© 2018 JETIR November 2018, Volume 5, Issue 11 www.jetir.org (ISSN-2349-5162) JETIRDS06191 Journal of Emerging Technologies and Innovative Research (JETIR) www.jetir.org 1297 Environmental Sustainability with eco-friendly green inventory model under Fuzzy logics considering carbon emission Seema Saxena *(1) , Rajesh Kumar Gupta (2) , Vikramjeet Singh (3) , Pushpinder Singh (4) , Nitin Kumar Mishra (5) 1,2,5 Department of Mathematics, Lovely Professional University, Phagwara , Punjab(India) 144411. 3 Department of Mathematics, IKGPTU Campus, Batala, Punjab(India) 143506. 4 Department of civil engineering University of Windsor, Windsor, Canada. Abstract Environmental consistency is the study of environmental interac- tions to prevent environmental degradation.To allow and preserve nat- ural resources and long-term environmental quality. The key to being environmentally friendly is environmental sustainability. Global warm- ing is one of the biggest threats to our planet. The cause of global warming emission of greenhouse gases (GHG). This article describes the green patterns of different social costs. Reduce carbon emissions strategies to achieve environmental sustainability with carbon sensi- tive products. Finally, determination of the favorable order amount and the total cost of the system in both the scenarios. The document ends with a numerical example validating the study. Keywords: Fuzzy, Heptagonal Fuzzy number, green, Inventory 1 INTRODUCTION In the present scenario of competitiveness prevailing in the market, the manufacturers and the units are not close to the retailer or selling outlets. The products, when received at the vendee end, is bound to have certain percentage of defective goods. These imperfect goods are to an extent realized as low-cost products in the system or are treated as waste products. If these goods go waste they are thrown in the surroundings and pollute the environment in many ways. To have sustainability in preserving the environment, it is important to treat these goods in a prominent manner. Also these goods, add to the cost of the inventory system in the form of deterioration, shortages and sometimes lost sales, and if unintentionally sold to a consumer can lead to the loss of goodwill of the product and the organization. Thus to ensure effective inventory management, quality of the items and the reputation of the brand/organization, the goods can be repaired, remanufactured or even recycled for their absorption in the system. Green inventory system not only is the way to protect the environment against the hazards of these waste/imperfect goods but also adds in the revenue generation of the inventory system. Adequate work including several facets and aspects of the green system is available. Detailed reviews on the green system design is done in the world by [1]. A detailed and comprehensive review of the green supply chain management is done by [2]. He incorporated various facets of green system as the importance of green inventory, design of green system, and the operations done for green inventory system. [3] investigated a detailed state of the art review of the green supply management and discussed the usage of green inventory like the ecofriendly raw materials, recycled papers used in packaging, reducing dependency on the petroleum and its products and many others. [4] modeled a three level supply chain from the supplier to manufacturer/retailer to the customers. They also involved the influence of the emission of the carbon on the production process. The research study derives some significant conclusions regarding a decline in the emission of carbon due to an increase in the order size. A supply chain model for the retailer and the supplier is formulated by [5] where the optimality of the refilling time and cost is determined. In a fuzzy environment an analysis on the flood management is done by [6]. An optimal value of time period with partially back order is determined with a check in the optimal value to the total cost of the system is done by [7]. Furthermore taking deterioration of weibull nature [8] modeled a problem for minimum cost valuation in an inventory problem. Under the impact of inflation [9] presented a study with trade credit in determining the most favorable cost value. An ordering period with the minimum value of cost for the retailer is determined in the research work done by [10]. In addition to, an inventory framework proceeding in the direction of saving the environment is done by [11]. To come to a more accurate solution to an inventory assignment, [12] presented a study by fuzzifying the cost parameters which are subjected to the uncertainity prevailing in the market. [13] worked on the concept