On Solving Single-Period Inventory Model under Hybrid Uncertainty
Inventory decisional environment of short life-cycle
products is full of uncertainties arising from randomness and
fuzziness of input parameters like customer demand requiring
modeling under hybrid uncertainty. Prior inventory models
incorporating fuzzy demand have unfortunately ignored stochastic
variation of demand. This paper determines an unambiguous optimal
order quantity from a set of n fuzzy observations in a newsvendor
inventory setting in presence of fuzzy random variable demand
capturing both fuzzy perception and randomness of customer
demand. The stress of this paper is in providing solution procedure
that attains optimality in two steps with demand information
availability in linguistic phrases leading to fuzziness along with
stochastic variation. The first step of solution procedure identifies
and prefers one best fuzzy opinion out of all expert opinions and the
second step determines optimal order quantity from the selected
event that maximizes profit. The model and solution procedure is
illustrated with a numerical example.
[1] D. Petrovic, R. Petrovic, M. Vujosevic, "Fuzzy models for the newsboy
problem," International Journal of Production Economics, vol.45, pp.
435-441, 1996.
[2] O. Dey and D. Chakraborty, "A Single Period Inventory Model with A
Truncated Normally Distributed Fuzzy Random Variable Demand,"
International Journal of Systems Science, vol. 43, pp. 518-525,2012.
[3] H. Behret and C. Kahraman, A Fuzzy Optimization Model for Single-
Period Inventory Problem, Proceedings of the World Congress on
Engineering 2011, vol 2, July 6 - 8, 2011, London, U.K.
[4] M. Khouja, "The Single-Period (News-Vender) Inventory Problem: A
Literature Review and Suggestions for Future Research," Omega,
vol.27, pp. 537-553, 1999.
[5] L. Li., S. N. Kabadi, K. P. K. Nair, "Fuzzy Models for Single-Period
Inventory Problem," Fuzzy Sets Systems, vol. 132 pp. 273-289, 2002.
[6] C. Kao, W. K. Hsu, "A Single Period Inventory Model with Fuzzy
Demand," Computers and Mathematics with Applications, vol. 43 no.6-
7, pp. 841-848, Mar-Apr 2002.
[7] Z. Shao, X. Ji, "Fuzzy Multi-Product Constrained Newsboy Problem,"
Applied Mathematics and Computation, vol.180,no.1,pp. 7-15,Sep.2006.
[8] P. Dutta, D. Chakraborty, A. R. Roy, "An Inventory Model For Single
Period Products with Reordering Opportunities Under Fuzzy Demand,"
Computers and Mathematics with Applications,vol.53,no.10, pp. 1502-
1517,May 2007.
[9] M. L. Puri, D.A. Ralescu, "Fuzzy Random Variables", Journal of
Mathematical. Analysis and Applications, vol. 114,no.2, pp.409-422,
Mar.1986.
[10] Y. Feng, L.Hu, H. Shu, "The Variance and Covariance of Fuzzy
Random Variables and their Applications," Fuzzy Sets and Systems,
vol.120, no.3, pp. 487-497, Jun.2001.
[11] M. K. Luhandjula, "Fuzzy Random Variable: A Mathematical Tool for
Combining Randomness and Fuzziness," African Journal of Science and
Technology,vol.5,no.2,pp.51-59,2004.
[12] P. Dutta, D. Chakraborty, A. R. Roy, "A Single Period Inventory Model
with Fuzzy Random Variable Demand," Mathematical and Computer
Modeling. Vol.41, no,8-9,pp.915-922, Apr-May 2005.
[13] S. H. Chen, C. H. Hsieh, "Graded Mean Integration Representation Of
Generalized Fuzzy Number," Journal of Chinese Fuzzy Systems
Association, vol. 5, pp. 1-7, 1999.
[1] D. Petrovic, R. Petrovic, M. Vujosevic, "Fuzzy models for the newsboy
problem," International Journal of Production Economics, vol.45, pp.
435-441, 1996.
[2] O. Dey and D. Chakraborty, "A Single Period Inventory Model with A
Truncated Normally Distributed Fuzzy Random Variable Demand,"
International Journal of Systems Science, vol. 43, pp. 518-525,2012.
[3] H. Behret and C. Kahraman, A Fuzzy Optimization Model for Single-
Period Inventory Problem, Proceedings of the World Congress on
Engineering 2011, vol 2, July 6 - 8, 2011, London, U.K.
[4] M. Khouja, "The Single-Period (News-Vender) Inventory Problem: A
Literature Review and Suggestions for Future Research," Omega,
vol.27, pp. 537-553, 1999.
[5] L. Li., S. N. Kabadi, K. P. K. Nair, "Fuzzy Models for Single-Period
Inventory Problem," Fuzzy Sets Systems, vol. 132 pp. 273-289, 2002.
[6] C. Kao, W. K. Hsu, "A Single Period Inventory Model with Fuzzy
Demand," Computers and Mathematics with Applications, vol. 43 no.6-
7, pp. 841-848, Mar-Apr 2002.
[7] Z. Shao, X. Ji, "Fuzzy Multi-Product Constrained Newsboy Problem,"
Applied Mathematics and Computation, vol.180,no.1,pp. 7-15,Sep.2006.
[8] P. Dutta, D. Chakraborty, A. R. Roy, "An Inventory Model For Single
Period Products with Reordering Opportunities Under Fuzzy Demand,"
Computers and Mathematics with Applications,vol.53,no.10, pp. 1502-
1517,May 2007.
[9] M. L. Puri, D.A. Ralescu, "Fuzzy Random Variables", Journal of
Mathematical. Analysis and Applications, vol. 114,no.2, pp.409-422,
Mar.1986.
[10] Y. Feng, L.Hu, H. Shu, "The Variance and Covariance of Fuzzy
Random Variables and their Applications," Fuzzy Sets and Systems,
vol.120, no.3, pp. 487-497, Jun.2001.
[11] M. K. Luhandjula, "Fuzzy Random Variable: A Mathematical Tool for
Combining Randomness and Fuzziness," African Journal of Science and
Technology,vol.5,no.2,pp.51-59,2004.
[12] P. Dutta, D. Chakraborty, A. R. Roy, "A Single Period Inventory Model
with Fuzzy Random Variable Demand," Mathematical and Computer
Modeling. Vol.41, no,8-9,pp.915-922, Apr-May 2005.
[13] S. H. Chen, C. H. Hsieh, "Graded Mean Integration Representation Of
Generalized Fuzzy Number," Journal of Chinese Fuzzy Systems
Association, vol. 5, pp. 1-7, 1999.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55256", author = "Madhukar Nagare and Pankaj Dutta", title = "On Solving Single-Period Inventory Model under Hybrid Uncertainty", abstract = "Inventory decisional environment of short life-cycle
products is full of uncertainties arising from randomness and
fuzziness of input parameters like customer demand requiring
modeling under hybrid uncertainty. Prior inventory models
incorporating fuzzy demand have unfortunately ignored stochastic
variation of demand. This paper determines an unambiguous optimal
order quantity from a set of n fuzzy observations in a newsvendor
inventory setting in presence of fuzzy random variable demand
capturing both fuzzy perception and randomness of customer
demand. The stress of this paper is in providing solution procedure
that attains optimality in two steps with demand information
availability in linguistic phrases leading to fuzziness along with
stochastic variation. The first step of solution procedure identifies
and prefers one best fuzzy opinion out of all expert opinions and the
second step determines optimal order quantity from the selected
event that maximizes profit. The model and solution procedure is
illustrated with a numerical example.", keywords = "Fuzzy expected value, Fuzzy random demand,
Hybrid uncertainty, Optimal order quantity, Single-period inventory", volume = "6", number = "4", pages = "433-6", }