Carbon emissions, reworking, and waste management are the big challenges to achieving the goal of environmental sustainability in the production-inventory model. Here, a production-inventory model is developed, taking into account an imperfect production process and taking the cognizance of all these critical issues. In the current study, the production rate is tuned according to the demand and three different levels of production are considered in the model. The proportion of faulty products is taken as a random variable. Further, to control the deterioration rate, investment in preservation technology is being considered. A carbon tax is imposed because of carbon emissions due to various operational activities associated with the production system. An optimal production rate and lot size are derived such that the profit of the production system is maximized. In order to demonstrate the proposed model, numerical examples are given. Furthermore, sensitivity analysis is done to present management insights. Results show that waste management and reworking help to accomplish the goal of environmental sustainability. Additionally, inflation shows the true state of the economy.
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