An EPQ model with imperfect items using interval grey numbers
DOI:
https://doi.org/10.11121/ijocta.01.2015.00204Keywords:
EPQ, Grey System Theory, Inventory Management, Rework, Imperfect ItemsAbstract
The classic economic production quantity (EPQ) model has been widely used to determine the optimal production quantity. However, the analysis for finding an EPQ model has many weaknesses which lead many researchers and practitioners to make extensions in several aspects on the original EPQ model. The basic assumption of EPQ model is that 100% of manufactured products are non-defective that is not valid for many production processes generally.
The purpose of this paper is to develop an EPQ model with grey demand rate and cost values with maximum backorder level allowed with the good quality items in units under an imperfect production process. The imperfect items are considered to be low quality items which are sold to a particular purchaser at a lower price and, the others are reworked and scrapped. A mathematical model is developed and then an industrial example is presented on the wooden chipboard production process for illustration of the proposed model.
Downloads
References
Taft, E. W., The most economical production lot. Iron Age, 101, 1410-1412 (1918).
Salameh, M. K., Jaber, M. Y., Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64, 59-64 (2000). Crossref
Liao, J. J., On an EPQ model for deteriorating items under permissible delay in payments. Applied Mathematical Modelling, 31, 393-403 (2007). Crossref
Darwish, M., EPQ model with varying setup cost. International Journal of Production Economics, 113, 297-306 (2008). Crossref
Jaber, M. Y., Goyal, S. K., Imran, M., Economic production quantity model for items with imperfect quality subject to learning effects. International Journal of Production Economics, 115, 143-150 (2008). Crossref
Pentico, D. W., Matthew, J. D., Toews, C., The deterministic EPQ with partial backordering: a new approach. Omega, 37, 624-636 (2009). Crossref
Teng, J. T., Chang, C. T., Optimal manufacturer's replenishment policies in the EPQ model under two levels of trade credit policy. European Journal of Operational Research, 195, 358-363 (2009). Crossref
Mahata, G. C., An EPQ-based inventory model for exponentially deteriorating items under retailer partial trade credit policy in supply chain. Expert Systems with Applications, 39, 3537–3550 (2012). Crossref
Rosenblatt, M. J., Lee, H. L., Economic production cycles with imperfect production processes. IEE Transactions, 18, 48-55 (1986). Crossref
Kim, C. H., Hong, Y., An optimal production run length in deteriorating production processes. International Journal of Production Economics, 58, 183-189 (1999). Crossref
Hayek, P. A., Salameh, M. K., Production lot sizing with the reworking of imperfect quality items produced. Production Planning and Control, 12(6), 584-590 (2001). Crossref
Chiu, Y. P., 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 (2003). Crossref
Papachristos, S., Konstantaras, I., Economic ordering quantity models for items with imperfect quality. International Journal of Production Economics, 100, 148–154 (2006). Crossref
Pan, J. C. H., Yang, M. F., Integrated inventory models with fuzzy annual demand and fuzzy production rate in a supply chain. International Journal of Production Research, 46(3), 753-770 (2008). Crossref
Chiu, S. W., Wang, S. L., Chiu, Y. S. P., Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns. European Journal of Operational Research, 180(2), 664-676 (2007). Crossref
Lo, S. T., Wee, H. M., Huang, W. C., An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation. International Journal of Production Economics, 106, 248–260 (2007). Crossref
Ojha, D., Sarker, B. R., Biswas, P., An optimal batch size for an imperfect production system with quality assurance and rework. International Journal of Production Research, 45:14, 3191-3214 (2007). Crossref
Wee, H. M., Widyadana, G. A., Economic production quantity models for deteriorating items with rework and stochastic preventive maintenance time. International Journal of Production Research, 50 (11), 2940-2952 (2012). Crossref
Chung, C. J., Widyadana, G. A., Wee, H. M., Economic production quantity model for deteriorating inventory with random machine unavailability and shortage, International Journal of Production Research, 49(3), 883-902 (2011). Crossref
Chen, S. H., Wang, S. T., Chang, S. M., Optimization of fuzzy production inventory model with repairable defective products under crisp or fuzzy production quantity. International Journal of Operations Research, 2 (2), 31-37 (2005).
Halim, K. A., Giri, B. C., Chaudhuri, K. S., Fuzzy EPQ models for an imperfect production system. International Journal of Systems Science, 40 (1), 45-52 (2009). Crossref
Roy, A., Maity, K., Kar, S., Maiti, M., A production-inventory model with remanufacturing for defective and usable items in fuzzy-environment. Computers and Industrial Engineering, 56, 87-96 (2009). Crossref
Pan, E., Jin, Y., Wang, S., Cang, T., An integrated EPQ model based on a control chart for an imperfect production process. International Journal of Production Research, 50 (23), 6999-7011 (2012). Crossref
Chang, H. C., An application of fuzzy sets theory to the EOQ model with imperfect quality items. Computers and Operation Research, 31, 2079-2092 (2004). Crossref
Mula, J., Peidro, D., Poler, R., The effectiveness of a fuzzy mathematical programming approach for supply chain production planning with fuzzy demand. International Journal of Production Economics, 128, 136-143 (2010). Crossref
Islam, S., Roy, T. K., A fuzzy EPQ model with flexibility and reliability consideration and demand dependent unit production cost under a space constraint: A fuzzy geometric approach. Applied Mathematics and Computation, 176, 531-544 (2006). Crossref
Kazemi, N., Ehsani, E., Jaber, M. Y., An inventory model with backorders with fuzzy parameters and decision variables. International Journal of Approximate Reasoning, 51, 964-972 (2010). Crossref
Mondal, S., Maiti, M., Multi-item fuzzy EOQ models using genetic algorithm. Computers and Industrial Engineering, 44 (1), 105-117 (2003). Crossref
Pasandideh, S. H. R., Niaki, S. T. A., A genetic algorithm approach to optimize a multi-products EPQ model with discrete delivery orders and constrained space. Applied Mathematics and Computation, 195, 506-514 (2008). Crossref
Pal, S., Maiti, M. K., Maiti, M., An EPQ model with price discounted promotional demand in an imprecise planning horizon via Genetic Algorithm. Computers and Industrial Engineering, 57 (1), 181-187 (2009). Crossref
Bhunia, A. K., Kundu, S., Sannigrahi, T., Goyal, S. K., An application of tournament genetic algorithm in a marketing oriented economic production lot-size model for deteriorating items. International Journal of Production Economics, 119 (1), 112–121 (2009). Crossref
Zhang, R. Q., Kaku, I., Xiao, Y. Y., Deterministic EOQ with partial back ordering and correlated demand caused by cross-selling. European Journal of Operational Research, 210 (3), 537-551 (2011). Crossref
Zhao, P., Wang, H., Gao, H., Improved particle swarm optimization algorithm for stochastic EOQ models with multi-item and multi-storehouse. Proceedings of the IEEE International Conference on Information Acquisition, August 20-23, Welhal, Shandong, China (2006).
Deng, J., Control problems of grey systems. Systems and Control Letters, 1(5), 288–294 (1982). Crossref
Eroglu, A., Sutcu, A., Sulak, H., An economic production quantity model with random defective rate in imperfect production processes. Journal of Faculty of Engineering and Architecture of Gazi University, 23(4), 923-929 (2008).
Zadeh, L. A., Fuzzy Sets. Information Control, 8, 338-353 (1965). Crossref
Tseng, M. L., A causal and effect decision making model of service quality expectation using grey-fuzzy DEMATEL approach. Expert Systems with Applications, 36, 7738-7748 (2009). Crossref
Deng, J., Introduction to grey system theory. The Journal of Grey System, 1, 1–24 (1989).
Liu, S., Lin, Y., Grey Information: Theory and Practical Applications. Springer, Germany (2006).
Yamaguchi, D., Li, G. D., Chen, L. C., Nagai, M., Reviewing Crisp, Fuzzy, Grey and Rough Mathematical Models. Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Service, Nov 18-20, Nanjing, China (2007). Crossref
Liu, S., Lin, Y., Grey Systems: Theory and Applications. Springer, Germany (2010). Crossref
Downloads
Published
How to Cite
Issue
Section
License
Articles published in IJOCTA are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in IJOCTA, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
This work is licensed under a Creative Commons Attribution 4.0 International License.
