Optimal production run time for an imperfect production inventory system with rework, random breakdowns and inspection costs
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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.
KeywordsInventory Production run time Scrap Rework Random breakdowns Inspection costs
The author expresses sincere appreciation to the editor and anonymous reviewers for their efforts to improve the quality of this paper.
- Glock CH, Jaber MY (2013a) An economic production quantity (EPQ) model for a customer-dominated supply chain with defective items, reworking and scrap. Int J Serv Oper Manag 14:236–251Google Scholar
- Lin GC, Lin HD (2007) Determining a production run time for an imperfect production–inventory system with scrap. J Sci Ind Res 66:724–735Google Scholar
- Nobil AH, Sedigh AHA, Tiwari S, Wee HM (2018) An imperfect multi-item single machine production system with shortage, rework, and scrapped considering inspection, dissimilar deficiency levels, and non-zero setup times. Scientia Iranica. https://doi.org/10.24200/sci.2018.4984.1031 CrossRefGoogle Scholar
- Suntag C (1993) Inspection and inspection quality management. ASQC, MilwaukeeGoogle Scholar
- Ting CK, Chiu YSP, Chan CCH (2011) Optimal lot sizing with scrap and random breakdown occurring in backorder replenishing period. Math Comput Appl 16(2):329–339Google Scholar
- Wee HM, Wang WT, Kuo TC, Cheng YL, Huang YD (2014) An economic production quantity model with non-synchronized screening and rework. Appl Math Comput 233:127–138Google Scholar