Economic production quantity model with defective items, imperfect rework process, and lost sales

Chusnul  Aprilianti; Annisa Kesy Garside; Amelia  Khoidir; Thomy Eko  Saputro

doi:10.30656/jsmi.v8i1.7580

Authors

Chusnul Aprilianti Universitas Muhammadiyah Malang
Annisa Kesy Garside Universitas Muhammadiyah Malang https://orcid.org/0000-0003-1692-0277
Amelia Khoidir Universitas Muhammadiyah Malang https://orcid.org/0009-0006-8172-3455
Thomy Eko Saputro Universitas Muhammadiyah Malang

DOI:

https://doi.org/10.30656/jsmi.v8i1.7580

Keywords:

Defective items, Economic production quantity, Imperfect rework process, Inventory management, Lost sales, Production lot size

Abstract

This study proposes an economic production quantity (EPQ) model that comprehensively addresses scrap items, imperfect quality items, rework processes, and shortages. The model incorporates various types of defective items, including scrap, imperfect quality, and rework able items, and implements immediate rework processes upon the completion of regular production. Shortages are treated as lost sales, enhancing the accuracy of inventory cost estimations. Numerical experiments demonstrate the optiÂmalÂity of production lot sizes and underscore the impact of production and demand rate adjustments on overall inventory costs. Sensitivity analysis further elucidates the influence of imperfect quality items on inventory costs. This EPQ model offers a comprehensive approach to efficient and effective finished product inventory management by integrating considerÂations for scrap items, imperfect quality items, and rework processes. AddiÂtionally, a furniture manufacturing company case is presented to illustrate the practical application of the proposed model.

Downloads

Download data is not yet available.

References

L.-F. Hsu and J.-T. Hsu, â€˜Economic production quantity (EPQ) models under an imperfect production process with shortages backorderedâ€™, Int. J. Syst. Sci., vol. 47, no. 4, pp. 852â€“867, Mar. 2016, doi: https://doi.org/10.1080/00207721.2014.906768.

S. H. R. Pasandideh, S. T. A. Niaki, A. H. Nobil, and L. E. CÃ¡rdenas-BarrÃ³n, â€˜A multiproduct single machine economic production quantity model for an imperfect production system under warehouse construction costâ€™, Int. J. Prod. Econ., vol. 169, pp. 203â€“214, 2015, doi: https://doi.org/10.1016/j.ijpe.2015.08.004.

A. A. Taleizadeh, H.-M. Wee, and S. G. Jalali-Naini, â€˜Economic production quantity model with repair failure and limited capacityâ€™, Appl. Math. Model., vol. 37, no. 5, pp. 2765â€“2774, 2013, doi: https://doi.org/10.1016/j.apm.2012.06.006.

H. Mokhtari, â€˜A joint internal production and external supplier order lot size optimization under defective manufacturing and reworkâ€™, Int. J. Adv. Manuf. Technol., vol. 95, no. 1, pp. 1039â€“1058, 2018, doi: https://doi.org/10.1007/s00170-017-1290-1.

L. Moussawi-Haidar, M. Salameh, and W. Nasr, â€˜Production lot sizing with quality screening and reworkâ€™, Appl. Math. Model., vol. 40, no. 4, pp. 3242â€“3256, 2016, doi: https://doi.org/10.1016/j.apm.2015.09.095.

A. H. Tai, â€˜Economic production quantity models for deteriorating/imperfect products and service with reworkâ€™, Comput. Ind. Eng., vol. 66, no. 4, pp. 879â€“888, 2013, doi: https://doi.org/10.1016/j.cie.2013.09.007.

A. H. Nobil and A. A. Taleizadeh, â€˜A single machine EPQ inventory model for a multi-product imperfect production system with rework process and auctionâ€™, Int. J. Adv. Logist., vol. 5, no. 3â€“4, pp. 141â€“152, Nov. 2016, doi: https://doi.org/10.1080/2287108X.2016.1207975.

S. S. Kalantari and A. A. Taleizadeh, â€˜Mathematical modelling for determining the replenishment policy for deteriorating items in an EPQ model with multiple shipmentsâ€™, Int. J. Syst. Sci. Oper. Logist., vol. 7, no. 2, pp. 164â€“171, Apr. 2020, doi: https://doi.org/10.1080/23302674.2018.1542753.

A. Gharaei, S. A. Hoseini Shekarabi, and M. Karimi, â€˜Modelling And optimal lot-sizing of the replenishments in constrained, multi-product and bi-objective EPQ models with defective products: Generalised Cross Decompositionâ€™, Int. J. Syst. Sci. Oper. Logist., vol. 7, no. 3, pp. 262â€“274, Jul. 2020, doi: https://doi.org/10.1080/23302674.2019.1574364.

H. Ã–ztÃ¼rk, â€˜A deterministic production inventory model with defective items, imperfect rework process and shortages backorderedâ€™, Int. J. Oper. Res., vol. 39, no. 2, pp. 237â€“261, 2020, doi: https://doi.org/10.1504/IJOR.2020.109756.

Y.-H. Lin, Y.-C. Chen, and W.-Y. Wang, â€˜Optimal production model for imperfect process with imperfect maintenance, minimal repair and reworkâ€™, Int. J. Syst. Sci. Oper. Logist., vol. 4, no. 3, pp. 229â€“240, Jul. 2017, doi: https://doi.org/10.1080/23302674.2016.1160452.

G. Viji and K. Karthikeyan, â€˜An economic production quantity model for three levels of production with Weibull distribution deterioration and shortageâ€™, Ain Shams Eng. J., vol. 9, no. 4, pp. 1481â€“1487, 2018, doi: https://doi.org/10.1016/j.asej.2016.10.006.

S. Ganesan and R. Uthayakumar, â€˜EPQ models for an imperfect manufacturing system considering warm-up production run, shortages during hybrid maintenance period and partial backorderingâ€™, Adv. Ind. Manuf. Eng., vol. 1, p. 100005, 2020, doi: https://doi.org/10.1016/j.aime.2020.100005.

M. Najafi, A. Ghodratnama, and H. R. Pasandideh, â€˜Solving a deterministic multi product single machine EPQ model withpartial backordering, scrapped products and reworkâ€™, Int. J. Supply Oper. Manag., vol. 5, no. 1, pp. 11â€“27, 2018, https://doi.org/10.22034/2018.1.2.

E. A. Silver, D. F. Pyke, and D. J. Thomas, Inventory and production management in supply chains. CRC press, 2016, [Online]. Available: https://books.google.co.id/books?id=uY2ODwAAQBAJ.

R. J. Tersine, Principles of Inventory and Materials Management. Prentice Hall, 1993, [Online]. Available: https://books.google.co.id/books?id=wCkfAQAAIAAJ.

G. Hadley and T. M. Whitin, Analysis of Inventory Systems. Prentice-Hall, 1963, [Online]. Available: https://books.google.co.id/books?id=TZk8AAAAIAAJ.

E. W. Taft, â€˜The most economical production lotâ€™, Iron Age, vol. 101, no. 18, pp. 1410â€“1412, 1918.

Y.-S. P. Chiu, C.-A. K. Lin, H.-H. Chang, and V. Chiu, â€˜Mathematical modelling for determining economic batch size and optimal number of deliveries for EPQ model with quality assuranceâ€™, Math. Comput. Model. Dyn. Syst., vol. 16, no. 4, pp. 373â€“388, Nov. 2010, doi: https://doi.org/10.1080/13873954.2010.511199.

R. H. Ballou, Instructorâ€™s Manual Business Logistics Management: Planning and Control. Prentice-Hall, 1985, [Online]. Available: https://books.google.co.id/books?id=XewmtwAACAAJ.

K. KostiÄ‡, â€˜Inventory control as a discrete system control for the fixed-order quantity systemâ€™, Appl. Math. Model., vol. 33, no. 11, pp. 4201â€“4214, 2009, doi: https://doi.org/10.1016/j.apm.2009.03.004.

H. M. Wee, J. Yu, and M. C. Chen, â€˜Optimal inventory model for items with imperfect quality and shortage backorderingâ€™, Omega, vol. 35, no. 1, pp. 7â€“11, 2007, doi: https://doi.org/10.1016/j.omega.2005.01.019.

M. Y. Jaber, S. K. Goyal, and M. Imran, â€˜Economic production quantity model for items with imperfect quality subject to learning effectsâ€™, Int. J. Prod. Econ., vol. 115, no. 1, pp. 143â€“150, 2008, doi: https://doi.org/10.1016/j.ijpe.2008.05.007.

A. Mukhopadhyay and A. Goswami, â€˜Economic production quantity (EPQ) model for three type imperfect items with rework and learning in setupâ€™, An Int. J. Optim. Control Theor. Appl., vol. 4, no. 1, pp. 57â€“65, 2014, doi: https://doi.org/10.11121/ijocta.01.2014.00170.

D. A. Schrady, â€˜A deterministic inventory model for reparable itemsâ€™, Nav. Res. Logist. Q., vol. 14, no. 3, pp. 391â€“398, Jan. 1967, doi: https://doi.org/10.1002/nav.3800140310.

N. Li, F. T. S. Chan, S. H. Chung, and A. H. Tai, â€˜An EPQ Model for Deteriorating Production System and Items with Reworkâ€™, Math. Probl. Eng., vol. 2015, p. 957970, 2015, doi: https://doi.org/10.1155/2015/957970.

B. Sarkar, L. E. CÃ¡rdenas-BarrÃ³n, M. Sarkar, and M. L. Singgih, â€˜An economic production quantity model with random defective rate, rework process and backorders for a single stage production systemâ€™, J. Manuf. Syst., vol. 33, no. 3, pp. 423â€“435, 2014, doi: https://doi.org/10.1016/j.jmsy.2014.02.001.

E. Ebrahimi, B. Shirazi, I. Mahdavi, and A. Arshadi Khamseh, â€˜Toward a sustainable economic production quantity model employing triple bottom line strategy: Uncertain multi-objective optimization with lost sales and full back-orderâ€™, Sci. Iran., 2022, doi: https://doi.org/10.24200/SCI.2022.59478.6267.

M. Al-Salamah, â€˜Economic production quantity in an imperfect manufacturing process with synchronous and asynchronous flexible rework ratesâ€™, Oper. Res. Perspect., vol. 6, p. 100103, 2019, doi: https://doi.org/10.1016/j.orp.2019.100103.

M. Sanjai and S. Periyasamy, â€˜An inventory model for imperfect production system with rework and shortagesâ€™, Int. J. Oper. Res., vol. 34, no. 1, pp. 66â€“84, Dec. 2018, doi: https://doi.org/10.1504/IJOR.2019.096939.

A. Guha and D. Bose, â€˜A note on â€œEconomic production quantity in batch manufacturing with imperfect quality, imperfect inspection, and destructive and non-destructive acceptance sampling in a two-tier marketâ€â€™, Comput. Ind. Eng., vol. 146, p. 106609, 2020, doi: https://doi.org/10.1016/j.cie.2020.106609.

A. I. Malik and B. Sarkar, â€˜Disruption management in a constrained multi-product imperfect production systemâ€™, J. Manuf. Syst., vol. 56, pp. 227â€“240, 2020, doi: https://doi.org/10.1016/j.jmsy.2020.05.015.

D. Castellano and C. H. Glock, â€˜Economic production quantity with inventory rationing for a decaying itemâ€™, IFAC-PapersOnLine, vol. 55, no. 10, pp. 2998â€“3003, 2022, doi: https://doi.org/10.1016/j.ifacol.2022.10.188.

N. KaragÃ¼l and A. EroÄŸlu, â€˜Production lot sizing with quality screening, rework and shortages backordered TT - Kalite kontrol, tamir ve sonradan karÅŸÄ±lama ile Ã¼retim parti bÃ¼yÃ¼klÃ¼klerinin belirlenmesiâ€™, Pamukkale Ãœniversitesi MÃ¼hendislik Bilim. Derg., vol. 28, no. 4, pp. 604â€“612, 2022, [Online]. Available: https://dergipark.org.tr/en/download/article-file/2624083.

S. Priyan, P. Mala, and M. Palanivel, â€˜A cleaner EPQ inventory model involving synchronous and asynchronous rework process with green technology investmentâ€™, Clean. Logist. Supply Chain, vol. 4, p. 100056, 2022, doi: https://doi.org/10.1016/j.clscn.2022.100056.