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Designing a new computational approach of partial backlogging on the economic production quantity model for deteriorating items with non-linear holding cost under inflationary conditions

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Abstract

This paper discusses the production inventory model over an infinite time horizon. Here we consider demand as a function of stock and time. Deterioration is a function of time and time-varying production. Our objective is to minimize the total cost which is a function of set up cost, holding cost, shortage cost, and opportunity cost due to lost sales. The traditional costs such as purchasing cost, shortage cost and opportunity cost due to lost sales are kept constant. We consider holding cost to be a non-linear function of time. Shortages are allowed and are partially backlogged. Here, time durations are the decision variables. Numerical examples are given to illustrate the model.

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References

  1. Abad P.L.: Optimal pricing and lot sizing under conditions of perishability and partial backordering. Manag. Sci. 42(8), 1093–1104 (1996)

    Article  MATH  Google Scholar 

  2. Aggarwal S.P.: A note on an order level inventory model for a system with constant rate of deterioration. Opsearch 15, 184–187 (1978)

    MATH  MathSciNet  Google Scholar 

  3. Alcali E., Geunes J., Pardalos P.M., Romeijn H.E., Shen Z.J.: Applications of Supply Chain Management and E-commerce Research in Industry. Kluwer Academic Publishers, Dordrecht (2004)

    Google Scholar 

  4. Bose S., Goswami A., Chaudhuri K.S.: An EOQ model for deteriorating items with linear time-dependent demand rate and shortages under inflation and time discounting. J. Oper. Res. Soc. 46(6), 771–782 (1995)

    MATH  Google Scholar 

  5. Buzacott J.A.: Economic order quantities with inflation. Oper. Res. Q. 26(3), 553–558 (1975)

    Article  MathSciNet  Google Scholar 

  6. Chen J.M., Chen L.T.: Pricing and lot-sizing for a deteriorating item in a periodic review inventory system with shortages. J. Oper. Res. Soc. 55(8), 892–901 (2004)

    Article  MATH  Google Scholar 

  7. Chung K.J., Chu P., Lan S.P.: A note on EOQ models for deteriorating items under stock-determent selling rate. Eur. J. Oper. Res. 124(3), 550–559 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chung K.J., Ting P.S.: A heuristic for replenishment of deteriorating items with a linear trend in demand. J. Oper. Res. Soc. 44(12), 1235–1241 (1993)

    MATH  Google Scholar 

  9. Datta T.K., Pal A.K.: Deterministic inventory systems for deteriorating items with inventory level-dependent demand rate and shortages. Opsearch 27, 213–224 (1990)

    MATH  Google Scholar 

  10. Dave U., Patel L.K.: (T, S i ) Policy inventory model for deteriorating items with time proportional demand. J. Oper. Res. Soc. 32(2), 137–142 (1981)

    MATH  Google Scholar 

  11. Dye C.Y., Ouyang L.Y.: An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging. Eur. J. Oper. Res. 163(3), 776–783 (2005)

    Article  MATH  Google Scholar 

  12. Geunes J., Pardalos P.M., Romeijn H.E.: Supply Chain Optimization: Applications and Algorithms. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  13. Geunes J., Pardalos P.M.: Supply Chain Optimization. Kluwer Academic Publishers, Dordrecht (2003)

    Google Scholar 

  14. Ghare P.N., Schrader G.F.: A model for exponentially decaying inventory. J. Ind. Eng. 15, 238–243 (1963)

    Google Scholar 

  15. Giri B.C., Chaudhuri K.S.: Deterministic models of perishable inventory with stock-dependent demand rate and non linear holding cost. Eur. J. Oper. Res. 105(3), 467–474 (1998)

    Article  MATH  Google Scholar 

  16. Goyal S.K., Giri B.C.: Recent trends in modeling of deteriorating inventory. Eur. J. Oper. Res. 134(1), 1–16 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  17. Goyal S.K., Giri B.C.: The production-inventory problem of a product with time varying demand, production and deterioration rates. Eur. J. Oper. Res. 147(3), 549–557 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  18. Haiping U., Wang H.: An economic ordering policy model for deteriorating items with time proportional demand. Eur. J. Oper. Res. 46(1), 21–27 (1990)

    Article  MATH  Google Scholar 

  19. Hariga M.: Lot sizing models for deteriorating items with time-dependent demand. Int. J. Syst. Sci. 26(12), 2391–2401 (1995)

    Article  MATH  Google Scholar 

  20. Hariga M.: Optimal EOQ models for deteriorating items with time-varying demand. J. Oper. Res. Soc. 47(10), 1228–1246 (1996)

    MATH  Google Scholar 

  21. Hariga M.: Effects of inflation and time value of money on an inventory model with time-dependent demand rate and shortages. Eur. J. Oper. Res. 81(3), 512–520 (1995)

    Article  MATH  Google Scholar 

  22. Manna S.K., Chaudhuri K.S., Chiang C.: Replenishment policy for EOQ models with time-dependent quadratic demand and shortages. Int. J. Oper. Res. 2(3), 321–337 (2007)

    Article  MATH  Google Scholar 

  23. Manna S.K., Lee C.C., Chiang C.: EOQ model for non-instantaneous deteriorating items with time-varying demand and partial backlogging. Int. J. Ind. Syst. Eng. 4(3), 241–254 (2009)

    Google Scholar 

  24. Migdalas A., Baourakis G., Pardalos P.M.: Supply Chain and Finance. Springer, New York (2004)

    MATH  Google Scholar 

  25. Padmanabhan G., Vrat P.: EOQ models for perishable items under stock-dependent selling rate. Eur. J. Oper. Res. 86(2), 281–292 (1995)

    Article  MATH  Google Scholar 

  26. Pardalos P.M., Tsitsiringos V.: Financial Engineering, Supply Chain and E-commerce. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  27. Sachan R.S.: On (T, S i ) Policy inventory model for deteriorating items with time proportional demand. J. Oper. Res. Soc. 35(11), 1013–1019 (1984)

    MATH  Google Scholar 

  28. Sarkar B.R., Jamal A.M.M., Wang S.: Supply chain model for perishable products under inflation and permissible delay in payment. Comput. Oper. Res. 27(1), 59–75 (2000)

    Article  Google Scholar 

  29. Su C.T., Tong L.I., Liao H.C.: An inventory model under inflation for stock dependent consumption rate and exponential decay. Opsearch 33(2), 71–82 (1996)

    MATH  Google Scholar 

  30. Wee H.M.: Economic production lot size model for deteriorating items with partial back-ordering. Comput. Ind. Eng. 24(3), 449–458 (1993)

    Article  Google Scholar 

  31. Wee H.M.: A replenishment policy for items with a price-dependent demand and a varying rate of deterioration. Prod. Plan. Control 8(5), 494–499 (1997)

    Article  Google Scholar 

  32. Wee H.M., Law S.T.: Economic production lot size for deteriorating items taking account of the time value of money. Comput. Oper. Res. 26(6), 545–558 (1999)

    Article  MATH  Google Scholar 

  33. Wu K.S., Ouyang L.Y., Yang C.T.: An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging. Int. J. Prod. Econ. 101(2), 369–384 (2006)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Chikkaiah Naicker College, Erode, 638004, Tamil Nadu, India

    M. Valliathal

  2. Department of Mathematics, Gandhigram University, Gandhigram, 624302, Tamil Nadu, India

    R. Uthayakumar

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  1. M. Valliathal
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  2. R. Uthayakumar
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Correspondence to M. Valliathal.

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Valliathal, M., Uthayakumar, R. Designing a new computational approach of partial backlogging on the economic production quantity model for deteriorating items with non-linear holding cost under inflationary conditions. Optim Lett 5, 515–530 (2011). https://doi.org/10.1007/s11590-010-0216-8

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