Green logistics under imperfect production system: A Rough age based Multi-Objective Genetic Algorithm approach

Imperfect economic production lot size (EPL) models are considered with time dependent defective rate. Here, defective production starts after the passage of some time from production commencement. Produced defective units are partially reworked and sold as fresh units. Under the environmental regulation, a cost (carbon tax) is charged by the government to mitigate global warming by reducing carbon emission (CE). Management also uses carbon trading when upper limit of carbon emission is given by the government. These costs bring a contradiction to a production manager. For more profit, if more production is decided, then CE and tax due to that are more. The models are formulated as single- and multi-objective profit maximization problems and solved using Rough age based single- and multi-objective Genetic Algorithms (RMOGAs). Numerical experiments are performed and graphical presentation of the results are depicted to illustrate the models. An algorithm with example for a firm management to achieve the maximum profit is also presented.