Document Type : Original Article
Authors
1 Assistant Professor, University of Kurdistan.
2 Associate Professor, University of Kurdistan.
3 Graduated Master, University of Kurdistan.
4 PhD Student, University of Kurdistan.
Abstract
In this paper, the economic production is considered by considering defective products during production, a percentage of which can be recycled at a fixed cost, also machine failure, and variable demand. It is assumed that the products are produced at a fixed rate, but the machine may break down during production. Machine failure during production is a random variable that follows an exponential distribution with a specified parameter. If the machine breaks down during production, production stops immediately and the machine is repaired, and this study assumes that the machine repair time is a fixed value. Also, unlike the classical models, the demand for the manufactured product is expressed as a non-incremental function of time. The main goal is to determine the optimal policies for reproducing the problem in such a way that the total annual cost is minimized. For this purpose, first, a mathematical model is presented, then, the average cost per unit of time is determined, and based on the concepts of global optimization, the optimal values are determined. Finally, by solving a numerical example, the problem is analyzed. The results show that, the repair time has a great impact on the cost of the entire system, and as it increases, the system cost increases exponentially.
Keywords
Main Subjects
Al-Salamah, M. (2019). Economic production quantity in an imperfect manufacturing process with synchronous and asynchronous flexible rework rates. Operations research perspectives, (6), 100103.
- Asghar, I., B. Sarkar, & Kim, S. J. (2019). Economic analysis of an integrated production–inventory system under stochastic production capacity and energy consumption. Energies, 12(16), 3179.
- Chang, H. C. (2013). An economic production quantity model with consolidating shipments of imperfect quality items: A note. International Journal of Production Economics, 144(2), 507-509.
- 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.
- Colledani, M. & Angius, A. (2019). Integrated production and reconfiguration planning in modular plug-and-produce production systems. CIRP Annals, 68(1), 435-438.
- Dal Borgo, E., & Meneghetti, A. (2019). Production and shipment planning for Project Based Enterprises: Exploiting learning-forgetting phenomena for sustainable assembly of Curtain Walls. Computers & Industrial Engineering, 131, 488-501.
- Fekri, M. (2019). Optimal run time for an EPQ model with scrap, rework, setup time and machine breakdown (failure) under learning effect assumption. arXiv preprint arXiv:1912.11263.
- Groenevelt, H., L. Pintelon, & Seidmann, A. (1992). Production lot sizing with machine breakdowns. Management Science, 38(1), 104-123.
- 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)
- Ko, C. H. & Wang, S.-F. (2010). GA-based decision support systems for precast production planning. Automation in construction, 19(7), 907-916.
- Liao, G. L. (2015). Production and maintenance policies for an EPQ model with perfect repair, rework, free-repair warranty, and preventive maintenance. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 46(8), 1129-1139.
- Rajabi, Z., Sadeghi, H., & Mahmoodi, A. (2020). Determining The Optimal Ordering Policy In A Multi-Period Stochastic Model With The Uncertainty Purchase Price. Journal of Industrial Engineering Research in Production Systems, 8(16), 95-111.
- Sadeghi, H. (2019). A forecasting system by considering product reliability, POQ policy, and periodic demand. Journal of Quality Engineering and Production Optimization, 4(2), 133-148.
- Sadeghi, H. (2019). Optimal pricing and replenishment policy for production system with discrete demand. International Journal of Industrial Engineering and Management Science, 6(2), 37-50.
- Sadeghi, H., Golpîra, H., & Khan, S.A.R. (2021). Optimal integrated production-inventory system considering shortages and discrete delivery orders. Computers & Industrial Engineering, 156, 107233.
- Sadeghi, H., A. Mahmoodi, & Rajabi, Z. (2022). Economic Order Quantity with Discrete Demand and Delivery Orders. Journal of Industrial Management Perspective, 12(2), 113-133 (In Persian)
- Sadeghi, H., Makui, A., & Heydari, M. (2016). Multilevel production systems with dependent demand with uncertainty of lead times. Mathematical Problems in Engineering.
- Sarkar, B., Cárdenas-Barrón, L.E., Sarkar, M., & Singgih, M.L. (2014). An economic production quantity model with random defective rate, rework process and backorders for a single stage production system. Journal of Manufacturing Systems, 33(3), 423-435.
- Sharma, A., Singh, C., Verma, P., & Malik, A. (2022). Flexible Inventory System of Imperfect Production Under Deterioration and Inflation. Yugoslav Journal of Operations Research, 32(4), 515-528.
- Siemon, M., Schiffer, M., & Walther, G. (2021). Integrated purchasing and production planning for a non-Ferrous metal production network., Omega, 98, 102136.
- Taheri, S.A., Mokhtari, H., & Fallahi, A. (2021). An Economic Production Quantity Model with Probabilistic Machine Breakdown and Multiple Shipments Policy. Journal of Industrial Management Perspective, 11(4), 223-252 (In Persian)
- Taleizadeh, A.A., Cárdenas-Barrón, L.E., & Mohammadi, B. (2014). A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process. International Journal of Production Economics, 150, 9-27.
- Taleizadeh, A.A., Soleymanfar, V.R., & Govindan, K. (2018). Sustainable economic production quantity models for inventory systems with shortage. Journal of cleaner production, 174, 1011-1020.
- Wee, H.M. & Widyadana, G.A. (2013). A production model for deteriorating items with stochastic preventive maintenance time and rework process with FIFO rule. Omega, 41(6), 941-954.
- Yang, L., Ma, C., Yang, Y., Zhang, E., & Lv, H. (2020). Estimating the regional eco-efficiency in China based on bootstrapping by-production technologies. Journal of Cleaner Production, 243, 118550.
)