Use of “e” and “g” operators to a fuzzy production inventory control model for substitute items

¹ Department of Basic Science and Humanities, Global Institute of Science and Technology, Haldia, Purba Medinipur - 721657, West Bengal, India
² Department of Applied Sciences, Haldia Institute of Technology, Haldia, Purba Medinipur - 721657, West Bengal, India
³ Department of Mathematics, Mugberia Gangadhar Mahavidyalaya, Bhupatinagar, Purba Medinipur - 721425, West Bengal, India
⁴ Department of Mathematics, National Institute of Technology, Durgapur - 713209, West Bengal, India

^* Corresponding author: devnarayan87@gmail.com

Received: 12 January 2017
Accepted: 11 June 2017

Abstract

In this paper, a fuzzy optimal control model for substitute items with stock and selling price dependent demand has been developed. Here the state variables (stocks) are assumed to be fuzzy variables. So the proposed dynamic control system can be represented as a fuzzy differential system which optimize the profit of the production inventory control model through Pontryagin’s maximum principle. The proposed fuzzy control problem has been transformed into an equivalent crisp differential system using “e” and “g” operators. The deterministic system is then solved by using Newton’s forward-backward method through MATLAB. Finally some numerical results are presented both in tabular and graphical form.