A Sustainable Supply Chain Model with Variable Production Rate and Remanufacturing for Imperfect Production Inventory System under Learning in Fuzzy Environment

In the present paper, a sustainable supply chain model is investigated with a variable production rate and remanufacturing for the production of defective items under the effect of learning fuzzy theory, where the lower and upper variations in fuzzy demand rate are affected by learning parameters and backorders are also allowed. Our proposed model reveals a springy manufacturing inventory organization that makes various types of items, and imperfect items can be created through the method of manufacturing things in a fuzzy environment. When the screening process is completed, defective items are remanufactured immediately, and a limited financial plan and space limitations are assumed concerning the product assembly. We minimized the total fuzzy inventory cost with different distributions (beta, triangular, double triangular, uniform, andχ²(chi−square)) concerning the production rate, lot size, and backorder under learning in a fuzzy environment where the costs of screening, manufacturing, carrying, carbon emissions, backorders, and remanufacturing are included. The Kuhn–Tucker optimization technique is applied to solve non-linear equations that are based on some distributions. Numerical examples, sensitivity analysis, managerial insights and observations, limitations, future work, and applications are provided for the validation of our proposed model, and the industrial scope of this proposed work is included.