4OR

, Volume 8, Issue 3, pp 281–297

A stochastic periodic review integrated inventory model involving defective items, backorder price discount, and variable lead time

Research paper

Abstract

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.

Keywords

Integrated inventory model Periodic review Protection interval Backorder price discount Lead time 

MSC classification (2000)

90B05 

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References

  1. Banerjee A (1986) A joint economic-lot-size model for purchaser and vendor. Decis Sci 17: 292–311CrossRefGoogle Scholar
  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): 65–76Google Scholar
  3. Chung KL, Hou KL (2003) An optimal production run time with imperfect production process and allowable shortages. Comput Oper Res 30: 483–490CrossRefGoogle Scholar
  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): 137–139Google Scholar
  5. Goyal SK (1976) An integrated inventory model for a single supplier-single customer problem. Int J Prod Res 15(1): 107–111CrossRefGoogle Scholar
  6. Goyal SK (1988) A joint economics-lot-size model for purchaser and vendor: a comment. Decis Sci 19(1): 236–241CrossRefGoogle Scholar
  7. Goyal SK, Nebebe F (2000) Determination of economic production-shipment policy for a single-vendor-single-buyer system. Eur J Oper Res 121: 175–178CrossRefGoogle Scholar
  8. Ha D, Kim SL (1997) Implementation of JIT purchasing: an integrated approach. Prod Plan Control 8(2): 152–157CrossRefGoogle Scholar
  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): 2463–2475CrossRefGoogle Scholar
  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: 346–350CrossRefGoogle Scholar
  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): 496–510CrossRefGoogle Scholar
  12. Joglekar P (1988) Comments on “A quantity discount pricing model to increase vendor profits”. Manag Sci 34: 1391–1398CrossRefGoogle Scholar
  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: 431–441CrossRefGoogle Scholar
  14. Lin YJ (2008) A periodic review inventory model involving fuzzy expected demand short and fuzzy backorder rate. Comput Ind Eng 54: 666–676CrossRefGoogle Scholar
  15. Lu L (1995) A one-vendor multi-buyer integrated inventory model. Eur J Oper Res 81: 312–323CrossRefGoogle Scholar
  16. Montgomery DC, Bazaraa MS, Keswani AK (1973) Inventory models with a mixture of backorders and lost sales. Nav Res Logistics 20: 255–263CrossRefGoogle Scholar
  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: 598–607CrossRefGoogle Scholar
  18. Ouyang LY, Chuang BR (2001) A periodic review inventory-control system with variable lead time. Int J Inf Manag Sci 12(1): 1–13Google Scholar
  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: 255–266CrossRefGoogle Scholar
  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): 355–368CrossRefGoogle Scholar
  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: 349–358CrossRefGoogle Scholar
  22. Ouyang LY, Chuang BR, Lin YJ (2007b) Effective investment to reduce lost sales in a periodic review inventory model. OR Spectr 29: 681–697CrossRefGoogle Scholar
  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): 195–208Google Scholar
  24. Paknejad MJ, Nasri F, Affisco JF (1995) Defective units in a continuous (s, Q) review system. Int J Prod Res 33: 2767–2777CrossRefGoogle Scholar
  25. Pan CHJ, Hsiao YC (2001) Inventory models with back-order discounts and variable lead time. Int J Syst Sci 32(7): 925–929CrossRefGoogle Scholar
  26. Pan CHJ, Yang JS (2002) A study of an integrated inventory with controllable lead time. Int J Prod Res 40(5): 1263–1273CrossRefGoogle Scholar
  27. Porteus EL (1986) Optimal lot sizing, process quality improvement and setup cost reduction. Oper Res 34: 137–144CrossRefGoogle Scholar
  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): 1170–1177CrossRefGoogle Scholar
  29. Rosenblatt MJ, Lee HL (1986) Economic production cycles with imperfect production processes. IIE Trans 18: 48–55CrossRefGoogle Scholar
  30. Salameh MK, Jaber MY (2000) Economic production quantity model for items with imperfect quality. Int J Prod Econ 64: 59–64CrossRefGoogle Scholar
  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): 613–630CrossRefGoogle Scholar
  32. Taylor BW III (1999) Introduction to management science, 6th edn. Hall, New JerseyGoogle Scholar
  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): 853–863CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.General Education CenterSt. John’s UniversityTaipei CountyTaiwan

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