Investigating the effect of learning on setup cost in imperfect production systems using two-way inspection plan for rework under screening constraints

Document Type : Article

Authors

Department of Operational Research, Faculty of Mathematical Sciences, University of Delhi, India

Abstract

In the modern industrial environment, there is a continuous need for the advancement and improvement of the organization’s operations. Learning is an inherent property which is time-dependent and comes with experience. In view of this, the present framework considers the process of learning for an imperfect production system which aids in reducing the setup cost with the level of maturity gained, hence, providing positive results for the organization. Because of machine disturbances/ malfunctions, defectives are manufactured with a known probability density function. To satisfy the demand with good products only, the manufacturer invests in a two-way inspection process with multiple screening constraints. The first inspection misclassifies some of the items and delivers inaccuracies, viz., Type-I and Type–II. The loss due to inspection at the first stage is managed efficiently through a second inspection which is presumed to be free from errors. The study mutually optimizes the production and backordering quantities in order to maximize the expected total profit per unit time. Numerical analysis and detailed sensitivity analysis is carried out to validate the hypothesis and further cater to some valuable implications.

Keywords

Main Subjects


  1. References:

    1. Improvement and setup cost reduction", Oper. Res., 34(1), pp. 137{144 (1986).
    2. Rosenblatt, M.J. and Lee, H.L. Economic production cycles with imperfect production processes", IIE T., 18(1), pp. 48{55 (1986).
    3. Lee, H.L. and Rosenblatt, M.J. Simultaneous determination of production cycle and inspection schedules in a production system", Manage. Sci., 33(9), pp. 1125{1136 (1987).
    4. Kim, C.H. and Hong, Y. An optimal production run length in deteriorating production processes", Int. J. Prod. Econ., 58(2), pp. 183{189 (1999).
    5. Ben-Daya, M. and Hariga, M. Economic lot scheduling problem with imperfect production processes", J. Oper. Res. Soc., 51(7), pp. 875{881 (2000). 6. Salameh, M.K. and Jaber, M.Y. Economic production quantity model for items with imperfect quality", Int. J. Prod. Econ., 64(1), pp. 59{64 (2000). 7. C_ardenas-Barr_on, L.E. Observation on:Economic production quantity model for items with imperfect quality"[Int. J. Production Economics 64 (2000) 59- 64]", Int. J. Prod. Econ., 67(2), p. 201 (2000). 8. Huang, C.K. An integrated vendor-buyer cooperative inventory model for items with imperfect quality", Prod. Plan. Control, 13(4), pp. 355{361 (2002). 9. Chung, K.J. and Hou, K.L. An optimal production run time with imperfect production processes and allowable shortages", Comput. Oper. Res., 30(4), pp. 483{490 (2003). 10. Yeh, R.H., Ho, W.T., and Tseng, S.T. Optimal production run length for products sold with warranty", Eur. J. Oper. Res., 120(3), pp. 575{582 (2000). 11. Ben-Daya, M. and Rahim, A. Optimal lot-sizing, quality improvement and inspection errors for multistage production systems", Int. J. Prod. Res., 41(1), pp. 65{79 (2003). 12. Huang, C.K. An optimal policy for a single-vendor single-buyer integrated production-inventory problem with process unreliability consideration", Int. J. Prod. Econ., 91(1), pp. 91{98 (2004). 13. Hsieh, C.C. and Lee, Z.Z. Joint determination of production run length and number of standbys in a deteriorating production process", Eur. J. Oper. Res., 162(2), pp. 359{371 (2005). 14. Chen, C.K. and Lo, C.C. Optimal production run length for products sold with warranty in an imperfect production system with allowable shortages", Math. Comput. Model., 44(3), pp. 319{331 (2006). 15. Wee, H.M., Yu, J., and Chen, M.C. Optimal inventory model for items with imperfect quality and shortage backordering", Omega, 35(1), pp. 7{11 (2007). 16. Raouf, A., Jain, J.K., and Sathe, P.T. A costminimization model for multicharacteristic component inspection", AIIE T., 15(3), pp. 187{194 (1983). 17. Du_uaa, S.O. and Khan, M. An optimal repeat inspection plan with several classi_cations", J. Oper. Res. Soc., 53(9), pp. 1016{1026 (2002). 18. Du_uaa, S.O. and Khan, M. Impact of inspection errors on the performance measures of a general repeat inspection plan", Int. J. Prod. Res., 43(23), pp. 4945{ 4967 (2005). 19. Zhou, Y., Chen, C., Li, C., and Zhong, Y. A synergic economic order quantity model with trade credit, shortages, imperfect quality and inspection errors", Appl. Math. Model., 40(2), pp. 1012{1028 (2016). 20. Al-Salamah, M. Economic production quantity in batch manufacturing with imperfect quality, imperfect inspection, and destructive and non-destructive acceptance sampling in a two-tier market", Comput. Ind. Eng., 93, pp. 275{285 (2016). 21. Khan, M., Hussain, M., and C_ardenas-Barr_on, L.E. Learning and screening errors in an EPQ inventory model for supply chains with stochastic lead time demands", Int. J. Prod. Res., 55(16), pp. 4816{4832 (2017). 22. Khanna, A., Kishore, A., and Jaggi, C.K. Strategic production modeling for defective items with imperfect inspection process, rework, and sales return under twolevel trade credit", Int. J. Ind. Eng. Comput., 8(1), pp. 85{118 (2017). 23. Pal, S. and Mahapatra, G.S. A manufacturingoriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages", Comput. Ind. Eng., 106, pp. 299{314 (2017). 24. Sett, B.K., Sarkar, S., and Sarkar, B. Optimal bu_er inventory and inspection errors in an imperfect production system with preventive maintenance", T. Int. J. Adv. Manuf. Tech., 90(1{4), pp. 545{560 (2017). 25. Hayek, P.A. and Salameh, M.K. Production lot sizing with the reworking of imperfect quality items produced", Prod. Plan. Control, 12(6), pp. 584{590 (2001). 26. Chiu, Y.P. Determining the optimal lot size for the _nite production model with random defective rate, the rework process, and backlogging", Eng. Optim., 35(4), pp. 427{437 (2003). 27. Chiu, S.W., Gong, D.C., and Wee, H.M. E_ects of random defective rate and imperfect rework process on economic production quantity model", Jap. J. Ind. Appl. Math., 21(3), pp. 375{389 (2004). 28. Chiu, Y.S.P., Lin, H.D., and Cheng, F.T. Optimal production lot sizing with backlogging, random defective rate, and rework derived without derivatives", P. I. Mech. Eng. B-J. Eng., 220(9), pp. 1559{1563 (2006). A. Kishore et al./Scientia Iranica, Transactions E: Industrial Engineering 27 (2020) 3265{3288 3283 29. Chiu, S.W., Ting, C.K., and Chiu, Y.S.P. Optimal production lot sizing with rework, scrap rate, and service level constraint", Math. Comput. Model., 46(3), pp. 535{549 (2007). 30. Sana, S.S. A production-inventory model in an imperfect production process", Eur. J. Oper. Res., 200(2), pp. 451{464 (2010). 31. Sarkar, B., Sana, S.S., and Chaudhuri, K. Optimal reliability, production lot size and safety stock in an imperfect production system", Int. J. Math. Oper. Res., 2(4), pp. 467{490 (2010). 32. Sarkar, B., Sana, S.S., and Chaudhuri, K. An economic production quantity model with stochastic demand in an imperfect production system", Int. J. Serv. Oper. Manag., 9(3), pp. 259{283 (2011). 33. Dey, O. and Giri, B.C. Optimal vendor investment for reducing defect rate in a vendor-buyer integrated system with imperfect production process", Int. J. Prod. Econ., 155, pp. 222{228 (2014). 34. Chiu, S.W. Production lot size problem with failure in repair and backlogging derived without derivatives", Eur. J. Oper. Res., 188(2), pp. 610{615 (2008). 35. Lin, T.Y. Optimal policy for a simple supply chain system with defective items and returned cost under screening errors", J. Oper. Res. Soc. Jpn., 52(3), pp. 307{320 (2009). 36. Yoo, S.H., Kim, D., and Park, M.S. Economic production quantity model with imperfect-quality items, two-way imperfect inspection and sales return", Int. J. Prod. Econ., 121(1), pp. 255{265 (2009). 37. Hsu, J.T. and Hsu, L.F. Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns", Comput. Ind. Eng., 64(1), pp. 389{402 (2013). 38. Wee, H.M., Wang, W.T., and Yang, P.C. A production quantity model for imperfect quality items with shortage and screening constraint", Int. J. Prod. Res., 51(6), pp. 1869{1884 (2013). 39. C_ardenas-Barr_on, L.E., Chung, K.J., and Trevi~no- Garza, G. Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris", Int. J. Prod. Econ., 155, pp. 1{7 (2014). 40. Taleizadeh, A.A., Khanbaglo, M.P.S., and C_ardenas- Barr_on, L.E. An EOQ inventory model with partial backordering and reparation of imperfect products", Int. J. Prod. Econ., 182, pp. 418{434 (2016). 41. Wang, W.T., Wee, H.M. Cheng, Y.L., Wen, C.L., and C_ardenas-Barr_on, L.E. EOQ model for imperfect quality items with partial backorders and screening constraint", Eur. J. Ind. Eng., 9(6), pp. 744{773 (2015). 42. Jaggi, C.K., Khanna, A., and Kishore, A. Production inventory policies for defective items with inspection errors, sales return, imperfect rework process and backorders", In K. Singh, M. Pandey, L. Solanki, S. B. Dandin, & P. S. Bhatnagar (Eds.), AIP Conf. Proc., 1715(1), p. 020062 (2016). 43. Moussawi-Haidar, L., Salameh, M., and Nasr, W. Production lot sizing with quality screening and rework", Appl. Math. Model., 40(4), pp. 3242{3256 (2016). 44. Liao, G.L. Production and maintenance policies for an EPQ model with perfect repair, rework, free-repair warranty, and preventive maintenance", IEEE T. Syst. Man CY.-S., 46(8), pp. 1129{1139 (2016). 45. Pal, S., Mahapatra, G.S., and Samanta, G.P. A threelayer supply chain EPQ model for price-and stockdependent stochastic demand with imperfect item under rework", J. Uncert. Anal. Appl., 4(1), p. 10 (2016). 46. Shah, N.H., Patel, D.G., and Shah, D.B. EPQ model for returned/reworked inventories during imperfect production process under price-sensitive stockdependent demand", Oper. Res., 18(2), pp. 1{17 (2016). 47. Sekar, T. and Uthayakumar, R. A multi-production inventory model for deteriorating items considering penalty and environmental pollution cost with failure rework", Uncert. Sup. Chain Manag., 5(3), pp. 229{ 242 (2017). 48. Benkherouf, L., Skouri, K., and Konstantaras, I. Optimal batch production with rework process for products with time-varying demand over _nite planning horizon", Oper. Res. Eng. Cyb. Sec., 113, pp. 57{68 (2017). 49. Chen, T.H. Optimizing pricing, replenishment and rework decision for imperfect and deteriorating items in a manufacturer-retailer channel", Int. J. Prod. Econ., 183, pp. 539{550 (2017). 50. Sha_ee-Gol, S., Nasiri, M.M., and Taleizadeh, A.A. Pricing and production decisions in multi-product single machine manufacturing system with discrete delivery and rework", Opsearch, 53(4), pp. 873{888 (2016). 51. Jawla, P. and Singh, S. Multi-item economic production quantity model for imperfect items with multiple production setups and rework under the e_ect of preservation technology and learning environment", Int. J. Ind. Eng. Comput., 7(4), pp. 703{716 (2016). 52. C_ardenas-Barr_on, L.E., Trevi~no-Garza, G., Taleizadeh, A.A., and Vasant, P. Determining replenishment lot size and shipment policy for an EPQ inventory model with delivery and rework", Math. Prob. Eng., 2015 (2015). 3284 A. Kishore et al./Scientia Iranica, Transactions E: Industrial Engineering 27 (2020) 3265{3288 53. Nobil, A.H., Sedigh, A.H.A., and C_ardenas-Barr_on, L.E. Multi-machine economic production quantity for items with scrapped and rework with shortages and allocation decisions", Scient. Iran., Transactions E, 25(4), pp. 2331{2346 (2018). 54. Chung, K.J., Ting, P.S., and C_ardenas-Barr_on, L.E. A simple solution procedure to solve the multidelivery policy into economic production lot size problem with partial rework", Scient. Iran., Transactions E, 24(5), pp. 2640{2644 (2017). 55. Nobil, A.H., Afshar Sedigh, A.H., Tiwari, S., and Wee, H.M. An imperfect multi-item single machine production system with shortage, rework, and scrapped considering inspection, dissimilar de_ciency levels, and non-zero setup times", Scient Iran, 26(1), pp. 557{570 (2019). 56. Adler, G.L. and Nanda, R. The e_ects of learning on optimal lot size determination multiple product case", AIIE T., 6(1), pp. 21{27 (1974). 57. Sule, D.R. A note on production time variation in determining EMQ under inuence of learning and forgetting", AIIE T., 13(1), pp. 91{95 (1981). 58. Urban, T.L. Analysis of production systems when run length inuences product quality", Int. J. Prod. Res., 36(11), pp. 3085{3094 (1998). 59. Jaber, M.Y. and Bonney, M. The economic manufacture/ order quantity (EMQ/EOQ) and the learning curve: past, present, and future", Int. J. Prod. Econ., 59(1), pp. 93{102 (1999). 60. Jaber, M.Y. and Bonney, M. Lot sizing with learning and forgetting in set-ups and in product quality", Int. J. Prod. Econ., 83(1), pp. 95{111 (2003). 61. Jaber, M.Y. Lot sizing for an imperfect production process with quality corrective interruptions and improvements, and reduction in setups", Comput. Ind. Eng., 51(4), pp. 781{790 (2006). 62. Darwish, M.A. EPQ models with varying setup cost", Int. J. Prod. Econ., 113(1), pp. 297{306 (2008). 63. Khan, M., Jaber, M.Y., Gui_rida, A.L., and Zolfaghari, S. A review of the extensions of a modi_ed EOQ model for imperfect quality items", Int. J. Prod. Econ., 132(1), pp. 1{12 (2011). 64. Konstantaras, I., Skouri, K., and Jaber, M.Y. Inventory models for imperfect quality items with shortages and learning in inspection", Appl. Math. Model., 36(11), pp. 5334{5343 (2012). 65. Mukhopadhyay, A. and Goswami, A. Economic Production Quantity (EPQ) model for three type imperfect items with rework and learning in setup", An Int. J. Optim. Control: Th. Appl. (IJOCTA), 4(1), pp. 57{ 65 (2013). 66. Gautam, P. and Khanna, A. An imperfect production inventory model with setup cost reduction and carbon emission for an integrated supply chain", Uncert. Sup. Chain Manag, 6(3), pp. 271{286 (2018).