Joint determination of purchasing and production lot sizes in an unreliable production system

Document Type : Article

Authors

1 Department of Industrial Engineering, University of Bojnord, P.O. Box 94531-55111, Bojnord, Iran

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

Abstract

This paper discusses a production-inventory system under random machine breakdown. Holding safety stock is the common way to mitigate the effect of random machine breakdown on shortages that may occur during machine repair time. Since holding safety stock can be costly, especially for expensive products, this paper investigates an alternative strategy in which it is assumed that the production manager can purchase the same products from a supplier in order to meet the demands that may be lost due to the depletion of the inventory after the machine breakdown. The supplier has known lead-time and reliability with the quality assured products. Despite holding safety stock, purchasing occurs only when the machine breakdown happens. The question is about the optimal amount of production and purchasing lot sizes to minimize the total expected costs. The optimality of the model is investigated when failure and repair time follow an exponential distribution, and a computational algorithm for finding the optimal lot sizes is presented. A comparison between the purchasing strategy and holding safety stock is performed through a sensitivity analysis regarding some effective parameters. This study shows using the purchasing strategy when holding or production cost rises is more beneficial than holding safety stock.

Keywords

References

References:
1. Chakraborty, T. and Giri, B.C. "Joint determination of optimal safety stocks and production policy for an imperfect production system", Applied Mathematical Modelling, 36(2), pp. 712-722 (2012). https://doi.org/10.1016/j.apm.2011.07.012.
2. Peymankar, M., Dehghanian, F., Ghiami, Y., et al. "The effects of contractual agreements on the economic production quantity model with machine breakdown", International Journal of Production Economics, 201(C), pp. 203-215 (2018). https://doi.org/10.1016/j.ijpe.2018.05.006.
3. Groenevelt, H., Pintelon, L., and Seidmann, A. "Production batching with machine breakdowns and safety stocks", Operations Research, 40(5), pp. 959- 971 (1992). https://doi.org/10.1287/opre.40.5.959.
4. Cheung, K.L. and Hausman, W.H. "Joint determination of preventive maintenance and safety stocks in an unreliable production environment", Naval Research Logistics, 44(3), pp. 257-272 (1997). https://doi.org/10.1002/(SICI)1520- 6750(199704)44:3<257::AID-NAV2>3.0.CO;2-7.
5. 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, 74(1-3), pp. 147-155 (2001). https://doi.org/10.1016/S0925- 5273(01)00121-9.
6. Abboud, N.E. "Discrete-time Markov productioninventory model with machine breakdowns", Computers and Industrial Engineering, 39(1-2), pp. 95-107 (2001). DOI: 10.1016/S0360-8352(00)00070-X.
7. Giri, B., Yun, W.Y., and Dohi, T. "Optimal design of unreliable production-inventory systems with variable production rate", European Journal of Operational Research, 162(2), pp. 372-386 (2005). https://doi.org/10.1016/j.ejor.2003.10.015.
8. 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, 99(1-2), pp. 131-143 (2006). https://doi.org/10.1016/j.ijpe.2004.12.012.
9. Gharbi, A., Kenne, J.P., and Beit, M. "Optimal safety stocks and preventive maintenance periods in unreliable manufacturing systems", International Journal of Production Economics, 107(2), pp. 422-434 (2007). DOI: 10.1016/J.IJPE.2006.09.018. 
10. El-Ferik, S. "Economic production lot-sizing for an unreliable machine under imperfect age-based maintenance policy", European Journal of Operational Research, 186(1), pp. 150-163 (2008). https://doi.org/10.1016/j.ejor.2007.01.035.
11. Chakraborty, T., Giri, B.C., and Chaudhuri, K.S. "Production lot sizing with process deterioration and machine breakdown", European Journal of Operational Research, 185, pp. 606-618 (2008).
12. Sana, S.S. and Chaudhuri, K. "An EMQ model in an imperfect production process", International Journal of Systems Science, 41(6), pp. 635-646 (2010). https://doi.org/10.1080/00207720903144495.
13. Sana, S.S. "A production-inventory model in an imperfect production process", European Journal of Operational Research, 200(2), pp. 451-464 (2010). https://doi.org/10.1016/j.ejor.2009.01.041.
14. Chiu, Y.S.P., Lin, H.D., and Chang, H.H. "Mathematical modeling for solving manufacturing run time problem with defective rate and random machine breakdown", Computers and Industrial Engineering, 60(4), pp. 576-584 (2011). https://doi.org/10.1016/j.cie.2010.12.015.
15. Sana, S.S. "A production-inventory model of imperfect quality products in a three-layer supply chain", Decision Support Systems, 50(2), pp. 539-547 (2011). https://doi.org/10.1016/j.dss.2010.11.012.
16. Sana, S.S. "Preventive maintenance and optimal buffer inventory for products sold with warranty in an imperfect production system", International Journal of Production Research, 50(23), pp. 6763-6774 (2012). https://doi.org/10.1080/00207543.2011.623838.
17. Prakash, O., Roy, A.R., and Goswami, A. "Manufacturing inventory model with discrete random machine breakdown and discrete stochastic corrective and preventive repair time", International Journal of Procurement Management, 6(4), p. 394 (2013). https://doi.org/10.1504/IJPM.2013.054750.
18. Zhang, Y., Lu, Z., and Xia, T. "A dynamic method for the production lot sizing with machine failures", International Journal of Production Research, 52(8), pp. 2436-2447 (2014). https://doi.org/10.1080/00207543.2013.871591.
19. Paul, S.K., Sarker, R., and Essam, D. "Managing disruption in an imperfect production-inventory system", Computers and Industrial Engineering, 84(C), pp. 101-112 (2015). https://doi.org/10.1016/j.cie.2014.09.013.
20. Taleizadeh, A., Samimi, H., Sarkar, B., et al. "Stochastic machine breakdown and discrete delivery in an imperfect inventory-production system", Journal of Industrial and Management Optimization, 13(3), pp. 1511-1535 (2017). DOI: 10.3934/jimo.2017005.
21.Ozturk, H., Optimal Production Run Time for an Imperfect Production Inventory System with Rework, Random Breakdowns and Inspection Costs, Springer Berlin Heidelberg (2018). 
22. Nobil, A.H., Sedigh, A.H.A., Tiwari, S., et al. "An imperfect multi-item single-machine production system with shortage, rework, and scrap considering inspection, dissimilar de ciency levels, and non-zero setup times", Scientia Iranica, Transactions E: Industrial Engineering, 26(1), pp. 557-570 (2019). DOI: 10.24200/sci.2018.4984.1031.
23. Poursoltan, L., Seyedhosseini, S.M., and Jabbarzadeh, A. "An extension to the economic production quantity problem with deteriorating products considering random machine breakdown and stochastic repair time", International Journal of Engineering, Transactions B., 33(8), pp. 1567-1578 (2020). DOI: 10.5829/ije.2020.33.08b.15.
24. Pal, B. and Adhikari, S. "Random machine breakdown and stochastic corrective maintenance period on an economic production inventory model with buffer machine and safe period", RAIRO Operations Research, 55, pp. 1129-1149 (2021).
https://doi.org/10.1051/ro/2020069.
25. Deiranlou, M., Dehghanian, F., and Pirayesh, M.A. "The simultaneous effect of holding safety stock and purchasing policies on the economic production quantity model subject to random machine breakdown", International Journal of Engineering, Transactions B., 32(11), pp. 1643-1655 (2019). DOI: 10.5829/ije.2019.32.11b.16.
26. De, S.K. and Sana, S.S. "The (p, q, r, l) model for stochastic demand under Intuitionistic fuzzy aggregation with Bonferroni mean", Journal of Intelligent Manufacturing, 27(2), pp. 4-21 (2016).
27. Ross, S.M., Introduction to Probability Models, Academic Press (2014).
Scientia Iranica
Volume 31, Issue 18
Transactions on Industrial Engineering (E)
November and December 2024
Pages 1659-1673

Files

Share

How to cite

Statistics