Multi-objective Sustainable Fuzzy Economic Production Quantity (SFEPQ) Model with Demand as Type-2 Fuzzy Number: A Fuzzy Differential Equation Approach

Year 2019, Volume: 48 Issue: 1, 112 - 139, 01.02.2019

B. K. Debnath P. Majumder U. K. Bera

Abstract

A sustainable fuzzy economic production quantity (SFEPQ) inventory model is formulated by introducing the concept of fuzzy differential equation (FDE) due to dynamic behavior of the production-demand system. Generalized Hukuhara (gH) differentiability proceedure is applied to solve FDE. Since the demand parameter is taken as trapezoidal type-2 fuzzy number, to get corresponding defuzzified values, first critical value (CV)-based reduction method is applied on demand function to transfer into type-1 fuzzy variable which turns to hexagonal fuzzy number in form. After that $\alpha$-cut of a hexagonal fuzzy number is used to find the upper and lower value of demand. To apply the $\alpha$-cut operation on FDE, we divided the interval [0,1] into two sub-intervals [0,0.5] and [0.5,1] and gH-differentiation is applied on this sub-intervals. The objective of this paper is to maximize the profit and simultaneously minimize the carbon emission cost occurring due to the process of inventory management. Finally, the non-linear objective functions are solved by using of multi-objective genetic algorithm and sensitivity analyses on various parameters are also performed in numerically and graphically.

Keywords

Sustainable economic production quantity model, type-2 fuzzy demand, $\alpha$- cut of hexagonal fuzzy number, fuzzy differential equation, generalized Hukuhara differentiation

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