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Optimal production run time for an imperfect production inventory system with rework, random breakdowns and inspection costs

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  • Harun Öztürk

    (Suleyman Demirel University)

Abstract

In real-life manufacturing systems, the presence of defective products in a lot is inevitable. While these products may be just scrapped in the food industry, in high-tech industries where the final product is very expensive, they may be reworked at a cost. A common assumption in the literature is that the inspection time needed to identify defective items is completed when the production process ends. However, the assumption of continuous inspection during production complicates the analysis, making it impractical for most production systems, especially when the production rate is high, and the proportion of defective items is low, making continuous inspection during production very expensive. In addition, such factors as process deterioration or other uncontrollable factors in the production process may interrupt the production of the lot. To address these practical issues, this paper integrates inspection time and the failure of production facilities into an imperfect production inventory model with rework, where the production run time is a decision variable and an inspection process continues even after a production run; the paper demonstrates significant effects on the optimal solutions, with shortages not allowed. Under these assumptions, a mathematical model is derived, and the concavity of the expected total profit function is proved. Optimal policy is obtained by applying the analytic method. Special cases of the model are studied and a numerical example with sensitivity analysis is provided to draw insights. Moreover, this numerical example is used to compare general and special cases.

Suggested Citation

  • Harun Öztürk, 2021. "Optimal production run time for an imperfect production inventory system with rework, random breakdowns and inspection costs," Operational Research, Springer, vol. 21(1), pages 167-204, March.
    • Handle: RePEc:spr:operea:v:21:y:2021:i:1:d:10.1007_s12351-018-0439-5
    DOI: 10.1007/s12351-018-0439-5
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    1. Evan L. Porteus, 1986. "Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction," Operations Research, INFORMS, vol. 34(1), pages 137-144, February.
    2. Salameh, M. K. & Jaber, M. Y., 2000. "Economic production quantity model for items with imperfect quality," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 59-64, March.
    3. Harry Groenevelt & Liliane Pintelon & Abraham Seidmann, 1992. "Production Lot Sizing with Machine Breakdowns," Management Science, INFORMS, vol. 38(1), pages 104-123, January.
    4. Chiu, Singa Wang & Wang, Shan-Ling & Chiu, Yuan-Shyi Peter, 2007. "Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns," European Journal of Operational Research, Elsevier, vol. 180(2), pages 664-676, July.
    5. Chakraborty, Tulika & Giri, B.C. & Chaudhuri, K.S., 2008. "Production lot sizing with process deterioration and machine breakdown," European Journal of Operational Research, Elsevier, vol. 185(2), pages 606-618, March.
    6. Yoo, Seung Ho & Kim, DaeSoo & Park, Myung-Sub, 2009. "Economic production quantity model with imperfect-quality items, two-way imperfect inspection and sales return," International Journal of Production Economics, Elsevier, vol. 121(1), pages 255-265, September.
    7. Flapper, Simme Douwe P. & Teunter, Ruud H., 2004. "Logistic planning of rework with deteriorating work-in-process," International Journal of Production Economics, Elsevier, vol. 88(1), pages 51-59, March.
    8. Gede Agus Widyadana & Hui Ming Wee, 2012. "An economic production quantity model for deteriorating items with preventive maintenance policy and random machine breakdown," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(10), pages 1870-1882.
    9. M. Berg & M. J. M. Posner & H. Zhao, 1994. "Production-Inventory Systems with Unreliable Machines," Operations Research, INFORMS, vol. 42(1), pages 111-118, February.
    10. Kamran Moinzadeh & Prabhu Aggarwal, 1997. "Analysis of a Production/Inventory System Subject to Random Disruptions," Management Science, INFORMS, vol. 43(11), pages 1577-1588, November.
    11. Taleizadeh, Ata Allah & Cárdenas-Barrón, Leopoldo Eduardo & Mohammadi, Babak, 2014. "A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process," International Journal of Production Economics, Elsevier, vol. 150(C), pages 9-27.
    12. Liu, John J. & Yang, Ping, 1996. "Optimal lot-sizing in an imperfect production system with homogeneous reworkable jobs," European Journal of Operational Research, Elsevier, vol. 91(3), pages 517-527, June.
    13. Chiu, Singa Wang & Chou, Chung-Li & Wu, Wen-Kuei, 2013. "Optimizing replenishment policy in an EPQ-based inventory model with nonconforming items and breakdown," Economic Modelling, Elsevier, vol. 35(C), pages 330-337.
    14. Hau L. Lee & Meir J. Rosenblatt, 1987. "Simultaneous Determination of Production Cycle and Inspection Schedules in a Production System," Management Science, INFORMS, vol. 33(9), pages 1125-1136, September.
    15. Wee, Hui Ming & Widyadana, Gede Agus, 2013. "A production model for deteriorating items with stochastic preventive maintenance time and rework process with FIFO rule," Omega, Elsevier, vol. 41(6), pages 941-954.
    16. Khan, M. & Jaber, M.Y. & Guiffrida, A.L. & Zolfaghari, S., 2011. "A review of the extensions of a modified EOQ model for imperfect quality items," International Journal of Production Economics, Elsevier, vol. 132(1), pages 1-12, July.
    17. Gwo-Liang Liao, 2016. "Optimal economic production quantity policy for a parallel system with repair, rework, free-repair warranty and maintenance," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6265-6280, October.
    18. T. Bielecki & P. R. Kumar, 1988. "Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems," Operations Research, INFORMS, vol. 36(4), pages 532-541, August.
    19. Glock, C. H., 2013. "The machine breakdown paradox: How random shifts in the production rate may increase company profits," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 62254, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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