Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30054
On Solving Single-Period Inventory Model under Hybrid Uncertainty

Authors: Madhukar Nagare, Pankaj Dutta


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

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF


[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.