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Lost sales reduction and quality improvement with variable lead time and fuzzy costs in an imperfect production system. (English) Zbl 1405.90019

Summary: This article investigates the effects of lost sales reduction and quality improvement in an imperfect production process under imprecise environment with simultaneously optimizing reorder point, order quantity, and lead time. This study assumes that the demand during lead time follows a mixture of normal distributions and the cost components are imprecise and vague. Under these assumptions, the aim is to study the lost sales reduction and the quality improvement in an uncertainty environment. The objective function in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method (MGMIRM). For the defuzzified objective function, theoretical results are developed to establish optimal policies. Finally, some numerical examples and sensitivity analysis are provided to examine the effects of non-stochastic uncertainty.

MSC:

90B05 Inventory, storage, reservoirs
90B50 Management decision making, including multiple objectives
90B30 Production models
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[1] C.J. Liao and C.H. Shyu, An analytical determination of lead time with normal demand. Int. J. Oper. Prod. Manag. 11 (1991) 72-78 · doi:10.1108/EUM0000000001287
[2] M. Ben-Daya and A. Raouf, Inventory models involving lead time as decision variable. J. Oper. Res. Soci. 45 (1994) 579-582 · Zbl 0805.90037 · doi:10.1057/jors.1994.85
[3] L.Y. Ouyang, N.C. Yeh and K.S. Wu, Mixture inventory model with backorders and lost sales for variable lead time. J. Oper. Res. Soc. 47 (1996) 829-832 · Zbl 0856.90041 · doi:10.1057/jors.1996.102
[4] I. Moon and S. Choi, A note on lead time and distributional assumptions in continuous review inventory models. Comput. Oper. Res. 25 (1998) 1007-1012 · Zbl 1042.90509 · doi:10.1016/S0305-0548(97)00103-2
[5] M. Hariga and M. Ben-Daya, Some stochastic inventory models with deterministic variable lead time. Euro. J. Oper. Res. 113 (1999) 42-51 · Zbl 0933.90005 · doi:10.1016/S0377-2217(97)00441-4
[6] L.Y. Ouyang and B.R. Chuang, Mixture inventory model involving variable lead time and controllable backorder rate. Comput. Ind. Eng. 40 (2001) 339-348 · doi:10.1016/S0360-8352(01)00033-X
[7] P. Chu, K.L. Yang and P.S. Chen, Improved inventory models with service level and lead time. Comput. Oper. Res. 32 (2005) 285-296 · Zbl 1073.90005 · doi:10.1016/j.cor.2003.07.001
[8] W.C. Lee, J.W. Wu and C.L. Lei, Computational algorithmic procedure for optimal inventory policy involving ordering cost reduction and back-order discounts when lead time demand is controllable. Appl. Math. Comput. 189 (2007) 186-200 · Zbl 1401.90032
[9] Y.J. Lin, Minimax distribution-free procedure with backorder price discount. Int. J. Prod. Econ. 111 (2008) 118-128 · doi:10.1016/j.ijpe.2006.11.016
[10] E.L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction. Oper. Res. 34 (1) (1986) 137-144 · Zbl 0591.90043 · doi:10.1287/opre.34.1.137
[11] M.J. Rosenblatt and H.L. Lee, Economic production cycles with imperfect production processes. IIE Trans. 18 (1986) 48-55 · doi:10.1080/07408178608975329
[12] G. Keller and H. Noori, Impact of investing in quality improvement on the lot size model. Omega.15 (1988) 595-601 · doi:10.1016/0305-0483(88)90033-3
[13] I. Moon, Multi-product economic lot size models with investments costs for setup reduction and quality improvement: review and extensions. Int. J. Pro. Res. 32 (1994) 2795-2801 · Zbl 0899.90104 · doi:10.1080/00207549408957100
[14] J.D. Hong and J.C. Hayya, Dynamic lot sizing with setup reduction. Comput. Indus. Eng. 24 (1993) 209-218 · doi:10.1016/0360-8352(93)90009-M
[15] L.Y. Ouyang and H.C. Chang, Impact of investing in quality improvement on (Q, r, L) model involving the imperfect production process. Prod. Plan Cont. 11 (2000) 598-607 · doi:10.1080/095372800414160
[16] L.Y. Ouyang, C.K. Chen and H.C. Chang, Quality improvement, setup cost and lead time reductions in lot size reorder point models with an imperfect production process. Comput. Oper. Res. 29 (2002) 1701-1717 · Zbl 1259.90005 · doi:10.1016/S0305-0548(01)00051-X
[17] B. Sarkarand I. Moon, Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process. Int. J. Prod. Econ. 155 (2014) 204-213 · doi:10.1016/j.ijpe.2013.11.014
[18] J.W. Wuand H.Y. Tsai, Mixture inventory model with back orders and lost sales for variable lead time demand with the mixtures of normal distribution. Int. J. Sys. Sci. 32 (2001) 259-268 · Zbl 1006.90010 · doi:10.1080/00207720121523
[19] W.C. Lee, Inventory model involving controllable backorder rate and variable lead time demand with the mixtures of distribution. Appl. Math. Comput. 160 (2005) 701-717 · Zbl 1087.90009
[20] W.C. Lee, J.W. Wu and C.L. Lei, Computational algorithmic procedure for optimal inventory policy involving ordering cost reduction and back-order discounts when lead time demand is controllable. Appl. Math. Comput. 189 (2007) 186-200 · Zbl 1401.90032
[21] J.W. Wu, W.C. Lee and C.L. Lei, Optimal Inventory Policy Involving Ordering Cost reduction, back-order discounts, and variable lead time demand by minimax criterion. Math. Prob. Eng. 19 (2009) 928-932 · Zbl 1187.90031
[22] B.R. Cobb, Mixture distributions for modelling demand during lead time. J. Oper. Res. Soc. 64 (2013) 217-228 · doi:10.1057/jors.2012.39
[23] H.J. Lin, Reducing lost-sales rate on the stochastic inventory model with defective goods for the mixtures of distributions. App. Math. Mod. 37 (2013) 3296-3306 · Zbl 1351.90013 · doi:10.1016/j.apm.2012.07.020
[24] C.H. Hseih, Optimization on fuzzy production inventory models. Inf. Sci. 146 (2002) 29-40 · Zbl 1028.90001 · doi:10.1016/S0020-0255(02)00212-8
[25] C.K. Kao and W.K. Hsu, Lot size-reorder point inventory model with fuzzy demands. Comput. Math. App. 43 (2002) 1291-1302. · Zbl 1008.90501
[26] G.Y. Tutuncu, O. Akoz, A. Apaydin and D. Petrovic, Continuous review inventory control in the presence of fuzzy costs. Int. J. Prod. Eco. 113 (2008) 775-784 · doi:10.1016/j.ijpe.2007.10.011
[27] T. Vijayan and M. Kumaran, Models with a mixture of backorders and lost sales under fuzzy cost. Euro. J. Oper. Res. 189 (2008) 105-119 · Zbl 1152.90324 · doi:10.1016/j.ejor.2007.05.049
[28] R. Handfield, D. Warsing and X.M. Wu, (Q, r) inventory policies in a fuzzy uncertain supply chain environment. Euro. J. Oper. Res. 197 (2009) 609-619 · Zbl 1159.90420 · doi:10.1016/j.ejor.2008.07.016
[29] N.H. Shah and H. Soni, Continuous review inventory model for fuzzy price dependent demand. Int. J. Mod. Oper. Manage. 3 (2011) 209-222
[30] S.S. Nezhad, S.M. Nahavandia and J. Nazemi, Periodic and continuous inventory models in the presence of fuzzy costs. Int. J. Indus. Eng. Comput. 2 (2011) 167-178
[31] R.S. Kumar, M.K. Tiwari and A. Goswami, Two-echelon fuzzy stochastic supply chain for the manufacturer-buyer integrated production-inventory system. J. Int. Man. (2014) 1-14
[32] R.S. Kumar and A. Goswami, Fuzzy stochastic EOQ inventory model for items with imperfect quality and shortages are backlogged. Adv. Mod. Opt. 15 (2013) 261-279 · Zbl 1413.90015
[33] R.S. Kumar and A. Goswami, EPQ model with learning consideration, imperfect production and partial backlogging in fuzzy random environment. Int. J. Sys. Sci. 46 (2015) 1486-1497 · Zbl 1317.90086 · doi:10.1080/00207721.2013.775384
[34] O. Dey and D. Chakraborty, A fuzzy random continuous review inventory system. Int. J. prod. Econ. 132 (2011) 101-106 · doi:10.1016/j.ijpe.2011.03.015
[35] R.S. Kumar and A. Goswami, A continuous review productioninventory system in fuzzy random environment: Minmax distribution free procedure. Comput. Ind. Eng. 79 (2015) 65-75 · doi:10.1016/j.cie.2014.10.022
[36] R.S. Kumar and A. Goswami, A fuzzy random EPQ model for imperfect quality items with possibility and necessity constraints. Appl. Sof. Comput. 34 (2015) 838-850 · doi:10.1016/j.asoc.2015.05.024
[37] B.K. Wong and V.S. Lai, A survey of the application of fuzzy set theory in production and operations management. Int. J. Prod. Econ. 129 (2011) 157-168 · doi:10.1016/j.ijpe.2010.09.013
[38] W.C. Lee, Inventory model involving controllable backorder rate and variable lead time demand with the mixtures of distribution. App. Math. Comput. 160 (2005) 701-717 · Zbl 1087.90009 · doi:10.1016/j.amc.2003.11.039
[39] B.S. Everitt and D.J. Hand, Finite Mixture Distribution. Chapman and Hall, London (1981) · Zbl 0466.62018 · doi:10.1007/978-94-009-5897-5
[40] B. Sarkar, B. Mandal and S. Sarkar, Quality improvement and backorder price discount under controllable lead time in an inventorymodel. J. Manuf. Sys. 35 (2015) 26-36 · doi:10.1016/j.jmsy.2014.11.012
[41] S.H. Chen, Operations on fuzzy numbers with function principle. Tamk. J. Manag. Sci.6 (1986) 13-25 · Zbl 0576.03017
[42] S.H. Chen and C.H. Hsieh, Optimization of fuzzy backorder inventory models. In Vol. 1 of IEEE SMC’99 Conference Proceedings, Tokyo, Japan (1999) 240-244
[43] B. Sarkar, K. Chaudhuri and I. Moon, Manufacturing setup cost reduction and quality improvement for the distribution free continuous-review inventory model with a service level constraint. J. Manuf. Sys. 34 (2015) 74-82 · doi:10.1016/j.jmsy.2014.11.003
[44] B. Sarkar and A.S. Mahapatra, Periodic review fuzzy inventory model with variable lead time and fuzzy demand. Int. Tran. Oper. Res. (2015) 1-31
[45] B. Sarkar and S. Saren, Product inspection policy for an imperfect production system with inspection errors and warranty cost. Euro. J. Oper. Res. 248 (2016) 263-271 · Zbl 1346.90287 · doi:10.1016/j.ejor.2015.06.021
[46] B. Sarkar, H. Gupta, K. Chaudhuri and S.K. Goyal, An integrated inventory model with variable lead time, defective units and delay in payments. Appl. Math. Comput. 237 (2014) 650-658 · Zbl 1334.90012
[47] I. Moon, E. Shin and B. Sarkar, Min-max distribution free continuous-review model with a service level constraint and variable lead time. Appl. Math. Comput. 229 (2014) 310-315 · Zbl 1364.90025
[48] B. Sarkar, An inventory model with reliability in an imperfect production process. Appl. Math. Comput. 218 (2012a) 4881-4891. · Zbl 1239.90008
[49] B. Sarkar, An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production. Appl. Math. Comput. 218 (2012b) 8295-8308 · Zbl 1245.90007
[50] B. Sarkar, S.S. Sana and K. Chaudhuri, An economic production quantity model with stochastic demand in an imperfect production system. Int. J. Ser. Oper. Manag. 9 (2011a) 259-282
[51] B. Sarkar, S.S. Sana and K. Chaudhuri, An imperfect production process for time varying demand with inflation and time value of money - an EMQ model. Exp. Sys. Appl. 38 (2011b) 13543-13548
[52] B. Sarkar and I. Moon, An EPQ model with inflation in an imperfect production system. Appl. Math. Comput. 217 (2011c) 6159-6167 · Zbl 1208.90012
[53] B. Sarkar, S.S. Sana and K. Chaudhuri, A stock-dependent inventory model in an imperfect production process, Int. J. Proc. Manag. 3:4 (2010) 361-378
[54] B. Sarkar, S.S. Sana and K. Chaudhuri, Optimal reliability, production lot size and safety stock in an imperfect production system. Int. J. Math. Oper. Res. 2 (2010b) 467-490 · Zbl 1201.90069 · doi:10.1504/IJMOR.2010.033441
[55] B. Sarkar, A. Majumder, M. Sarkar, B.K. Dey and G. Roy, Two-echelon supply chain model with manufacturing quality improvement and setup cost reduction. J. Indus. Manag. Opt. 13 (2017) 1085-1104 · Zbl 1404.90032
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