Determination of Optimal Supply When Demand Is a Sum of Components

Vijayakumar Raman; Venkatesan Thirunavukkarasu; Muthu Chinnathambi

doi:doi:10.11648/j.mma.20170206.13

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Determination of Optimal Supply When Demand Is a Sum of Components

Vijayakumar Raman, Venkatesan Thirunavukkarasu, Muthu Chinnathambi

Published in Mathematical Modelling and Applications (Volume 2, Issue 6)

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), 2024. 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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TY  - JOUR
T1  - Determination of Optimal Supply When Demand Is a Sum of Components
AU  - Vijayakumar Raman
AU  - Venkatesan Thirunavukkarasu
AU  - Muthu Chinnathambi
Y1  - 2017/12/14
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170206.13
DO  - 10.11648/j.mma.20170206.13
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
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EP  - 74
PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.mma.20170206.13
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.
VL  - 2
IS  - 6
ER  -

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Author Information

Vijayakumar Raman

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

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

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Determination of Optimal Supply When Demand Is a Sum of Components
AU  - Vijayakumar Raman
AU  - Venkatesan Thirunavukkarasu
AU  - Muthu Chinnathambi
Y1  - 2017/12/14
PY  - 2017
N1  - https://doi.org/10.11648/j.mma.20170206.13
DO  - 10.11648/j.mma.20170206.13
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 68
EP  - 74
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20170206.13
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.
VL  - 2
IS  - 6
ER  -

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