Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach

P. Vasanthi; C. V. Seshaiah

doi:doi:10.11648/j.acm.20130206.12

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Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach

P. Vasanthi, C. V. Seshaiah

Published in Applied and Computational Mathematics (Volume 2, Issue 6)

Received: 17 September 2013 Published: 10 November 2013

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Abstract

A multi item inventory model with demand dependent on unit price and leading time with limited storage space and set up cost is considered in this paper. The varying production and leading time crashing costs are considered to be continuous functions of unit price and leading time respectively. The model is solved using Karush Kuhn Tucker conditions approach with optimal order quantity, unit price and leading time as decision variables. In most of the real world situations, the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. In this paper the unit cost has been imposed in fuzzy environment. An optimal total cost is obtained which is illustrated with numerical example for a single item.

Published in	Applied and Computational Mathematics (Volume 2, Issue 6)
DOI	10.11648/j.acm.20130206.12
Page(s)	124-126
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), 2013. Published by Science Publishing Group

Keywords

Inventory, Demand Dependent on Unit Cost, Lead Time, KKT Conditions, Fuzzy Unit Cost

References

[1]	M.O.Abou-El-Ata, and K.A.M.Kotb, Multi-Item EOQ Inventory Model with Varying Holding cost under two restrictions; A Geometric Programming Approach, Planning and Control, 6(1997), 608-611.
[2]	R.E.Bellman and L.A.Zadeh,Decision – Making in a Fuzzy Environment Management Science, 17(4), (1970), B141-B164.
[3]	M.Ben-Daya and Raouf, Inventory Models involving Lead time as a Decision Variable, Journal of the Operational Research Society, Vol.45 (5), 1994, 579-582.
[4]	T.C.E.Cheng, An Economic Order Quantity Model with Demand dependent Unit cost, European Journal of Operations Research, 40(1989), 252-256.
[5]	J.Juneau and E.R.Coates, An Economic Order Quantity Model for Time Varying Demand, Journal of Modern Engineering, 2(2001).
[6]	H.Jung and C.M.Klein, Optimal Inventory policies under decreasing cost functions via Geometric Programming, European Journal of Operations Research, 132(2001), 628-642.
[7]	B.M. Maloney and C.M.Kleing, Constrained Multi-item Inventory Systems: An Implicit Approach, Computers Operations Research, 6,(1993), 639-649.
[8]	N.K.Mandal, T.K.Roy and M.Maiti, Inventory Model of Deteriorated items with a Constraint: A Geometric Programming Approach, European Journal of Operations Research, 173(2006), 199-210.
[9]	Nirmal Kumar Mandal, T.K.Roy, M.Maiti, Multi-Objective Fuzzy Inventory Model with Three Constraints; A Geometric Programming Approach, Fuzzy Sets & Systems, 150 (2005), 87-106.
[10]	N.Ravi Shankar, G.Ananda Rao, J.Madhu Latha and V.Sireesha, Solving a Fuzzy Nonlinear Optimization Problem by Genetic Algorithm, International Journal of Contemporary Mathematical Sciences, Vol.5, No.16,(2010) 791-803.
[11]	J.T.Teng and H.L Yang, Deterministic Inventory lot Size Models with Time Varying Demand and Cost under Generalized Holding costs, Information and Management Sciences, Vol. 18 (2), 2007, 113-125.
[12]	L.A.Zadeh, Fuzzy Sets, Inform and Control, 1965, 338-353

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APA Style

P. Vasanthi, C. V. Seshaiah. (2013). Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach. Applied and Computational Mathematics, 2(6), 124-126. https://doi.org/10.11648/j.acm.20130206.12

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ACS Style

P. Vasanthi; C. V. Seshaiah. Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach. Appl. Comput. Math. 2013, 2(6), 124-126. doi: 10.11648/j.acm.20130206.12

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AMA Style

P. Vasanthi, C. V. Seshaiah. Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach. Appl Comput Math. 2013;2(6):124-126. doi: 10.11648/j.acm.20130206.12

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@article{10.11648/j.acm.20130206.12,
  author = {P. Vasanthi and C. V. Seshaiah},
  title = {Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {6},
  pages = {124-126},
  doi = {10.11648/j.acm.20130206.12},
  url = {https://doi.org/10.11648/j.acm.20130206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130206.12},
  abstract = {A multi item inventory model with demand dependent on unit price and leading time with limited storage space and set up cost is considered in this paper. The varying production and leading time crashing costs are considered to be continuous functions of unit price and leading time respectively. The model is solved using Karush Kuhn Tucker conditions approach with optimal order quantity, unit price and leading time as decision variables. In most of the real world situations, the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. In this paper the unit cost has been imposed in fuzzy environment. An optimal total cost is obtained which is illustrated with numerical example for a single item.},
 year = {2013}
}

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TY  - JOUR
T1  - Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach
AU  - P. Vasanthi
AU  - C. V. Seshaiah
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AB  - A multi item inventory model with demand dependent on unit price and leading time with limited storage space and set up cost is considered in this paper. The varying production and leading time crashing costs are considered to be continuous functions of unit price and leading time respectively. The model is solved using Karush Kuhn Tucker conditions approach with optimal order quantity, unit price and leading time as decision variables. In most of the real world situations, the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. In this paper the unit cost has been imposed in fuzzy environment. An optimal total cost is obtained which is illustrated with numerical example for a single item.
VL  - 2
IS  - 6
ER  -

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Author Information

P. Vasanthi

Department of Mathematics, Sri Ramakrishna Engineering College, Coimbatore-22, TN, India
C. V. Seshaiah

Department of Mathematics, Sri Ramakrishna Engineering College, Coimbatore-22, TN, India

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APA Style

P. Vasanthi, C. V. Seshaiah. (2013). Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach. Applied and Computational Mathematics, 2(6), 124-126. https://doi.org/10.11648/j.acm.20130206.12

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ACS Style

P. Vasanthi; C. V. Seshaiah. Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach. Appl. Comput. Math. 2013, 2(6), 124-126. doi: 10.11648/j.acm.20130206.12

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AMA Style

P. Vasanthi, C. V. Seshaiah. Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach. Appl Comput Math. 2013;2(6):124-126. doi: 10.11648/j.acm.20130206.12

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@article{10.11648/j.acm.20130206.12,
  author = {P. Vasanthi and C. V. Seshaiah},
  title = {Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {6},
  pages = {124-126},
  doi = {10.11648/j.acm.20130206.12},
  url = {https://doi.org/10.11648/j.acm.20130206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130206.12},
  abstract = {A multi item inventory model with demand dependent on unit price and leading time with limited storage space and set up cost is considered in this paper. The varying production and leading time crashing costs are considered to be continuous functions of unit price and leading time respectively. The model is solved using Karush Kuhn Tucker conditions approach with optimal order quantity, unit price and leading time as decision variables. In most of the real world situations, the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. In this paper the unit cost has been imposed in fuzzy environment. An optimal total cost is obtained which is illustrated with numerical example for a single item.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Multi Item Inventory Model With Demand Dependent On Unit Cost And Varying Lead Time Under Fuzzy Unit Production Cost; A Karush Kuhn Tucker Conditions Approach
AU  - P. Vasanthi
AU  - C. V. Seshaiah
Y1  - 2013/11/10
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130206.12
DO  - 10.11648/j.acm.20130206.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 124
EP  - 126
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20130206.12
AB  - A multi item inventory model with demand dependent on unit price and leading time with limited storage space and set up cost is considered in this paper. The varying production and leading time crashing costs are considered to be continuous functions of unit price and leading time respectively. The model is solved using Karush Kuhn Tucker conditions approach with optimal order quantity, unit price and leading time as decision variables. In most of the real world situations, the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. In this paper the unit cost has been imposed in fuzzy environment. An optimal total cost is obtained which is illustrated with numerical example for a single item.
VL  - 2
IS  - 6
ER  -

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