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.

中文翻译：

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学习模糊理论下劣质劣质品的低碳排放可持续供应链模型

在本文中，我们利用双重检验过程，在模糊环境下学习的情况下，针对有缺陷的劣化物品开发了一种低碳排放的两级供应链模型。碳排放是环境和人类生活的一个主要问题，因为碳排放来自不同类型的工厂、公司和行业等多种来源。在运输过程中供应物品时燃烧柴油和汽油也是碳排放的原因之一。当任何公司、企业或行业通过常规运输方式通过供应链供应其物品时，汽油和柴油等的燃烧会排放大量碳单位，从而影响供应链。碳排放可以通过一个国家政府发布的各种政策来控制，并且许多公司已经实施了这些政策来控制碳排放。当卖方根据需求向买方交付所需的批量，并且根据考虑，批量中存在一些缺陷品时，需求率本质上是不确定的。买方检查收到的整批货物，并将其分为有缺陷和无缺陷的变质物品两类，并立即以不同的价格出售。模糊概念消除了需求率的不确定性。本文涵盖了两个模型，假设模糊环境中学习下的质量筛选的两种条件：（i）买方显示质量筛选和（ii）质量检查成为卖方的责任。还假设了运输和仓储变质物品的碳足迹。本研究的目的是在批量大小和每个生产周期的订单数量方面最大限度地降低供应链的整体库存成本。联合优化交货批量大小和每个生产周期的订单数量将最大限度地降低供应链的整体模糊库存成本，并减少碳排放。我们采用两种具有真实数据（来自文献综述）的数值方法来证明所提出的模型 1 和模型 2 的合理性。本文还包括敏感性观察、管理见解、这些所提出模型的应用以及未来范围，即对企业、工业部门，尤其是在线市场更有利。本研究显示了最有效的参数（如学习效应、模糊参数、碳排放参数和库存成本）的影响，并对供应链的总库存成本产生积极影响。