102 doi: 10.4018/IJORIS.2015100102
[35]	G. Singer, E. Khmelnitsky, A production-inventory problem with price-sensitive demand, Appl. Math. Modell., 89 (2021), 688–699. https://doi.org/10.1016/j.apm.2020.06.072 doi: 10.1016/j.apm.2020.06.072
[36]	M. ElHafsi, J. Fang, E. Hamouda, Optimal production and inventory control of multi-class mixed backorder and lost sales demand class models, Eur. J. Oper. Res., 291 (2021), 147–161. https://doi.org/10.1016/j.ejor.2020.09.009 doi: 10.1016/j.ejor.2020.09.009
[37]	Y. Gao, Operator splitting method for the stochastic production–inventory model equation, Comput. Ind. Eng., 174 (2022), 108712. https://doi.org/10.1016/j.cie.2022.108712 doi: 10.1016/j.cie.2022.108712
[38]	A. K. Dhaiban, An integer optimal control model of production-inventory system, Stat. Optim. Inf. Computi., 10 (2022), 762–774. https://doi.org/10.19139/soic-2310-5070-747 doi: 10.19139/soic-2310-5070-747
[39]	M. Nakhaeinejad, H. Khademi Zare, M. Habibi, M. Reza Khodoomi, Improvement of multi-item order systems and inventory management models using optimal control theory, Trans. Inst. Meas. Control, 45 (2023), 104–119. https://doi.org/10.1177/01423312221109724 doi: 10.1177/01423312221109724
[40]	M. Schlenkrich, J. F. Cordeau, S. N. Parragh, Progressive hedging for multi-stage stochastic lot sizing problems with setup carry-over under uncertain demand, arXiv preprint arXiv: 2503.08477, 2025.
[41]	T. Daiana Tobares, M. Miguelina Mieras, F. O. Sanchez Varretti, J. L. Iguain, A. José Ramirez-Pastor, A physical model approach to order lot sizing, arXiv preprint arXiv: 2502.06856, 2025.
[42]	R. Pindyck, An application of the linear quadratic tracking problem to economic stabilization policy, IEEE Trans. Autom. Control, 17 (1972), 287–300. https://doi.org/10.1109/TAC.1972.1100010 doi: 10.1109/TAC.1972.1100010
[43]	R. Taparia, S. Janardhanan, R. Gupta, Lqr control of multiple product inventory systems for profit and warehouse capacity maximization, In 2020 International conference on emerging trends in communication, control and computing (ICONC3). IEEE, 1–5, 2020.
[44]	P. Ignaciuk, A. Bartoszewicz, Linear–quadratic optimal control strategy for periodic-review inventory systems, Automatica, 46 (2010), 1982–1993. https://doi.org/10.1016/j.automatica.2010.09.010 doi: 10.1016/j.automatica.2010.09.010
[45]	A. Foul, L. Tadj, Optimal control of a hybrid periodic-review production inventory system with disposal, Int. J. Oper. Res., 2 (2007), 481–494. https://doi.org/10.1504/IJOR.2007.014175 doi: 10.1504/IJOR.2007.014175
[46]	U. Mishra, An EOQ model with time dependent Weibull deterioration, quadratic demand and partial backlogging, Int. J. Appl. Comput. Math., 2 (2016), 545–563. https://doi.org/10.1007/s40819-015-0077-z doi: 10.1007/s40819-015-0077-z

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)