An Economic Production Quantity Model with Probabilistic Machine Breakdown and Multiple Shipments Policy

Document Type : Original Article

Authors

1 Master Student, Tarbiat Modares University

2 Associate Professor, Kashan University.

3 Master student, Sharif University of Technology.

Abstract

The classical economic production quantity (EPQ) model was developed to manage inventory costs in companies last decade ago. This model is extended in various directions in recent years. The classic EPQ has some unrealistic assumptions. The model assumes that all products are perfect, while the production of defective items is inevitable in the real-world environment. Another assumption relates to the continuous demand satisfaction, which ignores the commonly used multiple shipments policy in practice. Finally, the classic model does not consider the probabilistic breakdown of the machine and the required maintenance activities. The present work aims to develop a new imperfect EPQ model under probabilistic machine failure, corrective maintenance, and multiple shipments policy. Two cases are investigated: 1- Considering the production of a fixed percentage of imperfect items 2- Considering no production of defective items. Due to the complexity of the problem, a numerical bisection method is utilized to solve the problem and finding the best possible production time. This method's performance is evaluated by comparing it to the obtained solutions by MATLAB optimization toolbox for genetic and simulated annealing algorithms. Sensitivity analysis is performed, and finally, some directions for future research are suggested.

Keywords

Main Subjects

References

  1. Asadkhani J, Mokhtari H, Tahmasebpoor S (2021) Optimal lot-sizing under learning effect in inspection errors with different types of imperfect quality items. Oper Res. https://doi.org/10.1007/s12351-021-00624-7
  2. Cárdenas-Barrón, L. E. (2008). Optimal manufacturing batch size with rework in a single-stage production system–a simple derivation. Computers & Industrial Engineering, 55(4), 758-765.
  3. Cárdenas-Barrón, L. E., Sarkar, B., & Treviño-Garza, G. (2013). An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments. Applied Mathematical Modelling, 37(7), 5549-5554.
  4. Cheng, T. (1991). An economic order quantity model with demand-dependent unit production cost and imperfect production processes. IIE transactions, 23(1), 23-28.
  5. Chiu, S. W., Wang, S.-L., & Chiu, Y.-S. P. (2007). Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns. European Journal of Operational Research, 180(2), 664-676.
  6. Chiu, S. W., Chen, K.-K., Chiu, Y.-S. P., & Ting, C.-K. (2012). Notes on the mathematical modeling approach used to determine the replenishment policy for the EMQ model with rework and multiple shipments. Applied Mathematics Letters, 25(11), 1964-1968.
  7. Chiu, Y. P. (2003). Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging. Engineering optimization, 35(4), 427-437.
  8. Chiu, Y.-S. P., Chen, K.-K., Cheng, F.-T., & Wu, M.-F. (2010). Optimization of the finite production rate model with scrap, rework and stochastic machine breakdown. Computers & mathematics with applications, 59(2), 919-932.
  9. Chiu, Y.-S. P., Liu, S.-C., Chiu, C.-L., & Chang, H.-H. (2011). Mathematical modeling for determining the replenishment policy for EMQ model with rework and multiple shipments. Mathematical and Computer Modelling, 54(9-10), 2165-2174.
  10. Fallahi, A., Azimi-Dastgerdi, M., Mokhtari, H. (2021). A Sustainable Production-Inventory Model Joint with Preventive Maintenance and Multiple Shipments for Imperfect Quality Items. Scientia Iranica, (), -. doi: 10.24200/sci.2021.55927.4475
  11. Fallahi, A., Mokhtari, H., & Niaki, S. T. A. (2021). Designing a closed-loop blood supply chain network considering transportation flow and quality aspects. Sustainable Operations and Computers, 2, 170-189.
  12. Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10, 135-136, 152.
  13. Hasanpour, J., Hasani, A., & Ghodoosi, M. (2018). Delayed Payment Policy in the Inventory Model of Deteriorating Goods with Quadratic Demand in Order to Backlogging Shortage. Journal of Industrial Management Perspective, 7(4), 199-230. (In Persian)
  14. Hayek, P. A., & Salameh, M. K. (2001). Production lot sizing with the reworking of imperfect quality items produced. Production planning & control, 12(6), 584-590.
  15. Jamal, A., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at a single-stage production system. Computers & Industrial Engineering, 47(1), 77-89.
  16. Kalantari, S. S., & Taleizadeh, A. A. (2020). Mathematical modelling for determining the replenishment policy for deteriorating items in an EPQ model with multiple shipments. International Journal of Systems Science: Operations & Logistics, 7(2), 164-171.
  17. Kazemi, N., Abdul-Rashid, S. H., Ghazilla, R. A. R., Shekarian, E., & Zanoni, S. (2018). Economic order quantity models for items with imperfect quality and emission considerations. International Journal of Systems Science: Operations & Logistics, 5(2), 99-115.
  18. Lai, X., Chen, Z., & Bidanda, B. (2019). Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging. International Journal of Production Research, 57(19), 6061-6085.
  19. Mirzabaghi, M., & Jolai, F. (2017). Inventory Planning in a G/G/1/∞ Queuing System with Multiple Suppliers using Simulation and Response Surface Methodology. Journal of Industrial Management Perspective, 7(3), 9-26. (In Persian)
  20. Mokhtari, H., & Asadkhani, J. (2021). Economic order quantity for imperfect quality items under inspection errors, batch replacement and Multiple sales of returned items. Scientia Iranica, 28(5), 2890-2909.
  21. Mokhtari, H., & Asadkhani, J. (2020). Extended economic production quantity models with preventive maintenance. Scientia Iranica, 27(6), 3253-3264.
  22. Mokhtari, H., Hasani, A., & Fallahi, A. (2021). Multi-Product Constrained Economic Production Quantity Models for Imperfect Quality Items with Rework. International Journal of Industiral Engineering & Producion Research, 32(2), 1-23.
  23. Mokhtari, H., Salmasnia, A., & Asadkhani, J. (2020). A new production-inventory planning model for joint growing and deteriorating items. International Journal of Supply and Operations Management, 7(1), 1-16.
  24. Motallebi, S., & Zandieh, M. (2017). Determination of Inventory Management Policies in Process Manufacturing: Using Discrete Event Simulation. Journal of Industrial Management Perspective, 7(2), 83-108. (In Persian)
  25. Niaki, S., Taleizadeh, A., & Najafi, A. Economic Production Quantity Model with Scrapped Items and Limited Production Capacity. Scientia Iranica, 17(1), 58-69.
  26. Nobil, A. H., Sedigh, A. H. A., & Cárdenas-Barrón, L. E. (2020). Reorder point for the EOQ inventory model with imperfect quality items. Ain Shams Engineering Journal, 11(4), 1339-1343.
  27. Priyan, S., & Uthayakumar, R. (2017). Setup cost reduction EMQ inventory system with probabilistic defective and rework in multiple shipments management. International Journal of System Assurance Engineering and Management, 8(2), 223-241.
  28. Rezaei, J. (2016). Economic order quantity and sampling inspection plans for imperfect items. Computers & Industrial Engineering, 96, 1-7.
  29. Ritha, W., & Martin, N. (2013). Replenishment policy for EMQ model with rework, multiple shipments, switching and packaging. Int. J. Eng. Res. Technol, 2(1), 1-8.
  30. Rosenblatt, M. J., & Lee, H. L. (1986). Economic production cycles with imperfect production processes. IIE transactions, 18(1), 48-55. 31. Ritha, W., & Martin, N. (2013). Replenishment policy for EMQ model with rework, multiple shipments, switching and packaging. Int. J. Eng. Res. Technol, 2(1), 1-8.
  31. Taleizadeh, A. A., Kalantari, S. S., & Cárdenas-Barrón, L. E. (2016). Pricing and lot sizing for an EPQ inventory model with rework and multiple shipments. Top, 24(1), 143-155.
  32. Taleizadeh, A. A., Samimi, H., Sarkar, B., & Mohammadi, B. (2017). Stochastic machine breakdown and discrete delivery in an imperfect inventory-production system. Journal of Industrial & Management Optimization, 13(3), 1511.
  33. Taft, E. (1918). The most economical production lot. Iron Age, 101(18), 1410-1412.
  34. Ting, C.-K., Chiu, Y.-S. P., & Chan, C.-C. H. (2011). Optimal lot sizing with scrap and random breakdown occurring in backorder replenishing period. Mathematical and Computational Applications, 16(2), 329-339.
  35. Tsao, Y.-C., Lee, P.-L., Liao, L.-W., Zhang, Q., Vu, T.-L., & Tsai, J. (2020). Imperfect economic production quantity models under predictive maintenance and reworking. International Journal of Systems Science: Operations & Logistics, 7(4), 347-360.

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