An Integrated Production-Inventory Model for Deteriorating Items with Imperfect Quality and Shortage Backordering Considerations

  • H. M. Wee
  • Jonas C. P. Yu
  • K. J. Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3982)


In this study we present a production-inventory model for deteriorating item with vendor-buyer integration. A periodic delivery policy for a vendor and a production-inventory model with imperfect quality for a buyer are established. Such implicit assumptions (deteriorating items, imperfect quality) are reasonable in view of the fact that poor-quality items do exist during production. Defective items are picked up during the screening process. Shortages are completely backordered. The study shows that our model is a generalization of the models in current literatures. An algorithm and numerical analysis are given to illustrate the proposed solution procedure. Computational results indicate that our model leads to a more realistic result.


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  1. 1.
    Banerjee, A.: A joint economic lot size model for purchaser and vendor. Decision Science 17, 292–311 (1985)CrossRefGoogle Scholar
  2. 2.
    Cheng, T.C.E.: An economic order quantity model with demand-dependent unit production cost and imperfect production process. IIE Transactions 23(1), 23–28 (1991)CrossRefGoogle Scholar
  3. 3.
    Chung, K.J., Hou, K.L.: An optimal production run time with imperfect production processes and allowable shortages. Computers and Operations Research 20, 483–490 (2003)CrossRefGoogle Scholar
  4. 4.
    Dave, U.: On a discrete-in-time order-level inventory model for deteriorating items. Operational Research Quarterly 30, 349–354 (1979)MATHGoogle Scholar
  5. 5.
    Elsayed, E.A., Terasi, C.: Analysis of inventory systems with deteriorating items. International Journal of Production Research 21, 449–460 (1983)MATHCrossRefGoogle Scholar
  6. 6.
    Goyal, S.K.: Determination of optimum production quantity for a two-stage production system. Operational Research Quarterly 28, 865–870 (1977)MATHCrossRefGoogle Scholar
  7. 7.
    Goyal, S.K.: A joint economic lot size model for purchaser and vendor: A comment. Decision Science 19, 236–241 (1988)CrossRefGoogle Scholar
  8. 8.
    Goyal, S.K., Gupta, Y.P.: Integrated inventory models: the buyer–vendor coordination. European Journal of Operational Research 41, 261–269 (1992)CrossRefGoogle Scholar
  9. 9.
    Goyal, S.K.: A one-vendor multi-buyer integrated inventory model: a comment. European Journal of Operational Research 82, 209–210 (1995)MATHCrossRefGoogle Scholar
  10. 10.
    Goyal, S.K., Gardenas-Barron, L.E.: Note on: economic production quantity model for items with imperfect quality – a practical approach. International Journal of Production Economics 77, 85–87 (2002)CrossRefGoogle Scholar
  11. 11.
    Goyal, S.K., Huang, C.K., Chen, H.K.: A simple integrated production policy of an imperfect item for vendor and buyer. Production Planning & Control 14(7), 596–602 (2003)CrossRefGoogle Scholar
  12. 12.
    Ghare, P.M., Schrader, S.F.: A model for an exponentially decaying inventory. Journal of Industrial Engineering 14, 238–243 (1963)Google Scholar
  13. 13.
    Ha, D., Kim, S.L.: Implementation of JIT purchasing: an integrated approach. Production Planning & Control 8(2), 152–157 (1997)CrossRefGoogle Scholar
  14. 14.
    Hahm, J., Yano, C.A.: The economic lot and delivery scheduling problem: the single item case. International Journal of Production Economics 28, 235–251 (1992)CrossRefGoogle Scholar
  15. 15.
    Hahm, J., Yano, C.A.: The economic lot and delivery scheduling problem: the common cycle case. IIE Transactions 27, 113–125 (1995)CrossRefGoogle Scholar
  16. 16.
    Heng, K.J., Labban, J., Linn, R.L.: An order-level lot-size inventory model for deteriorating items with finite replenishment rate. Computers & Industrial Engineering 20, 187–197 (1991)CrossRefGoogle Scholar
  17. 17.
    Hill, R.M.: The single-vendor single-buyer integrated production-inventory model with a generalized policy. European Journal of Operational Research 97, 493–499 (1997)MATHCrossRefGoogle Scholar
  18. 18.
    Hill, R.M.: The optimal production and shipment policy for the single-vendor single-buyer integrated production inventory problem. International Journal of Production Research 37, 2463–2475 (1999)MATHCrossRefGoogle Scholar
  19. 19.
    Hoque, M.A., Goyal, S.K.: An optimal policy for a single-vendor single-buyer integrated production-inventory system with capacity constraint of transport equipment. International Journal of Production Economics 65, 305–315 (2000)CrossRefGoogle Scholar
  20. 20.
    Kang, S., Kim, I.: A study on the price and production level of the deteriorating inventory system. International Journal of Production Research 21, 449–460 (1983)CrossRefGoogle Scholar
  21. 21.
    Lu, L.: A one-vendor multi-buyer integrated inventory model. European Journal of Operational Research 81, 312–323 (1995)MATHCrossRefGoogle Scholar
  22. 22.
    Porteus, E.L.: Optimal lot sizing, process quality improvement and setup cost reduction. Operations Research 34(1), 37–144 (1986)CrossRefGoogle Scholar
  23. 23.
    Raafat, F., Wolfe, P.M., Eldin, H.K.: An inventory model for deteriorating items. Computers & Industrial Engineering 20, 89–94 (1991)CrossRefGoogle Scholar
  24. 24.
    Rosenblatt, M.J., Lee, H.L.: Economic production cycles with imperfect production process. IIE Transaction 18, 48–55 (1986)CrossRefGoogle Scholar
  25. 25.
    Salameh, M.K., Jaber, M.Y.: Economic order quantity model for items with imperfect quality. International Journal of Production Economics 64, 59–64 (2000)CrossRefGoogle Scholar
  26. 26.
    Schwaller, R.L.: EOQ under inspection costs. Production and Inventory Management 29(3), 22 (1988)Google Scholar
  27. 27.
    Viswanathan, S.: Optimal strategy for the integrated vendor-buyer inventory model. European Journal of Operational Research 105, 38–42 (1998)MATHCrossRefGoogle Scholar
  28. 28.
    Wee, H.M., Yu, J., Chen, M.C.: Optimal inventory model for items with imperfect quality and shortage backordering. Omega (2005) (in press) (available online)Google Scholar
  29. 29.
    Yang, P.C., Wee, H.M.: A single-vendor and multiple-buyers production-inventory policy for a deteriorating item. European Journal of Operational Research 43, 570–581 (2002)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Zhang, X., Gerchak, Y.: Joint lot sizing and inspection policy in an EOQ model with random yield. IIE Transaction 22(1), 41 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • H. M. Wee
    • 1
  • Jonas C. P. Yu
    • 2
  • K. J. Wang
    • 3
  1. 1.Department of Industrial EngineeringChung Yuan Christian UniversityChungliTaiwan
  2. 2.Logistics Management DepartmentTakming CollegeTaipeiTaiwan
  3. 3.Department of Business AdministrationNational Dong Hwa UniversityHualienTaiwan

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