The Simultaneous Effect of Holding Safety Stock and Purchasing Policies on the Economic Production Quantity Model Subject to Random Machine Breakdown

Document Type : Original Article


Department of Industrial Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran


In this paper, we develop an economic production quantity (EPQ) model under machine breakdown and two types of repair (corrective and preventive). also, study the simultaneous effect of holding safety stock and purchasing policy. In order to avoid shortages occurring as a result of the random repair time, in addition to keep safety stock, we suppose that the manufacturer could purchase some quantities from an external supplier. This paper addresses the following question: how the manufacturer determine the optimal values of safety stock, production and purchasing lot sizes, simultaneously, to minimize the expected total cost? The introduced model is then compared with the situations in which the manufacturer only keeps safety stock or just uses an external supplier, respectively. The results through the analysis show that using the simultaneous policy when the system is prone to shortages due to long repair times, have more improvement in the performance of the system rather than using the safety stock or purchasing policies, separately.


1. Giri, B.C., Yun, W.Y. and Dohi, T., “Optimal design of
unreliable production–inventory systems with variable
production rate”, European Journal of Operational Research,
Vol. 162, No. 2, (2005), 372–386.  
2. Sana, S.S. and Chaudhuri, K., “An EMQ model in an imperfect
production process”, International Journal of Systems Science,
Vol. 41, No. 6, (2010), 635–646.  
3. Axsäter, S., “An improved decision rule for emergency
replenishments”, International Journal of Production
Economics, Vol. 157, (2014), 313–317.  
4. Johansen, S.G. and Thorstenson, A., “Emergency orders in the
periodic-review inventory system with fixed ordering costs and compound Poisson demand”, International Journal of
Production Economics, Vol. 157, (2014), 147–157.  
5. Pirayesh, M. and Yavari, M., “Determination of Economic
Production Quantity with Regard to Machine Failure”, In
International Conference on Advances in Mechanical,
Production and Industrial Engineering, (2014), 87–91.  
6. Peymankar, M., Dehghanian, F., Ghiami, Y. and Abolbashari,
M. H., “The effects of contractual agreements on the economic
production quantity model with machine breakdown”,
International Journal of Production Economics, Vol. 201,
(2018), 203–215.  
7. Groenevelt, H., Pintelon, L. and Seidmann, A., “Production lot
sizing with machine breakdowns”, Management Science, Vol.
38, No. 1, (1992), 104–123.  
8. Boone, T., Ganeshan, R., Guo, Y. and Ord, J. K., “The impact of
imperfect processes on production run times”, Decision
Sciences, Vol. 31, No. 4, (2000), 773–787.  
9. Abboud, N. E., “A discrete-time Markov production-inventory
model with machine breakdowns”, Computers & Industrial
Engineering, Vol. 39, No. 1–2, (2001), 95–107.  
10. Giri, B.C. and Yun, W. Y., “Optimal lot sizing for an unreliable
production system under partial backlogging and at most two
failures in a production cycle”, International Journal of
Production Economics, Vol. 95, No. 2, (2005), 229–243.  
11. Chiu, S.W., Wang, S.L. and Chiu, Y. S. P., “Determining the
optimal run time for EPQ model with scrap, rework, and
stochastic breakdowns”, European Journal of Operational
Research, Vol. 180, No. 2, (2007), 664–676.  
12. Chiu, S.W., Chen, K.K. and Yang, J. C., “Optimal replenishment
policy for manufacturing systems with failure in rework”,
Mathematical and Computer Modelling of Dynamical
Systems, Vol. 15, No. 3, (2009), 255–274.  
13. Cheung, K.L. and Hausman, W. H., “Joint determination of
preventive maintenance and safety stocks in an unreliable
production environment”, Naval Research Logistics (NRL),
Vol. 44, No. 3, (1997), 257–272.  
14. Dohi, T., Okamura, H. and Osaki, S., “Optimal control of
preventive maintenance schedule and safety stocks in an
unreliable manufacturing environment”, International Journal
of Production Economics, Vol. 74, No. 1–3, (2001), 147–155.  
15. Chakraborty, T., Giri, B.C. and Chaudhuri, K. S., “Production
lot sizing with process deterioration and machine breakdown”,
European Journal of Operational Research, Vol. 185, No. 2,
(2008), 606–618.  
16. Chelbi, A. and Rezg, N., “Analysis of a production/inventory
system with randomly failing production unit subjected to a
minimum required availability level”, International Journal of
Production Economics, Vol. 99, No. 1–2, (2006), 131–143.  
17. El-Ferik, S., “Economic production lot-sizing for an unreliable
machine under imperfect age-based maintenance policy”,
European Journal of Operational Research, Vol. 186, No. 1,
(2008), 150–163.  
18. Chakraborty, T. and Giri, B. C., “Joint determination of optimal
safety stocks and production policy for an imperfect production
system”, Applied Mathematical Modelling, Vol. 36, No. 2,
(2012), 712–722.  
19. Kuhn, H., “A dynamic lot sizing model with exponential
machine breakdowns”, European Journal of Operational
Research, Vol. 100, No. 3, (1997), 514–536.  
20. Moini, A. and Murthy, D. N. P., “Optimal lot sizing with
unreliable production system”, Mathematical and Computer
Modelling, Vol. 31, No. 10–12, (2000), 245–250.  
21. Gharbi, A., Kenné, J.P. and Beit, M., “Optimal safety stocks and 
preventive maintenance periods in unreliable manufacturing
systems”, International Journal of Production Economics,
Vol. 102, No. 7, (2007), 422–434.  
22. Al-Salamah, M., “Economic production quantity in batch
manufacturing with imperfect quality, imperfect inspection, and
destructive and non-destructive acceptance sampling in a twotier
market”, Computers & Industrial Engineering, Vol. 93,
(2016), 275–285.  
23. Shah, N.H., Patel, D.G. and Shah, D. B., “EPQ model for
returned/reworked inventories during imperfect production
process under price-sensitive stock-dependent demand”,
Operational Research, Vol. 18, No. 2, (2018), 343–359.  
24. Öztürk, H., “Optimal production run time for an imperfect
production inventory system with rework, random breakdowns
and inspection costs”, Operational Research, (2018), 1–38. 
25. Taleizadeh, A.A., Samimi, H., Sarkar, B. and Mohammadi, B.,
“Stochastic machine breakdown and discrete delivery in an
imperfect inventory-production system”, Journal of Industrial
& Management Optimization, Vol. 13, No. 3, (2016), 1511–1535.  
26. Sarkar, B., Sett, B.K. and Sarkar, S., “Optimal production run
time and inspection errors in an imperfect production system
with warranty”, Journal of Industrial & Management
Optimization, Vol. 14, No. 1, (2017), 267–282.  
27. Al-Salamah, M., “Economic production quantity with the
presence of imperfect quality and random machine breakdown
and repair based on the artificial bee colony heuristic”, Applied
Mathematical Modelling, Vol. 63, (2018), 68–83.  
28. Ross, S.M., “Introduction to probability models”, Academic
press, (2014).