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Determination of Optimal Supply When Demand Is a Sum of Components

Received: 27 September 2017     Accepted: 7 November 2017     Published: 14 December 2017
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Abstract

Among the various inventory systems our method is used to find the optimal supply size. To find the optimal supply size taking in to consideration the aspects like inventory holding cost per unit, cost of shortage per unit etc., In many situation the demand taken to be a random variable. The total demand is in turn a sum of three random variables namely (i) demand due to consumers (ii) demand due to the supply of the product to sister concerns or companies. (iii) Demand due to replacement of defective items that are not accepted and hence exchanged for new units Under these assumptions the optimal supply size is derived.

Published in Mathematical Modelling and Applications (Volume 2, Issue 6)
DOI 10.11648/j.mma.20170206.13
Page(s) 68-74
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Demand for the Product, Optimal Supply Size, Sum of Random Variables, Convolution Principle

References
[1] Amanda J. Schmitt, Lawrence V. Snyder, Zuo- Jun Max Shen (2008). Inventory Systems with Stochastic Demand and supply: Properties and Aproximations, http://ssrn.com, pp. 1-31.
[2] Barber. J. H. (1925). Economic control Inventory, New York Codes Book C0.
[3] Bellman. R. (1956a). On the theory of Dynamic programming – A ware housing problem, Management science, Volume 2, (No. 3): pp. 272–27.
[4] Bellman. R. (1956b). Dynamic programming and the smoothing problems, Management science, Volume 3, (No. 1): pp. 111-113.
[5] Beyer. D and Sethi. S. P. (1997). Average cost optimality in inventory Models with Markovian demands, Journal of Optimization theory and Applications, Vol. 92, No. 3, pp. 497–526.
[6] Bishop. G. R. (1957). On a Problems of production scheduling Operations Research, Vol. 5, (No. 1): pp. 97-103.
[7] Bowman, E. H., Richard D Irwin and Fetter, R. B. (1957). Analysis for production management. Home wood – Illinois.
[8] Brill Percy. H. And Ben A Chaouch (1995). An EOQ model with Random variables in demand- Management science, 41, 5 pp. 927–936.
[9] T. Venkatesan C. Muthu And R. Sathiyamoorthy (2010). Determination of Optimal Reserves between Two Machines in Series. Journal of Ultra Scientist of Physical Sciences, Vol. 22 (3) M, (2010), pp 853-861.
[10] T. Venkatesan C. Muthu And R. Sathiyamoorthy (2012). Determination of Optimal Reserve of Semi Finished products between three machines in series. Journal of Indian Academy of Mathematics, V0l. 34, No. 1 (2012), pp: 175-184.
[11] T. Venkatesan C. Muthu And R. Sathiyamoorthy (2016). Determination of Optimal Reserves between Three Machines in Series. International Journal of Advanced Research in Mathematics and Applications, Volume: 1 Issue: 1 May, 2016, ISSN_NO: 2350-028X.
[12] T. Venkatesan1, G. Arivazhagan And C. Muthu (2017). Some Applications of Order Statistics in Inventory Control. IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 13, Issue 1 Ver. IV (Jan. - Feb. 2017).
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  • APA Style

    Vijayakumar Raman, Venkatesan Thirunavukkarasu, Muthu Chinnathambi. (2017). Determination of Optimal Supply When Demand Is a Sum of Components. Mathematical Modelling and Applications, 2(6), 68-74. https://doi.org/10.11648/j.mma.20170206.13

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    ACS Style

    Vijayakumar Raman; Venkatesan Thirunavukkarasu; Muthu Chinnathambi. Determination of Optimal Supply When Demand Is a Sum of Components. Math. Model. Appl. 2017, 2(6), 68-74. doi: 10.11648/j.mma.20170206.13

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    AMA Style

    Vijayakumar Raman, Venkatesan Thirunavukkarasu, Muthu Chinnathambi. Determination of Optimal Supply When Demand Is a Sum of Components. Math Model Appl. 2017;2(6):68-74. doi: 10.11648/j.mma.20170206.13

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  • @article{10.11648/j.mma.20170206.13,
      author = {Vijayakumar Raman and Venkatesan Thirunavukkarasu and Muthu Chinnathambi},
      title = {Determination of Optimal Supply When Demand Is a Sum of Components},
      journal = {Mathematical Modelling and Applications},
      volume = {2},
      number = {6},
      pages = {68-74},
      doi = {10.11648/j.mma.20170206.13},
      url = {https://doi.org/10.11648/j.mma.20170206.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20170206.13},
      abstract = {Among the various inventory systems our method is used to find the optimal supply size. To find the optimal supply size taking in to consideration the aspects like inventory holding cost per unit, cost of shortage per unit etc., In many situation the demand taken to be a random variable. The total demand is in turn a sum of three random variables namely (i) demand due to consumers (ii) demand due to the supply of the product to sister concerns or companies. (iii) Demand due to replacement of defective items that are not accepted and hence exchanged for new units Under these assumptions the optimal supply size is derived.},
     year = {2017}
    }
    

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    AU  - Vijayakumar Raman
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    AB  - Among the various inventory systems our method is used to find the optimal supply size. To find the optimal supply size taking in to consideration the aspects like inventory holding cost per unit, cost of shortage per unit etc., In many situation the demand taken to be a random variable. The total demand is in turn a sum of three random variables namely (i) demand due to consumers (ii) demand due to the supply of the product to sister concerns or companies. (iii) Demand due to replacement of defective items that are not accepted and hence exchanged for new units Under these assumptions the optimal supply size is derived.
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Author Information
  • Department of Statistics, St. Joseph’s College, Trichy, Tamil Nadu, India

  • Department of Statistics, St. Joseph’s College, Trichy, Tamil Nadu, India

  • Department of Statistics, St. Joseph’s College, Trichy, Tamil Nadu, India

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