This article considers the single setup and multiple delivery policy between a single vendor and a single buyer. As the machine switches from the in-control stage to the out-of-control stage, the output of the manufactured item is found to be defective. Continuous investment has been made to reduce this imperfect production by improving the quality of the item. The main aim of this work is to achieve optimum setup cost and defective item percentage with minimum total supply chain cost under a triangular fuzzy number in addition to environmental cost such as carbon emission during the manufacturing and transportation.The model is solved in a general fuzzy and cloudy fuzzy environment using Yager’s index method, De and Beg’s ranking index method and comparisons are made for all cases and better results obtained in the cloudy fuzzy model. A couple of numerical examples have been considered to evaluate this model. Sensitivity analysis section is decorated for the optimal solution of the model with respect to major cost parameters of the system are carried out, and the implications of the analysis are discussed.

Inventory/ imperfect production, logarithmic reduction, quality improvement, price discount, lead time, carbon emission, pollution control, environmental sustainability, fuzzy number, cloudy fuzzy number.