Optimal control of production and maintenance: A cost-efficient approach through inventory and preventive strategies

i

This article has been updated. A Correction to this article was published on .

i

The Original Article was published on

i

The Original Article was published on

i

This article has been updated

i

This article was retracted on

i

This article has been updated

Abstract

Using an optimal control framework, the optimization of production and maintenance processes is investigated in this paper. We focused on analyzing system behavior, managing costs, and controlling quality. Differential equations are utilized to model the relationship between inventory level, production, and maintenance strategies. A cost function is built combining different cost elements, and the optimal production and maintenance rates were obtained. A sensitivity analysis is performed to assess the impact of different parameters on the total cost and on the optimal solution. The key findings demonstrated that higher initial inventory levels significantly decreased long-term costs and improved production efficiency. The optimal preventive maintenance strategy emphasized the importance of early investments in quality and maintenance, leading to sustained operational stability.

Keywords

inventory / deterioration / optimal control / production / maintenance / obsolescence

CHANGE HISTORY

A Correction to this paper has been published:
https://doi.org

The Retraction Note was updated to reflect reception of statements of disagreement from all authors.

This article has been retracted.Please see the Retraction Notice for more detail:
https://doi.org

References

[1] M. Ben-Daya, M. A. Rahim, Integrated production, quality & maintenance models: An Overview, in Integrated Models in Production Planning, Inventory, Quality, and Maintenance, (eds. M. A. Rahim and M. Ben-Daya ), Springer, Boston, 2012. https://doi.org/10.1007/978-1-4615-1635-41

[2] A. Van Horenbeek, J. Buré, D. Cattrysse, L. Pintelon, P. Vansteenwegen, Joint maintenance and inventory optimization systems: A review, Int. J. Prod. Econ., 143 (2013), 499-508. https://doi.org/10.1016/j.ijpe.2012.04.001

[3] D. I. Cho, P. L. Abad, M. Parlar, Optimal production and maintenance decisions when a system experience age-dependent deterioration, Optim. Control. Appl. Methods, 14 (1993), 153-167. https://doi.org/10.1002/oca.4660140302

[4] H. Maurer, J. H. R. Kimr, G. Vossen, On a state-constrained control problem in optimal production and maintenance, in Optimal Control and Dynamic Games-Applications in Finance, Management Science and Economics, (eds. C. Deissenberg and R. F. Hartl), Springer, Boston, 7 (2005). https://doi.org/10.1007/0-387-25805-117

[5] F. A. Bukhari, Adaptive control of a production and maintenance system with unknown deterioration and obsolescence rates, Int. J. Math. Sci. Appl., 1 (2012), 1273-1282. https://doi.org/10.4236/am.2011.29162

[6] F. A. Bukhari, A. El-Gohary, Optimal control of a production-maintenance system with deteriorating items, J. King Saud Univ. Sci. 24 (2012), 351-357. https://doi.org/10.1016/j.jksus.2011.08.001

[7] S. Li, Optimal control of production-maintenance system with deteriorating items, emission tax and pollution R&D investment, Int. J. Prod. Res., 52 (2014), 1787-1807. https://doi.org/10.1080/00207543.2013.848486

[8] M. Bakker, J. Riezebos, R. H. Teunter, Review of inventory systems with deterioration since 2001, Eur. J. Oper. Res., 221 (2012), 275-284. https://doi.org/10.1016/j.ejor.2012.03.004

[9] L. Janssen, T. Claus, J. Sauer, Literature review of deteriorating inventory models by key topics from 2012 to 2015, Int. J. Prod. Econ., 182 (2016), 86-112. https://doi.org/10.1016/j.ijpe.2016.08.019

[10] S. K. Goyal, B. C. Giri, Recent trends in modeling of deteriorating inventory, Eur. J. Oper. Res., 134 (2001), 1-16. https://doi.org/10.1016/S0377-2217(00)00248-4

[11] F. Raafat, Survey of literature on continuously deteriorating inventory models, J. Oper. Res. Soc., 42 (1991), 27-37. https://doi.org/10.2307/2582993

[12] V. Chaudhary, R. Kulshrestha, S. Routroy, State-of-the-art literature review on inventory models for perishable products, J. Adv. Manage. Res., 15 (2018), 306-346. https://doi.org/10.1108/JAMR-09-2017-0091

[13] J. Kaushik, Development of inventory models for deteriorating items considering uniform, price, and time-dependent demand-A review, Adv. Appl. Math. Sci., 21 (2022), 4083-4096.

[14] R. Li, H. Lan, J. R. Mawhinney, A review on deteriorating inventory study, J. Serv. Sci. Manage., 3 (2010), 117-129. https://doi.org/10.4236/jssm.2010.31015

[15] I. Z. Karaesmen, A. Scheller-Wolf, B. Deniz, Managing perishable and aging inventories: Review and future research directions, in Planning Production and Inventories in the Extended Enterprise. International Series in Operations Research & Management Science , (eds. K. Kempf, P. Keskinocak and R. Uzsoy), Springer, New York, 151 (2011). https://doi.org/10.1007/978-1-4419-6485-415

[16] J. Pahl, S. Voß, Integrating deterioration and lifetime constraints in production and supply chain planning: A survey, Eur. J. Oper. Res., 238 (2014), 654-674. https://doi.org/https://doi.org/10.1016/j.ejor.2014.01.060

[17] S. Nahmias, Perishable inventory theory: A review, Oper. Res., 30 (1982), 680-708. https://doi.org/10.1287/opre.30.4.680

[18] R. Sharan, S. A. Sayyed, Review of mathematical approaches on deteriorating inventory models, Afr. Diaspora J. Math., 25 (2022), 47-59.