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A Production Model with Stock-Dependent Demand, Partial Backlogging, Weibull Distribution Deterioration, and Customer Returns

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Proceedings of Fifth International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 436))

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Abstract

In this paper, we derive an economic production model having two-parameter Weibull distribution deterioration. In this model, we considered a demand rate that depends on price stock and indirectly on time. Shortage is allowed and partially backlogged. We assume that customer return is a factor of quantity sold, price, and inventory level. Time horizon is finite. Production is also dependent on demand. The goal of this production is to maximize the profit function. An illustrative example, sensitivity analysis, and a graphical representation are used to interpret the usefulness of this model.

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References

  1. Covert, R.P., Philip, G.C.: An EOQ model for items with weibull distribution deterioration: AIIE Trans. 5(4), 323–326, (1973)

    Google Scholar 

  2. Misra, R.B.: Optimum production lot size model for a system with deteriorating inventory. Int. J. Prod. Res. 13(5), 495– 505 (1975)

    Google Scholar 

  3. Choi, S., Hwang, H.: Optimization of production planning problem with continuously distributed time-lags. Int. J. Syst. Sci. 17(10), 1499–1508 (1986)

    Google Scholar 

  4. Aggarwal, V., Bahari-Hashani, H.: Synchronized production policies for deteriorating items in a declining market. IIE Trans. Oper. Eng. 23(2), 185–197 (1991)

    Google Scholar 

  5. Pakkala, T.P.M., Achary, K.K.: A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate. Eur. J. Oper. Res. 57(1), 157–167 (1992)

    Google Scholar 

  6. Wu, J.-W., Lin, C., Tan, B., Wen-Chuan.: An EOQ inventory model with time-varying demand and Weibull deterioration with shortages. Int. J. Syst. Sci. 31(6), 677–683 (2000)

    Google Scholar 

  7. Wu, K.S.: An EOQ inventory model for items with Weibull distribution deterioration, ramp type demand rate and partial backlogging. Prod. Planning Control 12(8), 787–793, (2001)

    Google Scholar 

  8. Lee, W.C., Wu, J.-W.: An EOQ model for items with Weibull distributed deterioration, shortages and power demand pattern. Int. J. Inf. Manag. Sci. 13(2), 19–34 (2002)

    Google Scholar 

  9. Banerjee, S., Agrawal, S.: A two-warehouse inventory model for items with three-parameter Weibull distribution deterioration, shortages and linear trend in demand. Int. Trans. Oper. Res. 15(6), 755–775 (2008)

    Google Scholar 

  10. Roy, T., Chaudhuri K.S.: A production-inventory model under stock-dependent demand, Weibull distribution deterioration and shortage. Int. Trans. Oper. Res. 16(3), 325–346 (2009)

    Google Scholar 

  11. Begum, R., Sahoo, R.R., Sahu, S.K., Mishra, M.: An EOQ model for varying items with Weibull distribution deterioration and price-dependent demand. J. Sci. Res. 2(1), 24–36 (2010)

    Google Scholar 

  12. Konstantaras, I., Skouri, K.: A note on a production-inventory model under stock-dependent demand, Weibull distribution deterioration, and shortage. Int. Trans. Oper. Res. 18(4), 527–531 (2011)

    Google Scholar 

  13. Shipi, P., Mahapatra, G.S., Samanta G.P.: EPQ model of ramp type demand with weibull deterioration under inflation and finite horizon in crisp and fuzzy environment. Int. J. Prod. Econ. 156, 159–166 (2014)

    Google Scholar 

  14. Datta, T.K., Paul, K., Pal, A.K.: Demand promotion by up-gradation under stock-dependent demand situation–a model. Int. J. Prod. Econ. 55, 31–38 (1998)

    Google Scholar 

  15. Balkhi, T.Z., Benkherouf, L.: On an inventory model for deteriorating items with stock dependent and time varying demand rates. Comput. Oper. Res. 31, 223–240 (2004)

    Google Scholar 

  16. Teng, J.T., Chang, C.T.: Economic production quantity models for deteriorating items with price and stock dependent demand. Comput. Oper. Res. 32, 297–308 (2005)

    Google Scholar 

  17. 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, 369–384 (2006)

    Google Scholar 

  18. Singh, S.R., Kumari, R., Kumar, N.: Replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial back logging with two-storage facility under inflation. Int. J. Oper. Res. Optim. 1(1), 161–179 (2010)

    Google Scholar 

  19. Singh, C., Singh, S.R.: An EPQ model with stock dependent demand under imprecise and inflationary environment using genetic algorithm. Int. J. Eng. Res. Technol. 1(4), (2012)

    Google Scholar 

  20. Biswajit, S., Sumon, S.: An improved inventory model with partial backlogging time varying deterioration and stock dependent demand. Econ. Model. 30, 924–932 (2013)

    Google Scholar 

  21. Yang, C.T.: Inventory model with both stock dependent demand and stock dependent holding cost rate. Int. J. Prod. Econ. 155, 214–221 (2014)

    Google Scholar 

  22. Hess, J.D., Mayhew, G.E.: Modeling merchandise returns in direct marketing. J. Interact. Mark. 4(2), 347–385 (1997)

    Google Scholar 

  23. Pasternack, B.A.: Optimal pricing and returns policies for perishable commodities. Mark. Sci. 4(2), 166–176 (1985)

    Google Scholar 

  24. Anderson, E.T., Hansen, K., Simister, D., Wang, L.K.: How are demand and return related? Theory and empirical evidence: Working paper, Kellogg school of management, Northwestern University (2006)

    Google Scholar 

  25. Ahmed, M.A., Saadany, E.L., Jaber Mohomad, Y.: A production\remanufacturing inventory model with price and quality dependent return rate. Comput. Ind. Eng. 58(3), 352–362 (2010)

    Google Scholar 

  26. Mesak Hani, I., Abdullahal, B., Babin Barry, J., Biron Laura, M., Antony, J.: Optimum advertising policy over time for subscriber services cost learning and customer’s disadoption. Eur. J. Oper. Res. 211(3), 642–649 (2011)

    Google Scholar 

  27. Wu, J., Ya-Lan, C.: Lot sizing policies for deteriorating items with expiration dates and partial trade credit risk customers. Int. J. Prod. Econ. 155, 292–301 (2014)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Acharya Narendra Dev College, University of Delhi, New Delhi, India

    Chaman Singh

  2. Department of Computer Science, D.N. College, CCS University, Meerut, 250001, Uttar Pradesh, India

    Kamna Sharma

  3. Department of Mathematics, CCS University, Meerut, 250001, Uttar Pradesh, India

    S. R. Singh

Authors
  1. Chaman Singh
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  2. Kamna Sharma
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  3. S. R. Singh
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Corresponding author

Correspondence to Chaman Singh .

Editor information

Editors and Affiliations

  1. Dept of Applied Sci & Eng, Indian Instit of Tech Roorkee, Roorkee, India

    Millie Pant

  2. Department of Mathematics, Indian Inst of Tech Roorkee, Roorkee, India

    Kusum Deep

  3. Chankyapuri, Rm 327, South Asian Univ, Akbar Bhawan, New Delhi, India

    Jagdish Chand Bansal

  4. Department of Mathematics and Comp Sci, Liverpool Hope University, LIVERPOOL, United Kingdom

    Atulya Nagar

  5. Department of Mathematics, National Inst of Tech Silchar, Silchar, Assam, India

    Kedar Nath Das

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© 2016 Springer Science+Business Media Singapore

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Chaman Singh, Kamna Sharma, Singh, S.R. (2016). A Production Model with Stock-Dependent Demand, Partial Backlogging, Weibull Distribution Deterioration, and Customer Returns. In: Pant, M., Deep, K., Bansal, J., Nagar, A., Das, K. (eds) Proceedings of Fifth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 436. Springer, Singapore. https://doi.org/10.1007/978-981-10-0448-3_2

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  • DOI: https://doi.org/10.1007/978-981-10-0448-3_2

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-0447-6

  • Online ISBN: 978-981-10-0448-3

  • eBook Packages: EngineeringEngineering (R0)

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