Abstract
This article investigates an integrated single-vendor single-buyer production-inventory model with imperfect production under a mixed environment where fuzziness and randomness appear simultaneously. The paper focuses on representing the annual customer demand as a triangular fuzzy number together with an associated probability. A further assumption is that the production process is not perfect and goes ‘out-of-control’ with a certain probability. This causes the vendor, in particular, and the supply chain, in general, to incur an additional warranty cost and also leads to the production of larger batch sizes to compensate the imperfection. In order to avoid these extra costs, the vendor makes an investment to improve the production process quality and hence reduce the number of defective items produced. The expected annual integrated total cost is derived with these assumptions under the n-shipment policy. A methodology is proposed to minimize crisp equivalent of the expected annual integrated total cost so as to obtain the optimal values of the number of shipments, the shipment lot-size, the safety stock factor and the ‘out-of-control’ probability. A numerical example is given to illustrate this proposed methodology and to highlight the advantage of investing in reducing the probability of the production process going ‘out-of-control’.
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References
Banerjee A (1986) A joint economic-lot-size model for purchaser and vendor. Decis Sci 17:292–311
Ben-Daya M, Hariga M (2000) Economic lot scheduling problem with imperfect production process. J Oper Res Soc 51:875–881
Ben-Daya M, Hariga M (2004) Integrated single vendor single buyer model with stochastic demand and variable lead-time. Int J Prod Econ 92:75–80
Carlsson C, Fuller R (2001) On possiblistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst 122:315–326
Chang HC, Yao JS, Ouyang LY (2004) Fuzzy mixture inventory model with variable lead-time based on probabilistic fuzzy set and triangular fuzzy number. Math Comput Model 39:287–304
Chang HC, Yao JS, Ouyang LY (2006) Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand. Eur J Oper Res 169:65–80
Chakraborty D, Jana DK, Roy TK (2015) Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments. Comput Ind Eng 88:166–180
Das BC, Das B, Mondal SK (2015) An integrated production inventory model under interactive fuzzy credit period for deteriorating item with several markets. Appl Soft Comput J 28:453–465
Dey O, Chakraborty D (2009) A fuzzy random periodic review inventory system. Eur J Oper Res 17:292–311
Dey O, Chakraborty D (2011) A fuzzy random continuous review inventory system. Int J Prod Econ 132:101–106
Dey O, Giri BC (2014) Optimal vendor investment for reducing defect rate in a vendor–buyer integrated system with imperfect production process. Int J Prod Econ 155:222–228
Dutta P, Chakraborty D, Roy AR (2005) A single-period inventory model with fuzzy random variable demand. Math Comput Model 41:915–922
Dutta P, Chakraborty D, Roy AR (2007) Continuous review inventory model in mixed fuzzy and stochastic environment. Appl Math Comput 188:970–980
Gil MA, Lopez-Diaz M, Ralescu DA (2006) Overview on the development of fuzzy random variables. Fuzzy Sets Syst 157:2546–2557
Glock CH (2009) A comment: integrated single vendor–single buyer model with stochastic demand and variable lead time. Int J Prod Econ 122:790–792
Glock CH (2012) Lead timer eduction strategies in a single-vendor single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand. Int J Prod Econ 136:37–44
Goyal SK (1976) An integrated inventory model for a single supplier-single customer problem. Int J Prod Res 15:107–111
Goyal SK (1988) A joint economic-lot-size model for purchaser and vendor: a comment. Decis Sci 19:236–241
Goyal SK, Cárdenas-Barrón LE (2002) Note on: economic production quantity model for items with imperfect quality—a practical approach. Int J Prod Econ 77:85–87
Ha D, Kim SL (1997) Implementation of JIT purchasing: an integrated approach. Prod Plan Control 8:152–157
Hill RM (1997) The single-vendor single-buyer integrated production-inventory model with a generalized policy. Eur J Oper Res 97:493–499
Hill RM (1999) The optimal production and shipment policy for the single-vendor single-buyer integrated production-inventory problem. Int J Prod Res 37:2463–2475
Hsiao Y-C (2008) Integrated logistic and inventory model for a two-stage supply chain controlled by the reorder and shipping points with sharing information. Int J Prod Econ 115:229–235
Huang CK (2004) An optimal policy for a single-vendor single-buyer integrated production-inventory problem with process unreliability consideration. Int J Prod Econ 91:91–98
Kalaiarasi K, Rajarathnam E (2015) Optimization of multi objective fuzzy integrated inventory model with demand dependent unit cost and lead time constraints. Int J Appl Eng Res 10:4707–4721
Kumar RS, Tiwari MK, Goswami A (2014) Two-echelon fuzzy stochastic supply chain for the manufacturer-buyer integrated production-inventory system. J Intell Manuf. doi:10.1007/s10845-014-0921-8
Kwakernaak H (1978) Fuzzy random variables—I: definitions and theorems. Inf Sci 15:1–29
Kwakernaak H (1979) Fuzzy random variables—II. Algorithms and examples for the discrete case. Inf Sci 17:253–278
Lee HL, Rosenblatt MJ (1987) Simultaneous determination of production cycles and inspection schedules in a production system. Manag Sci 33:1125–1137
Lin HJ (2012) An integrated supply chain inventory model. Yugosl J Oper Res. doi:10.2298/YJOR110506019L
Lin YJ (2008) A periodic review inventory model involving fuzzy expected demand short and fuzzy backorder rate. Comput Ind Eng 54:666–676
Mahata GC (2015) An integrated production-inventory model with backorder and lot for lot policy in fuzzy sense. Int J Math Oper Res 7:69–102
Nagar L, Dutta P, Jain K (2014) An integrated supply chain model for new products with imprecise production and supply under scenario dependent fuzzy random demand. Int J Syst Sci 45:873–887
Ouyang LY, Wu KS, Ho CH (2006) Analysis of optimal vendor–buyer integrated inventory policy involving defective items. Int J Adv Manuf Technol 29:1232–1245
Ouyang LY, Wu KS, Ho CH (2007) Integrated vendor–buyer inventory model with quality improvement and lead-time reduction. Int J Prod Econ 108:349–358
Pan CH, Yang JS (2002) A study of an integrated inventory with controllable lead time. Int J Prod Res 40:1263–1273
Puri ML, Ralescu DA (1986) Fuzzy random variables. J Math Anal Appl 114:409–422
Porteus EL (1986) Optimal lot sizing, process quality improvement and setup cost reduction. Oper Res 36:137–144
Rosenblatt MJ, Lee HL (1986) Economic production cycles with imperfect production process. IIE Trans 18:48–55
Salameh MK, Jaber MY (2000) Economic production quantity model with for items with imperfect quality. Int J Prod Econ 64:59–64
Schwaller RL (1988) EOQ under inspection costs. Prod Inventory Manag 29:22–24
Shu H, Zhou X (2013) An optimal policy for a single-vendor and a single-buyer integrated system with setup cost reduction and process-quality improvement. Int J Syst Sci. doi:10.1080/00207721.2013.786155
Soni HN, Patel KA (2015) Optimal policies for integrated inventory system under fuzzy random framework. Int J Adv Manuf Technol 78:947–959
Wu X (2014) Integrated inventory problem under trade credit in fuzzy random environment. Fuzzy Optim Decis Making 13:329–344
Zhang X, Gerchak Y (1990) Joint lot sizing and inspection policy in an EOQ model with random yield. IIE Trans 22:41–47
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The authors are grateful to the anonymous referees for their valuable comments and suggestions.
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Dey, O. A fuzzy random integrated inventory model with imperfect production under optimal vendor investment. Oper Res Int J 19, 101–115 (2019). https://doi.org/10.1007/s12351-016-0286-1
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DOI: https://doi.org/10.1007/s12351-016-0286-1