Modeling of a carbon emitted production inventory system with interval uncertainty via meta-heuristic algorithms

Abstract

Modeling of a production inventory system under uncertain economic situation is a difficult task. Tackling this difficulty, the proposed work attempts to formulate a production inventory model with time dependent defective rate, greenness of the product dependent demand and production rates under interval uncertainty. Consideration of carbon emission during the production with interval valued time dependent emission rate is also an important feature of the proposed model. Furthermore, reduction technology is taken into the account for reducing the large scale of carbon emission. The proposed model is formulated mathematically with the help of interval differential equations and interval parametric approach. Thereafter, various interval valued cost components as well as average profit related to the model are obtained using interval mathematics. To handle the interval valued average profit, center-radius technique of interval optimization is applied. To verify the validity of the developed model, four numerical examples are considered and solved by meta-heuristic algorithms. Also, sensitivity analyses are carried out on the best found policy with respect to different system parameters of this model.