AN ARITHMETIC-GEOMETRIC MEAN INEQUALITY APPROACH FOR DETERMINING THE OPTIMAL PRODUCTION LOT SIZE WITH BACKLOGGING AND IMPERFECT REWORK PROCESS

Chun-Tao Chang; Liang-Yuh Ouyang

doi:10.11948/2017015

2017 Volume 7 Issue 1

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2017 > 7(1): 224-235

Next Article Previous Article

Chun-Tao Chang, Liang-Yuh Ouyang. AN ARITHMETIC-GEOMETRIC MEAN INEQUALITY APPROACH FOR DETERMINING THE OPTIMAL PRODUCTION LOT SIZE WITH BACKLOGGING AND IMPERFECT REWORK PROCESS[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 224-235. doi: 10.11948/2017015

Citation:

Chun-Tao Chang, Liang-Yuh Ouyang. AN ARITHMETIC-GEOMETRIC MEAN INEQUALITY APPROACH FOR DETERMINING THE OPTIMAL PRODUCTION LOT SIZE WITH BACKLOGGING AND IMPERFECT REWORK PROCESS[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 224-235. doi: 10.11948/2017015

AN ARITHMETIC-GEOMETRIC MEAN INEQUALITY APPROACH FOR DETERMINING THE OPTIMAL PRODUCTION LOT SIZE WITH BACKLOGGING AND IMPERFECT REWORK PROCESS

1 Department of Statistics, Tamkang University, Tamsui, Taipei, Taiwan;
2 Department of Management Sciences, Tamkang University, Tamsui, Taipei, Taiwan

Fund Project:

Abstract

Abstract

Some classical studies on economic production quantity (EPQ) models with imperfect production processes have focused on determining the optimal production lot size. However, these models neglect the fact that the total production-inventory costs can be reduced by reworking imperfect items for a relatively small repair and holding cost. To account for the above phenomenon, we take the out of stock and rework into account and establish an EPQ model with imperfect production processes, failure in repair and complete backlogging. Furthermore, we assume that the holding cost of imperfect items is distinguished from that of perfect ones, as well as, the costs of repair, disposal, and shortage are all included in the proposed model. In addition, without taking complex differential calculus to determine the optimal production lot size and backorder level, we employ an arithmetic-geometric mean inequality method to determine the optimal solutions. Finally, numerical examples and sensitivity analysis are analyzed to illustrate the validity of the proposed model. Some managerial insights are obtained from the numerical examples.
- Production /
- random defective rate /
- failure in repair /
- backlogging /
- arithmetic-geometric mean inequality
MSC: 90B05

FullText(HTML)

References

[1]	M. Ben-Daya, The economic production lot-sizing problem with imperfect production processes and imperfect maintenance, International Journal of Production Economics, 76(2002), 257-264. Google Scholar
[2]	L. E. Cárdenas-Barrón, A simple method to compute economic order quantities:Some observations, Applied Mathematical Modelling, 34(2010), 1684-1688. Google Scholar
[3]	L. E. Cárdenas-Barrón, K. J. Chung and G. Treviño-Garza, Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris, International Journal of Production Economics, 155(2014), 1-7. Google Scholar
[4]	L. E. Cárdenas-Barrón, B. Sarkar and G. Treviño-Garza, An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments, Applied Mathematical Modelling, 37(2013), 5549-5554. Google Scholar
[5]	L. E. Cárdenas-Barrón, B. Sarkar and G. Treviño-Garza, Easy and improved algorithms to joint determination of the replenishment lot size and number of shipments for an EPQ model with rework, Mathematical and Computational Applications, 18(2013), 132-138. Google Scholar
[6]	L. E. Cárdenas-Barrón, A. A. Taleizadeh and G. Trevi~no-Garza, An improved solution to replenishment lot size problem with discontinuous issuing policy and rework, and the multi-delivery policy into economic production lot size problem with partial rework, Expert Systems with Applications, 39(2012), 13540-13546. Google Scholar
[7]	L. E. Cárdenas-Barrón, G. Treviño-Garza, A. A. Taleizadeh and V. Pandian, Determining replenishment lot size and shipment policy for an EPQ inventory model with delivery and rework, Mathematical Problems in Engineering, 2015(2015), Article ID 595498, 1-8. Google Scholar
[8]	T. C. E. Cheng, An economic order quantity model with demand-dependent unit production cost and imperfect production processes, ⅡE Transactions, 23(1991), 23-28. Google Scholar
[9]	Y. P. Chiu, Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging, Engineering Optimization, 35(2003), 427-437. Google Scholar
[10]	S. W. Chiu, Production lot size problem with failure in repair and backlogging derived without derivatives, European Journal of Operational Research, 188(2008), 610-615. Google Scholar
[11]	S. W. Chiu, C. B. Cheng, M. F. Wu and J. C. Yang, An algebraic approach for determining the optimal lot size for EPQ model with rework process, Mathematical and Computational Applications, 15(2010), 364-370. Google Scholar
[12]	P. A. Hayek and M. K. Salameh, Production lot sizing with the reworking of imperfect quality items produced, Production Planning and Control, 12(2001), 584-590. Google Scholar
[13]	K. L. Hou, L. C. Lin and T. Y. Lin, Optimal lot sizing with maintenance actions and imperfect production processes, International Journal of Systems Science, 46(2014), 2749-2755. Google Scholar
[14]	J. T. Hsu and L. F. Hsu, Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns, Computers and Industrial Engineering, 64(2013), 389-402. Google Scholar
[15]	A. M. M. Jamal, B. R. Sarker and S. Mondal, Optimal manufacturing batch size with rework process at a single-stage production system, Computers and Industrial Engineering, 47(2004), 77-89. Google Scholar
[16]	H. L. Lee and M. J. Rosenblatt, Simultaneous determination of production cycle and inspection schedules in a production system, Management Science, 33(1987), 1125-1136. Google Scholar
[17]	C. S. Lin, C. H. Chen and D. E. Kroll, Integrated production-inventory models for imperfect production processes under inspection schedules, Computers and Industrial Engineering, 44(2003), 633-650. Google Scholar
[18]	J. J. Liu and P. Yang, Optimal lot-sizing in an imperfect production system with homogeneous reworkable jobs, European Journal of Operational Research, 91(1996), 517-527. Google Scholar
[19]	M. J. Paknejad, F. Nasri and J. F. Affisco, Defective units in a continuous review (s,Q) system, International Journal of Production Research, 33(1995), 2767-2777. Google Scholar
[20]	B. Pal, S. S. Sana and K. Chaudhuri, Joint pricing and ordering policy for two echelon imperfect production inventory model with two cycles, International Journal of Production Economics, 155(2014), 229-238. Google Scholar
[21]	E. L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction, Operations Research, 34(1986), 137-144. Google Scholar
[22]	M. J. Rosenblatt and H. L. Lee, Economic production cycles with imperfect production processes, ⅡE Transactions, 18(1986), 48-55. Google Scholar
[23]	M. K. Salameh and M. Y. Jaber, Economic production quantity model for items with imperfect quality, International Journal of Production Economics, 64(2000), 59-64. Google Scholar
[24]	S. S. Sana, A production inventory model in an imperfect production process, European Journal of Operational Research, 200(2010), 451-464. Google Scholar
[25]	B. Sarker, An inventory model with reliability in an imperfect production process, Applied Mathematics and Computation, 218(2012), 4881-4891. Google Scholar
[26]	B. Sarker and I. Moon, An EPQ model with inflation in an imperfect production system, Applied Mathematics and Computation, 217(2011), 6159-6167. Google Scholar
[27]	B. Sarker, S. S. Sana and K. S. Chaudhuri, Optimal reliability, production lot size and safety stock in an imperfect production system, International Journal of Mathematics and Operational Research, 2(2010), 467-490. Google Scholar
[28]	A. H. Tai, Economic production quantity models for deteriorating/imperfect products and service with rework, Computers and Industrial Engineering, 66(2013), 879-888. Google Scholar
[29]	A. A. Taleizadeh, H. M. Wee and S. J. Sadjadi, Multi-product production quantity model with repair failure and partial backordering, Computers and Industrial Engineering, 59(2010), 45-54. Google Scholar
[30]	G. Treviño-Garza, K. K. Castillo-Villar and L. E. Cárdenas-Barrón, Joint determination of the lot size and number of shipments for a family of integrated vendor-buyer systems considering defective products, International Journal of Systems Science, 46(2015), 1705-1716. Google Scholar
[31]	H. M. Wee, W. T. Wang, T. C. Kuo, Y. L. Cheng and Y. D. Huang, An economic production quantity model with non-synchronized screening and rework, Applied Mathematics and Computation, 233(2014), 127-138. Google Scholar
[32]	S. H. Yoo, D. Kim and M. S. Park, Lot sizing and quality investment with quality cost analyses for imperfect production and inspection processes with commercial return, International Journal of Production Economics, 140(2012), 922-933. Google Scholar
[33]	X. Zhang and Y. Gerchak, Joint lot sizing and inspection policy in and EOQ model with random yield, ⅡE Transactions, 22(1990), 41-47. Google Scholar