Joint optimal inventory control and preventive maintenance policy with stochastic demand

Document Type: Research Paper


1 Department of Industrial Engineering, Alzahra University, Tehran, Iran

2 Department of Industrial Engineering, Faculty of Engineering, Kharazmi University,Tehran,Iran


Joint optimal inventory control and preventive maintenance is a rich area of academic research that is still in its infancy and has the potential to affect manufacturing systems' performance. Also, due to uncertainties in demand, maintenance and inventory loss are virtually unavoidable. Therefore, determining the optimal amount of inventory storage, the time to create an additional inventory for storage, and the time of maintenance operations is a concern of many manufacturers. In this paper, a joint optimization model has been developed. In which, for the proximity of reality, demand is considered as an uncertain parameter. The strategy is such that the production component is placed under maintenance as soon as it reaches the  level or in the event of a malfunction earlier than , stopped system and placed under maintenance and repairs. Inventory of  period with level  is created, which during maintenance operations, stochastic demand will be provided. Finally, a model for joint optimization of maintenance and inventory control with random failure is used that minimize the cost and create the maximum level of accessibility. A numerical study is conducted to show the effectiveness and applicability of the proposed integrated model. An accurate algorithm is provided to solve the model. The results show that the model is generally sensitive to the cost.


Main Subjects

Alaswad, S., Xiang, Y., (2017). A review on condition-based maintenance optimization models for stochastically deteriorating system. ReliabilEngSystSaf. 157,54–63.

Ayed, S., Sofiene, D., Nidhal, R. (2012). Joint optimization of maintenance and production policies considering random demand and variable production rate. IntJProdRes. 50(23), pp. 6870–6885.

Babaeimorad.S., Fattahi, P., Bagheri, H. (2019). Joint Optimization of Maintenance and Production Scheduling with Considering the Back of Order and Probabilistic Demand. Journal of Industrial Engineering Research in Production Systems. Volume 7., No. 14., pp. 47-57.

Berrade, M.D., Scarf, P.A. (2017). Cavalcante CAV. A study of postponed replacement in a delay time model. ReliabilEngSystSaf, 168, pp. 70–9.

Berthaut, F., Gharbi, A., Dhouib, K., (2011). Joint modified block replacement and production/inventory control policy for a failureprone manufacturing cell. Omega. 39, pp.642–654.

Çetinkaya, S,. and Lee, C-Y. (2000). Stock Replenishment and Shipment Scheduling for Vendor-Managed Inventory Systems. Management Science, 46(2), 217 – 232.

Chakraborty, T., Chauhan , S.S., Giri, B.C., (2013). Joint effect of stock threshold level and production policy on an unreliable production environment. Appl Math Model 37. pp. 6593–6608.

Chelbi, A., A-Kadi, D. (2004). Analysis of a production/inventory system with randomly failing production unit submitted to regular preventive maintenance. European Journal of Operational Research. 156(3), pp. 712–718.

Chen, Y.C. (2013). An optimal production and inspection strategy with preventive maintenance error and rework. J ManufSyst. 32(1), pp. 99–106.

Christer, A.H. (1999). Developments in delay time analysis for modelling plant maintenance. JOperResSoc. 50, pp. 1120–37.

Gan, S., Zhang, Z., Zhou, Y., Shi, J. (2015). Joint optimization of maintenance, buffer, and spare parts for a production system. Appl. Math. Model. 39 6032–6042.

Gan, Sh., Zhang, Zh., Shi, J. (2015). Joint optimization of maintenance, buffer, and spare parts for a production system. Applied Mathematical Modelling.

Ghodratnama, A., Rabbani, M., Tavakkoli-Moghaddam, R., Baboli, A. (2010). Solving a single-machine scheduling problem with maintenance, job deterioration and learning effect by simulated annealing. J ManufSyst. 29(1),pp.1–9.

Guo, W., Jin, J., Hu, S.J. (2013). Allocation of maintenance resources in mixed model assembly systems. J ManufSyst. 32(3), pp. 473–9 .

Horenbeek, V., Buré, A., Cattrysse, J., Pintelon, D., Vansteenwegen, L., (2013). Joint maintenance and inventory optimization systems: a review. Int J Prod Econ.143(2), pp. 499–508.

Hsieh, C-H. (2004). Optimization of Fuzzy Inventory Models under Fuzzy Demand and Fuzzy Lead Time. Tamsui Oxford Journal of Management Sciences, 20(2), 21-36.

Hwang, J. Q., and Samat, H. A. (2019). A Review on Joint Optimization of Maintenance with Production Planning and Spare Part Inventory Management. Materials Science and Engineering 530 (2019) 012048. doi:10.1088/1757-899X/530/1/012048.

Ilgin, M.A., Tunali, S. (2007). Joint optimization of spare parts inventory and maintenance policies using genetic algorithms. Int J AdvManufTechnol. 34(5), pp. 594–604.

Jafari, L., Naderkhani, F., Makis, V. (2017). Joint optimization of maintenance policy and inspection interval for a multi-unit series system using proportional hazards model. Journal of the Operational Research Society. Doi:10.1057/s41274-016-0160-9.

Kaio, N., Osaki, S. (1978). Optimum ordering policies with lead time for an operating unit in preventive maintenance. IEEE Trans Reliab. 27(4), pp. 270–1.

Kang, K. Subramaniam, V.(2018). Integrated control policy of production and preventive maintenance for a deteriorating manufacturing system. Computers & Industrial Engineering 118 .266–277.

Liao, G. (2012). Optimal economic production quantity policy for randomly failing process with minimal repair, backorder and preventive maintenance. IntJSystSci. 44(9): 1602–12.

Liu, X., Wang, W., Peng, R. (2015). An integrated production, inventory and preventive maintenance model for a multi-product production system. RelEng Sys Saf. 137, pp. 76–86.

Liu, X., Wang, W., Zhao, F., Peng, R., (2015). Joint lot-size and preventive maintenance optimization for a production system. International Journal of Performability Engineering. 11(1), pp. 91–96.

Lynch, P., Adendorff, K., Yadavalli, V.S.S. (2013). Optimal spares and preventive maintenance frequencies for constrained industrial systems. ComputInd Eng. 65(3), 378–87.

 Minou C.A.,O., KeizerRuud, H., Jasper,V. (2017). Joint condition-based maintenance and inventory optimization for systems with multiple components. European Journal of Operational Research. Volume 257, Issue 1. Pages 209-222.

Mjirda, A., Benmansour, R. , Allaoui,G.Goncalves, H. (2016). On the joint optimization of the periodic preventive maintenance and the spare parts inventory problem. IFAC-PapersOnLine. 49- 881–885.

Nguyen, D.Q., Bagajewicz, M. (2009). Optimization of preventive maintenance in chemical process plants. Working Paper.

Olde Keizer, M.C.A., Flapper, S.D.P., Teunter, R.H., (2017). Condition-based maintenance policies for systems with multiple dependent components: a review. EurJOper Res.261, pp. 405–20.

Panagiotidou, S. (2014). Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures. Eur J Oper Res. 235(1),  pp. 300–14.

Qinming, L.,   Ming, D., Chen, F.F., Wenyuan, L., Chunming, Y. (2019). Single-machine-based joint optimization of predictive maintenance planning and production scheduling. Robotics and Computer-Integrated Manufacturing. Volume 55. Part B . Pages 173-182.

Radhoui, M.,  Rezg, N., Chelbi, A. (2009). Integrated model of preventive maintenance, quality control and buffer sizing for unreliable and imperfect production systems. International Journal of Production Research. 47(2), pp. 389–402.

Rezg, N., Dellagi, S.,  Chelbi, A. (2008). Joint optimal inventory control and preventive maintenance policy. International Journal of Production Research. 46:19, pp. 5349-5365.

Ribeiro, M A., Silveira, J. L., and Qassim, R. Y. (2007). Joint optimisation of maintenance and buffer size in a manufacturing system. Eur. J. Oper. Res. 176 405–413.

Scarf, P.A., Cavalcante, C.A.V. (2012). Modelling quality in replacement and inspection maintenance. Int J Prod Econ. 135, pp. 372–81.

Van Horenbeek, A., Scarf, P.A., Cavalcante, C.A. (2013). The effect of maintenance quality on spare parts inventory for a fleet of assets. IEEE Trans Reliab. 62(3), pp.596–607.

Van Jaarsveld, W., Dekker, R. (2011). Spare parts stock control for redundant systems using reliability centered maintenance data. ReliabEngSystSaf. 96, pp. 1576–86.

Wang, W. (2012). An overview of the recent advances in delay-time-based maintenance modeling. ReliabilEngSystSaf. 106, pp.165–78.

Wang, H.Z. (2002). A survey of maintenance policies of deteriorating systems. EurJOper Res. 139, pp. 469–89.

Wang, L., Chu, J., Mao, W., (2008a.) A condition-based order-replacement policy for a single-unit system. Applied Mathematical Modelling. 32 11, 2274–2289.

Yeung, T.G.,  Cassady C.R. (2007). Schneider, Simultaneous optimization of x control chart and age-based preventive maintenance policies under an economic objective. IIE Trans. 40, pp. 147–159.

Zhang, X., Zeng , J. (2017). Joint optimization of condition-based opportunistic maintenance and spare parts provisioning policy in multiunit systems. European Journal of Operational Research. doi: 10.1016/j.ejor.2017.03.019.