Abstract
In this paper a production inventory model of a single item with a variable production rate and production time dependent selling price has been introduced. Realistically it is seen that for any business concern, demand is always uncertain. Henceforth, in this model, demand of an item has been assumed to be fuzzy but its membership function is not known in prior. It is also considered that the production rate is a decreasing function of the inverse efficiency of the system. Under these circumstances, a profit function of the model has been formulated. As demand is fuzzy with unknown membership function, hence to get expected maximum profit, the diffusion method including possibility probability distribution has been used and the risk estimation values for failure to attain different profit levels have been evaluated. Finally the proposed model has been demonstrated taking a numerical example and a comparison among different types of demand such as crisp, fuzzy with triangular and trapezoidal membership value and fuzzy with unknown membership value have been shown.
Similar content being viewed by others
References
Baker, R.C., Urban, T.L.: A deterministic inventory system with an inventory level dependent demand rate. J. Oper. Res. Soc. 39, 823–831 (1988)
Chang, H.C.: An application of fuzzy sets theory to the EOQ model with imperfect quality items. Comput. Oper. Res. 31, 2079–2092 (2004)
Chang, H.C., Yao, J.S., Ouyang, L.Y.: Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand. Eur. J. Oper. Res. 169, 65–80 (2006)
Datta, T.K., Paul, K.: An inventory system with stock dependent, price sensitive demand rate. Prod. Plan. Control. 12, 13–20 (2001)
Harris, F.: Operations and Cost. Factory Management Service. A.W. Shaw Co, Chicago (1915)
Huang, C.F., Moraga, C.: A Fuzzy risk model and its matrix algorithm. Int. J. Uncertain. Fuzzyness Knowl. Based Syst. 10, 347–362 (2002)
Huang, C.F.: A demonastration of reliability of the Interior Outer set model. Int. J. Gen. Syst. 33 (2–3), 205–222 (2002)
Liu, B., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value model. IEEE Trans. Fuzzy Syst. 10 (4), 445–450 (2002)
Mandal, B.N., Phaujdar, S.: An inventory model for deteriorating items and stock dependent consumption rate. J. Oper. Res. Soc. 40, 483–488 (1989)
Manna, S.K., Chaudhuri, K.S.: An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages. Eur. J. Oper. Res. 171, 557–566 (2006)
Ouyang, L.Y., Yao, J.S.: A minimax distribution free procedure for mixed inventory model involving variable lead time with fuzzy demand. Comput. Oper. Res. 29, 471–487 (2002)
Shen, Q., Zhao, R.Q.: Risk assessment of serious crime with fuzzy random theory. Inf. Sci. 180 (22), 4401–4411 (2010)
Teng, J.T., Chang, C.T.: Economic production quantity models for deteriorating items with price and stock dependent demand. Comput. Oper. Res. 32, 297–308 (2005)
Wu, D.D., Zhang, Y., Wu, D., Olson, D.L.: Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach. Eur. J. Oper. Res. 200, 774–787 (2010)
Zadeh, L.A.: Fuzzy Sets Inf. Control. 8, 338–356 (1965)
Zhang, R., Kaku, I., Xiao, Y.: Deterministic EOQ with partial backordering and correlated demand caused by cross-selling. Eur. J. Oper. Res. 210, 537–551 (2011)
Zou, Q., Zhou, J., Zhou, C., Guo, J., Deng, W., Deng, M., Liao, L.: Fuzzy risk analysis of flood disasters based on diffused interior outer set model: Expert Systems with Applications 39, 6213–6220 (2012)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Patra, K., Mondal, S.K. Risk analysis in a production inventory model with fuzzy demand, variable production rate and production time dependent selling price. OPSEARCH 52, 505–529 (2015). https://doi.org/10.1007/s12597-014-0189-y
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12597-014-0189-y