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

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.

Authors:

• Leila Jafari
• Viliam Makis

Keywords:

• Condition-based maintenance
• economic manufacturing quantity
• safety stock
• stochastic demand.

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.