A Sustainable Supply Chain Model with Low Carbon Emissions for Deteriorating Imperfect-Quality Items under Learning Fuzzy Theory

In this paper, we develop a two-level supply chain model with low carbon emissions for defective deteriorating items under learning in fuzzy environment by using the double inspection process. Carbon emissions are a major issue for the environment and human life when they come from many sources like different kinds of factories, firms, and industries. The burning of diesel and petrol during the supply of items through transportation is also responsible for carbon emissions. When any company, firm, or industry supplies their items through a supply chain by using of transportation in the regular mode, then a lot of carbon units are emitted from the burning of petrol and diesel, etc., which affects the supply chain. Carbon emissions can be controlled by using different kinds of policies issued by the government of a country, and lots of companies have implemented these policies to control carbon emissions. When a seller delivers a demanded lot size to the buyer, as per demand, and the lot size has some defective items, as per consideration, the demand rate is uncertain in nature. The buyer inspects the received whole lot and divides it into two categories of defective and no defective deteriorating items, as well as immediately selling at different price. The fuzzy concept nullifies the uncertain nature of the demand rate. This paper covers two models, assuming two conditions of quality screening under learning in fuzzy environment: (i) the buyer shows the quality screening and (ii) the quality inspection becomes the seller’s responsibility. The carbon footprint from the transporting and warehousing the deteriorating items is also assumed. The aim of this study is to minimize the whole inventory cost for supply chains with respect to lot size and the number of orders per production cycle. Jointly optimizing the delivery lot size and number of orders per production cycle will minimize the whole fuzzy inventory cost for the supply chain and also reduce the carbon emissions. We take two numerical approaches with authentic data (from the literature reviews) for the justification of the proposed model 1 and model 2. Sensitivity observations, managerial insights, applications of these proposed models, and future scope are also included in this paper, which is more beneficial for firms, the industrial sector, and especially for online markets. The impact of the most effective parameters, like learning effect, fuzzy parameter, carbon emissions parameter, and inventory cost are shown in this study and had a positive effect on the total inventory cost for the supply chain.