Production Planning System with Variable Demand and Stochastic Machine Breakdown

Document Type : Original Article

Authors

1 Assistant Professor, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.

2 Associate Professor, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.

3 Graduated Master, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.

4 PhD Student, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.

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

References

  1. Al-Salamah, M. (2019). Economic production quantity in an imperfect manufacturing process with synchronous and asynchronous flexible rework rates. Operations research perspectives, (6), 100103.

    1. 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.
    2. 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.
    3. 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.
    4. Colledani, M. & Angius, A. (2019). Integrated production and reconfiguration planning in modular plug-and-produce production systems. CIRP Annals, 68(1), 435-438.
    5. 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.
    6. 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.
    7. Groenevelt, H., L. Pintelon, & Seidmann, A. (1992). Production lot sizing with machine breakdowns. Management Science, 38(1), 104-123.
    8. 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)
    9. Ko, C. H. & Wang, S.-F. (2010). GA-based decision support systems for precast production planning. Automation in construction, 19(7), 907-916.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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)
    16. Sadeghi, H., Makui, A., & Heydari, M. (2016). Multilevel production systems with dependent demand with uncertainty of lead times. Mathematical Problems in Engineering.
    17. 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.
    18. 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.
    19. Siemon, M., Schiffer, M., & Walther, G. (2021). Integrated purchasing and production planning for a non-Ferrous metal production network., Omega, 98, 102136.
    20. 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)
    21. 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.
    22. 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.
    23. 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.
    24. 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.

Files

Share

How to cite

Statistics