Abstract
In this paper, we concentrated on developing a multi-item inventory model under fuzzy rough environment. Here, demand and holding cost rates are assumed as the functions of stock level. Fuzzy rough expectation method is used to transform the present fuzzy rough inventory model into its equivalent crisp model. A numerical example is provided to illustrate the proposed model. To show the validity of the proposed models, few sensitivity analyses are also presented under the major parameter, and the results are illustrated numerically and graphically.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)
Ishii, H., Konno, T.: A stochastic inventory problem with fuzzy shortage cost. Eur. J. Oper. Res. 106, 90–94 (1998)
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–208 (1990)
Morsi, N.N., Yakout, M.M.: Axiomatics for fuzzy rough sets. Fuzzy Sets Syst. 100, 327–342 (1998)
Radzikowska, M.A., Kerre, E.E.: A comparative study of rough sets. Fuzzy Sets Syst. 126, 137–155 (2002)
Liu, B.: Theory and Practice of Uncertain Programming. Physica-Verlag, Heidelberg (2002)
Mondal, M., Maity, K.A., Maiti, K.M., Maiti, M.: A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of many. Appl. Math. Model. 37, 3200–3215 (2013)
Xu, J., Zhao, L.: A multi-objective decision-making model with fuzzy rough coefficients and its application to the inventory problem. Inf. Sci. 180, 679–696 (2010)
Maiti, M.K., Maiti, M.: Production policy for damageable items with variable cost function in an imperfect production process via genetic algorithm. Math. Comput. Model. 42, 977–990 (2005)
Khouja, M.: The economic production lot size model under volume flexibility. Comput. Oper. Res. 22, 515–525 (1995)
Maity, K.A.: One machine multiple-product problem with production-inventory system under fuzzy inequality constraint. Appl. Soft Comput. 11, 1549–1555 (2011)
Xu, J., Zaho, L.: A class of fuzzy rough expected value multi-objective decision making model and its application to inventory problems. Comput. Math. Appl. 56, 2107–2119 (2008)
Lushu, S., Nair, K.P.K.: Fuzzy models for single-period inventory model. Fuzzy Sets Syst. 132, 273–289 (2002)
Li, F.D.: An approach to fuzzy multi-attribute decision-making under uncertainty. Inf. Sci. 169, 97–112 (2005)
Balkhi, Z.T., Foul, A.: A multi-item production lot size inventory model with cycle dependent parameters. Int. J. Math. Model. Methods Appl. Sci. 3, 94–104 (2009)
Hartley, R.: An existence and uniqueness theorem for an optimal inventory problem with forecasting. J. Math. Anal. Appl. 66, 346–353 (1978)
Lee, H., Yao, J.S.: Economic production quantity for fuzzy demand quantity and fuzzy production quantity. Eur. J. Oper. Res. 109, 203–211 (1998)
Taleizadeh, A.A., Sadjadi, S.J., Niaki, S.T.A.: Multi-product EPQ model with single machine, back-ordering and immediate rework process. Eur. J. Ind. Eng. 5, 388–411 (2011)
Dutta, P., Chakraborty, D., Roy, R.A.: An inventory model for single-period products with reordering opportunities under fuzzy demand. 53, 1502–1517 (2007)
Chang, T.C.: An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. Int. J. Prod. Econ. 88, 6159–6167 (2004)
Shi, Y., Yao, L., Xu, J.: A probability maximization model based on rough approximation and its application to the inventory problem. Int. J. Approx. Reason. 52, 261–280 (2011)
Wang, Y.: Mining stock price using fuzzy rough set system. Expert Syst. Appl. 24, 13–23 (2003)
Taleizadeh, A.A., Wee, M.H., Jolai, F.: Revisiting a fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Math. Comput. Model. 57, 1466–1479 (2013)
Kazemi, N., Olugu, U.E., Rashid, H.S., Ghazilla, R.A.R.: A fuzzy EOQ model with back orders and forgetting effect on fuzzy parameters: an empirical study. Comput. Ind. Eng. 96, 140–148 (2016)
Bazan, E., Jaber, Y.M., Zanoni, S.: A review of mathematical inventory models for reverse logistics and the future of its modelling: an environmental perspective. Appl. Math. Model. 40, 4151–4178 (2016)
Das, C.B., Das, B., Mondal, K.S.: An integrated production inventory model under interactive fuzzy credit period for deteriorating item with several markets. Appl. Soft Comput. 28, 453–465 (2015)
Xu, J., Zaho, L.: Fuzzy Link Multiple-Object Decision Making. Springer, Berlin (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Garai, T., Chakraborty, D., Roy, T.K. (2018). A Multi-item Inventory Model with Fuzzy Rough Coefficients via Fuzzy Rough Expectation. In: Kar, S., Maulik, U., Li, X. (eds) Operations Research and Optimization. FOTA 2016. Springer Proceedings in Mathematics & Statistics, vol 225. Springer, Singapore. https://doi.org/10.1007/978-981-10-7814-9_26
Download citation
DOI: https://doi.org/10.1007/978-981-10-7814-9_26
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-7813-2
Online ISBN: 978-981-10-7814-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)