×

zbMATH — the first resource for mathematics

A stochastic periodic review integrated inventory model involving defective items, backorder price discount, and variable lead time. (English) Zbl 1201.90013
Summary: The purpose of this article is to investigate a stochastic integrated supplier-retailer inventory problem. The model analyzed in this article explores the problem of the protection interval, the backorder price discount, the lead time, and the numbers of shipments from the supplier to the retailer in one production run as control variables to widen applications for an integrated periodic review inventory model. We consider the situation in which the supplier and the retailer establish a long-term strategic partnership and contract to jointly determine the best strategy. We assume that the protection interval demand follows a normal distribution. Our objective is to determine the optimal review period, the optimal backorder price discount, the optimal lead time, and the optimal number of shipments from the supplier to the retailer in one production run, so that the joint expected annual total cost incurred has the minimum value. Furthermore, an algorithm of finding the optimal solution is developed. Also, the sensitivity analysis included and a numerical example is given to illustrate the results of the proposed model.

MSC:
90B05 Inventory, storage, reservoirs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Banerjee A (1986) A joint economic-lot-size model for purchaser and vendor. Decis Sci 17: 292–311 · doi:10.1111/j.1540-5915.1986.tb00228.x
[2] Chuang BR, Ouyang LY, Lin YJ (2004) A minimax distribution free procedure for mixed inventory model with backorder discounts and variable lead time. J Stat Manag Syst 7(1): 65–76 · Zbl 1176.90013
[3] Chung KL, Hou KL (2003) An optimal production run time with imperfect production process and allowable shortages. Comput Oper Res 30: 483–490 · Zbl 1026.90029 · doi:10.1016/S0305-0548(01)00091-0
[4] Donaldson WA (1984) An equation for the optimal value of T, the inventory replenishment review period when demand is normal. J Oper Res Soc 35(2): 137–139 · Zbl 0542.90026
[5] Goyal SK (1976) An integrated inventory model for a single supplier-single customer problem. Int J Prod Res 15(1): 107–111 · doi:10.1080/00207547708943107
[6] Goyal SK (1988) A joint economics-lot-size model for purchaser and vendor: a comment. Decis Sci 19(1): 236–241 · doi:10.1111/j.1540-5915.1988.tb00264.x
[7] Goyal SK, Nebebe F (2000) Determination of economic production-shipment policy for a single-vendor-single-buyer system. Eur J Oper Res 121: 175–178 · Zbl 0948.91017 · doi:10.1016/S0377-2217(99)00013-2
[8] Ha D, Kim SL (1997) Implementation of JIT purchasing: an integrated approach. Prod Plan Control 8(2): 152–157 · doi:10.1080/095372897235415
[9] Hill RM (1999) The optimal production and shipment policy for the single-vendor single-buyer integrated production-inventory problem. Int J Prod Res 37(11): 2463–2475 · Zbl 0949.90567 · doi:10.1080/002075499190617
[10] Hou KL (2005) Optimal production run length for deterioration production system with a two-state continuous-time Markovian processes under allowable shortages. J Oper Res Soc 56: 346–350 · Zbl 1114.90030 · doi:10.1057/palgrave.jors.2601792
[11] Ho CH, Ouyang LY, Su CH (2008) Optimal pricing, shipment and payment policy for an integrated supplier-buyer inventory model with two-part trade credit. Eur J Oper Res 187(2): 496–510 · Zbl 1147.90002 · doi:10.1016/j.ejor.2007.04.015
[12] Joglekar P (1988) Comments on ”A quantity discount pricing model to increase vendor profits”. Manag Sci 34: 1391–1398 · doi:10.1287/mnsc.34.11.1391
[13] Kelle P, Al-khateeb F, Miller AP (2003) Partnership and negotiation support by joint optimal ordering/setup policies for JIT. Int J Prod Econ 81–82: 431–441 · doi:10.1016/S0925-5273(02)00357-2
[14] Lin YJ (2008) A periodic review inventory model involving fuzzy expected demand short and fuzzy backorder rate. Comput Ind Eng 54: 666–676 · doi:10.1016/j.cie.2007.10.002
[15] Lu L (1995) A one-vendor multi-buyer integrated inventory model. Eur J Oper Res 81: 312–323 · Zbl 0927.90005 · doi:10.1016/0377-2217(93)E0253-T
[16] Montgomery DC, Bazaraa MS, Keswani AK (1973) Inventory models with a mixture of backorders and lost sales. Nav Res Logistics 20: 255–263 · Zbl 0262.90020 · doi:10.1002/nav.3800200205
[17] Ouyang LY, Chang HC (2000) Impact of investing in quality improvement on (Q, r, L) model involving imperfect production process. Prod Plann Control 11: 598–607 · doi:10.1080/095372800414160
[18] Ouyang LY, Chuang BR (2001) A periodic review inventory-control system with variable lead time. Int J Inf Manag Sci 12(1): 1–13 · Zbl 1017.90004
[19] Ouyang LY, Wu KS, Ho CH (2004) Integrated vendor-buyer cooperative models with stochastic demand in controllable lead time. Int J Prod Econ 92: 255–266 · doi:10.1016/j.ijpe.2003.10.016
[20] Ouyang LY, Chuang BR, Lin YJ (2005) Periodic review inventory models with controllable lead time and lost sales rate reduction. J Chin Inst Ind Eng 22(5): 355–368
[21] Ouyang LY, Wu KS, Ho CH (2007a) An integrated vendor-buyer inventory model with quality improvement and lead time reduction. Int J Prod Econ 108: 349–358 · doi:10.1016/j.ijpe.2006.12.019
[22] Ouyang LY, Chuang BR, Lin YJ (2007b) Effective investment to reduce lost sales in a periodic review inventory model. OR Spectr 29: 681–697 · Zbl 1168.90335 · doi:10.1007/s00291-007-0081-8
[23] Ouyang LY, Chuang BR, Lin YJ (2007c) The inter-dependent reductions of lead time and ordering cost in periodic review inventory model with backorder price discount. Int J Inf Manag Sci 18(3): 195–208 · Zbl 1152.90458
[24] Paknejad MJ, Nasri F, Affisco JF (1995) Defective units in a continuous (s, Q) review system. Int J Prod Res 33: 2767–2777 · Zbl 0910.90128 · doi:10.1080/00207549508904844
[25] Pan CHJ, Hsiao YC (2001) Inventory models with back-order discounts and variable lead time. Int J Syst Sci 32(7): 925–929 · Zbl 1005.90007 · doi:10.1080/00207720010004449
[26] Pan CHJ, Yang JS (2002) A study of an integrated inventory with controllable lead time. Int J Prod Res 40(5): 1263–1273 · Zbl 1027.90024 · doi:10.1080/00207540110105680
[27] Porteus EL (1986) Optimal lot sizing, process quality improvement and setup cost reduction. Oper Res 34: 137–144 · Zbl 0591.90043 · doi:10.1287/opre.34.1.137
[28] Rahim MA, Al-Hajailan WI (2006) An optimal production run for an imperfect production process with allowable shortages and time-varying fraction defective rate. Int J Adv Manuf Technol 27(11–12): 1170–1177 · doi:10.1007/s00170-004-2301-6
[29] Rosenblatt MJ, Lee HL (1986) Economic production cycles with imperfect production processes. IIE Trans 18: 48–55 · doi:10.1080/07408178608975329
[30] Salameh MK, Jaber MY (2000) Economic production quantity model for items with imperfect quality. Int J Prod Econ 64: 59–64 · doi:10.1016/S0925-5273(99)00044-4
[31] Su CH, Ouyang LY, Ho CH, Chang CT (2007) Retailer’s inventory policy and supplier’s delivery policy under tow-level trade credit strategy. Asia Pac J Oper Res 24(5): 613–630 · Zbl 1162.90322 · doi:10.1142/S0217595907001413
[32] Taylor BW III (1999) Introduction to management science, 6th edn. Hall, New Jersey
[33] Yang JS, Pan CHJ (2004) Just-in-time purchasing: an integrated inventory model involving deterministic variable lead time and quality improvement investment. Int J Prod Res 42(5): 853–863 · Zbl 1069.90006 · doi:10.1080/00207540310001632448
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.