A sustainable pollution control fuzzy production inventory model with imperfect and breakable items through Pontryagin Maximum principle

Abstract

In present world the major cause of global warming and climate change are emission of carbon and greenhouse gas. Governments and policymakers around the world want to put their best efforts to control the pollution and climate change to save our environment. To reduce greenhouse gas emissions Government and policymakers takes carbon tax policy on carbon emission. Also in real world uncertainty is a pervasive phenomenon. Humans have a significant ability to make logical decisions based on uncertain information. For this purpose, we are developing a pollution control fuzzy production inventory model with imperfect and break-ability items under preservation technology investment and carbon tax policy. In this model, the break-ability rate is dependent on inventory level as the break-ability rate of breakable items depends on the collected stress of inventory stock level. Here the unit production cost is dependent on raw material cost, wear-tear cost and development cost. Carbon emission is controlled by investing in carbon reduction technology and a fraction of product items are imperfect. In this study demand of the product depends on selling price and inventory stock level of product. Finally, this optimal control problem solved by using Pontryagin Maximum principle and the optimal results are illustrated graphically and numerically using MATLAB software. Subsequently, some sensitivity analysis is investigated as the impact of parameters on total profit.