Title: Economic order quantity model under fuzzy sense with demand follows Bass's innovation diffusion process

Authors: Alok Kumar; K.K. Aggarwal; Udayan Chanda

Addresses: Department of Operational Research, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India ' Department of Operational Research, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India ' School of Business, Galgotias University, Greater Noida-201308, Uttar Pradesh, India

Abstract: The economic order quantity (EOQ) model is usually not paid attention to make the model more realistic. The realistic EOQ model can bring a significant change while evaluating the profit and loss of any organisation. In this paper a mathematical model has been developed for obtaining the EOQ in which the demand of the product is assumed to follow an innovative imitative behaviour as proposed by Bass (1969). The theory of innovation-diffusion has been incorporated in this model. To make the model more realistic an attempt has been made to solve the model in light of fuzzy set theory under the trapezoidal membership function. The coefficient of innovation, the coefficient of imitation and the inventory carrying cost are assumed to be fuzzy numbers with trapezoidal membership function. By the median rule of defuzzification, total cost formula has been derived in the fuzzy sense in order to obtain the optimal order quantity. The effectiveness of this model is illustrated with a numerical example and sensitivity analysis of the optimal solution with respect to different parameters of the system is performed.

Keywords: innovation diffusion; economic order quantity; EOQ; trapezoidal membership function; fuzzy variables; defuzzification; function principle; fuzzy logic; mathematical modelling; product demand; coefficient of innovation; coefficient of imitation; inventory carrying cost.

DOI: 10.1504/IJAOM.2013.055869

International Journal of Advanced Operations Management, 2013 Vol.5 No.3, pp.261 - 281

Received: 24 Aug 2011
Accepted: 27 Jul 2012
Published online: 28 Apr 2014 *

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