Optimal Production and Maintenance Policy for a Partially Observable Production System with Stochastic Demand

Authors: Leila Jafari, Viliam Makis

Abstract:

In this paper, the joint optimization of the economic manufacturing quantity (EMQ), safety stock level, and condition-based maintenance (CBM) is presented for a partially observable, deteriorating system subject to random failure. The demand is stochastic and it is described by a Poisson process. The stochastic model is developed and the optimization problem is formulated in the semi-Markov decision process framework. A modification of the policy iteration algorithm is developed to find the optimal policy. A numerical example is presented to compare the optimal policy with the policy considering zero safety stock.

Keywords: Condition-based maintenance, economic manufacturing quantity, safety stock, stochastic demand.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3300342

References:

[1] J. Sicilia, M. Gonzlez-De-la-Rosa, J. Febles-Acosta, and D. Alcaide-Lpez-de-Pablo, ”Optimal policy for an inventory system with power demand, backlogged shortages and production rate proportional to demand rate”, International Journal of Production Economics, 2014, 213, pp. 1-14.
[2] B. Pal, S.S. Sana, and K. Chaudhuri, ”A mathematical model on EPQ for stochastic demand in an imperfect production system”, Journal of Manufacturing Systems, 2013, 32, pp. 260-270.
[3] B. Bouslah, A. Gharbi, and R. Pellerin, ”Joint optimal lot sizing and production control policy in an unreliable and imperfect manufacturing system”, International Journal of Production Economics, 2013, 144, pp. 143-156.
[4] J.T. Hsu and L.F. Hsu, ”Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns”, Computers & Industrial Engineering, 2013, 64, pp. 389-402.
[5] A.H. Tai, ”Economic production quantity models for deteriorating/imperfect products and service with rework”, Computers & Industrial Engineering, 2013, 66, pp. 879-888.
[6] S.J. Sadjadi, S.A. Yazdian, and K. Shahanaghi, ”Optimal pricing, lot-sizing and marketing planning in a capacitated and imperfect production system”, Computers & Industrial Engineering, 2012, 62, pp. 349-358.
[7] H. Groenevelt, L. Pintelon, and A. Seidmann, ”Production lot sizing with machine breakdowns”, Management Science, 1992, 38, pp. 104-123.
[8] H. Groenevelt, L. Pintelon, and A. Seidmann, ”Production batching with machine breakdowns and safety stocks”, Operations Research, 1992, 40, 959-971.
[9] C.E. Tse and V. Makis, ”Optimization of the lot size and the time to replacement in a production system subject to random failure”, Third International Conference on Automation Technology, Taipei, Taiwan, 1994.
[10] M. Ben-Daya, ”The economic production lot-sizingproblem with imperfect production processes and imperfect maintenance”, International Journal of Production Research, 2002, 76, pp. 257-264.
[11] S.M. Suliman and S.H. Jawad, ”Optimization of preventive maintenance schedule and production lot size”, International Journal of Production Economics, 2012, 137, pp. 19-28.
[12] G.L. Liao and S.H. Sheu, ”Economic production quantity model for randomly failing production process with minimal repair and imperfect maintenance”, International Journal of Production Economics, 2011, 130, 118-124.
[13] H. Rivera-Gomez, A. Gharbi, and J.P. Kenne, ”Joint control of production, overhaul, and preventive maintenance for a production system subject to quality and reliability deteriorations”, International Journal of Advanced Manufacturing Technology, 2013, 69, pp. 2111-2130.
[14] L. Jafari, and V. Makis, ”Optimal lot sizing and maintenance policy for a partially observable production system”, Computers & industrial Engineering, 2016, 93 pp. 88-98.
[15] L. Jafari, and V. Makis, ”Joint optimal lot sizing and preventive maintenance policy for a production facility subject to condition monitoring”, International Journal of Production Economics, 2015, 169, pp. 156-168.
[16] H. Peng and G.V. Houtum, ”Joint optimization of condition-based maintenance and production lot-sizing”, European Journal of Operational Research, 2016, 253, pp. 94-107.
[17] N.H. Shah, D.G. Patel, and D. Shah, ”EPQ model for trended demand with rework and random preventive machine time”, ISRN Operations Research,2014, 2013, pp. 1-8.
[18] T.K. Das and S. Sarkar, ”Optimal preventive maintenance in a production inventory system”, IIE Transactions, 1999, 31, pp. 537-551.
[19] D.P. Song, ”Production and preventive maintenance control in a stochastic manufacturing system”, International Journal of Production Economics, 2009, 119, pp. 101-111.
[20] S.M. Iravani and I. Duenyas, ”Integrated maintenance and production control of a deteriorating production system”, IIE Transactions, 2002, 34,pp. 423-435.
[21] O. Prakash, A.R. Roy, and A. Goswami, ”Stochastic manufacturing system with process deterioration and machine breakdown”, International Journal of Systems Science, 2014, 45, pp. 2539-2551.
[22] T. Dohi, H. Okamura, and S. Osaki, ”Optimal Control of Preventive Maintenance Schedule and Safety Stocks in an Unreliable Manufacturing Environment”, International Journal of Production Economics, 2001, 74, pp. 147-155.
[23] B.C. Giri and T. Dohi, ”Exact Formulation of Stochastic EMQ Model for an Unreliable Production Systems”, Journal of the Operational Research Society, 2005, 56, pp. 563-575.
[24] S.S. Sana and K.S. Chaudhuri, ”An EMQ Model in an Imperfect Production Process”, International Journal of Systems Science, 2010, 41, pp.635-646.
[25] H.C. Tijms, Stochastic models- an algorithmic approach. John Wiley & Sons.
[26] J. Yang and V. Makis, ”Dynamic response of residual to external deviations in a controlled production process”, Technometrics, 2000, 42, pp.290-299.
[27] V. Makis, ”Multivariate bayesian control chart”, Operation Research, 2008, 56, pp. 487-496.
[28] V. Makis, ”Multivariate bayesian process control for a finite production run”, European Journal of Operation Research, 2009, 194, pp. 795-806.
[29] P.J. Imhof, ”Computing the distribution of quadratic forms in normal variables”, Biometrika, 1961, 48 (3), pp. 419-426.