CEBİRSEL BİR YAKLAŞIM KULLANILARAK DÜŞÜK KALİTE, TARAMA, YENİDEN İŞLEME/TAMİR ETME İLE ÜRETİM PARTİ HACMİNİN ELDE EDİLMESİ

Year 2019, Volume: 4 Issue: 2, 93 - 110, 01.12.2019

Harun Öztürk

Abstract

Birçok araştırmacı, optimal sipariş miktarı veya optimal üretim miktarının kapalı formda matematiksel eşitliklerini elde etmek için birinci ve ikinci dereceden kısmi türevlere izin veren geleneksel hesaplama yöntemlerini kullanmaktadır. Ancak, bu çalışma, ürün tarama işleminin üretim sırasında ve üretim sonunda yürütüldüğü ve üretilen kusurlu ürünlerin indirimli fiyatla satıldığı ya da belirli bir maliyetle yeniden işlendiği/tamir edildiği bir kusurlu üretim envanter sisteminde, üretim parti hacmi belirleme probleminin çözümlerine cebirsel bir yaklaşım sunmaktadır. Diferansiyel hesabı bilmeyen uygulamacılar veya birinci sınıf üniversite öğrencileri bu yaklaşımı kullanarak, envanter problemlerine daha kolay çözümler bulabilecektir.

Keywords

Stok kontrolü, EÜM, yeniden işleme/tamir etme, cebirsel yaklaşım, diferansiyel hesap

THE DERIVATION OF PRODUCTION LOT SIZING WITH IMPERFECT QUALITY, INSPECTION AND REWORK USING AN ALGEBRAIC APPROACH

Abstract

Many researchers use traditional computing processes that take the first and second-order partial derivatives to obtain closed form mathematical equations for the optimal order quantity or the optimal production quantity. However, this paper provides an algebraic approach to solving the production lot sizing problem in an imperfect production inventory system where an inspection process is conducted during and at the end of production, and any defective items produced are either sold at a discounted price or reworked/repaired at a cost. Using this approach, practitioners or first-year college students who lack knowledge of differential calculus may be able to find solutions to inventory problems more easily.

Keywords

Inventory control, EPQ, rework, algebraic approach, differential calculus

References

• Benkherouf, L., & Mohamed, O. (2017). Optimal manufacturing batch size with rework for a finite-horizon and time-varying demand rates inventory model. RAIRO-Operations Research, 57(1), 173-187.
• Cárdenas-Barrón, L.E. (2001). The economic production quantity (EPQ) with shortage derived algebraically. International Journal of Production Economics, 70, 289-292.
• Cárdenas Barrón, L.E. (2009). Economic production quantity with rework process at a single-stage manufacturing system with planned backorders. Computers & Industrial Engineering, 57, 1105-1113.
• Cárdenas-Barrón, L.E. (2011). The deriavtion of EOQ/EPQ inventory models with two backorders costsusing analytic geometry and algebra. Applied Mathematical Modelling, 35, 2394-2407.
• Chen, C. K., Lo, C. C., & Liao, Y. X. (2008). Optimal lot size with learning consideration on an imperfect production system with allowable shortages. International Journal of Production Economics, 113(1), 459–469.
• Chen K. -K., Wu, M. -F., Chiu, S.W., & Lee, C. -H. (2012). Alternative approach for solving replenishment lot size problem with discontinuous issuing policy and rework. Expert Systems with Applications, 39, 2232–2235.
• Chiu, S. W. (2008). Production lot size problem with failure in repair and backlogging derived without derivatives”, European Journal of Operational Research, 188, 610–615.
• Chiu, S. W., Chen, K. -K., & Chiu, Y.-S. P. (2012). Notes on the mathematical modelling approach used to determine the replenishment policy for the EMQ model with rework and multiple shipments. Applied Mathematics Letters, 25, 1964-1968.
• Chung, C. J., & Wee, H. M. (2007). Optimizing the economic lot size of a three-stage supply chain with backordering derived without derivatives. European Journal of Operational Research, 183, 933–943.
• Chung, K.-J. (2013). The algorithm to locate the optimal solution for production system subject to random machine breakdown and failure in rework for supply chain management. Journal of Optimization Theory and Applications, 158(3), 888-895, (2013).
• Chung, K. -J., Ting, P. -Sh., Cárdenas Barrón, L.E. (2017). A simple solution procedure for solving the multi-delivery policy into economic production lot size problem with partial rework. Scientia Iranica E, 24(5), 2640-2644.
• Grubbström, R.W., & Erdem, A. (1999). The EOQ with backlogging derived without derivatives. International Journal of Production Economics, 59, 529—530.
• Hayek, P. A., & Salameh, M.K. (2001). Production lot sizing with the reworking of imperfect quality items produced. Production Planning and Control, 12(6), 584-590.
• Jaber, M. Y., Zanoni, S., & Zavanella, L.E. (2014). Economic order quantity model for imperfect items with buy and repair options. International Journal of Production Economics, 155, 126-131.
• Jamal, A. M. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at a singlestage production system. Computers & Industrial Engineering, 47(1), 77-89.
• Liu, J. J., & Yang, P. (1996). Optimal lot-sizing in an imperfect productionsystem with homogeneous reworkable jobs. European Journal of Operational Research, 91, 517-527.
• Maddah, B., Salameh, M. K., & Karame, G.M. (2009). Lot sizing with random yield and different qualities. Applied Mathematical Modelling, 33(4), 1997-2009.
• Maddah, B., & Jaber, M.Y. (2008). Economic order quantity for items with imperfect quality: Revisited. International Journal of Production Economics, 112 (2), 808–815.
• Manna, A. K., Dey, J. K., & Mondal, S.K. (2017). Imperfect production inventory model with production rate dependent defective rate and advertisement dependent demand. Computers & Industrial Engineering, 104, 9–22.
• Minner, S. (2007). A note on how to compute economic order quantities without derivatives by cost comparisons. International Journal of Production Economics, 105, 293–296.
• Moussawi-Haidar, L., Salameh, M., & Nasr, W. (2016). Production lot sizing with quality screening and rework. Applied Mathematical Modelling, 40, 3242-3256.
• Nobil, A. H., Sedigh, A. H. A., & Cárdenas Barrón, L.E. (2016). A multi-machine multi-product EPQ problem for an imperfect manufacturing system considering utilization and allocation decisions. Expert Systems with Applications, 56, 310–319.
• Öztürk, H., Eroglu, A., & Lee, G.M. (2015.) An economic order quantity model for lots containing defective items with rework option. International Journal of Industrial Engineering, 22 (6), 683-704.
• Öztürk, H. (2016). A note on “Production lot sizing with quality screening and rework. Applied Mathematical Modelling, 43, 659–669.
• Paknejad, M. J., Nasri, F., & Affisco, J. F. (1995). Defective units in a continuous review (s, Q) system. International Journal of Production Research, 33(10), 2767-3777.
• Porteus, E. L. (1986). Optimal lot sizing, process quality improvement and setup cost reduction. Operations Research, 34, 137-144.
• Ronald, R., Yang, G. K., &Chu, P. (2004). Technical note: The EOQ and EPQ models with shortages derived without derivatives. International Journal of Production Economics, 92, 197–200.
• Rosenblatt, M. J., & Lee, H.L. (1986). Economic production cycles with imperfect production processes. IIE Transactions, 18, 48-55.
• Salameh, M. K., & Jaber, M.Y. (2000). Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64, 59-64.
• Sphicas, G. P. (2006). EOQ and EPQ with linear and fixed backorder costs: Two cases identified and models analyzed without calculus. International Journal of Production Economics, 100, 59–64.
• Teng J. -T., Cárdenas Barrón L. E., Lou, K. -R., & Wee H. M. (2013). Optimal economic order quantity for buyer–distributor–vendor supply chain with backlogging derived without derivatives. International Journal of Systems Science, 44(5). 986–994.
• Teng, H. -M., & Hsu, P. -H. (2015). Optimal production lots for items with imperfect production and screening processes without using derivatives. International Journal of Management and Enterprise Development, 14(2), 172-184.
• Teng, J. -T. (2009). A simple method to compute economic order quantities. European Journal of Operational Research, 198, 351–353.
• Teng, J. -T., Cárdenas-Barrón, L. E., & Lou, K. -R. (2011). The economic lot size of the integrated vendor-buyer inventory system derived without derivatives: A simple derivation. Applied Mathematics and Computation, 217:, 5972-5977.
• Urban, T. L. (1998). Analysis of production systems when run length influences product quality. International Journal of Production Research, 36(11), 3085-3094.
• Wee, H. M., & Chung, C. J. (2007). A note on the economic lot size of the integrated vendor–buyer inventory system derived without derivatives. European Journal of Operational Research, 177, 1289–1293.
• Yang, P. C., & Wee, H. M. (2002). The economic lot size of the integrated vendor-buyer inventory system derived without derivatives. Optımal Control Applications and Methods, 23, 163–169.
• Zhang, X., & Gerchak, Y. (1990). Joint lot sizing and ınspection policy in an EOQ model with random yield. IIE Transactions, 22(1), 41-47.