A Fuzzy Inventory Model for Imperfect Process, Obsolescence and its Greenhouse Gas Emissions under Vendor Managed Inventory – Consignment Stock (VMI-CS) Policy

Objectives: To discuss a green inventory management system with greenhouse gas emissions, obsolescence, imperfect process, and Vendor Managed Inventory – Consignment Stock (VMI – CS) policy in a fuzzy nature by employing hexagonal fuzzy numbers to tackle uncertain situations. Methods: To find the optimum solution, we use two methods such as centroid method and the graded mean integration representation method for hexagonal fuzzy numbers. We use different sets of data for Marchi et al’s model 1 and for the proposed model with obsolescence to verify the results. Here two supply chain models are proposed, where the crisp model is first discussed with total cost and optimum order quantity. As a second part, the fuzzy model is formulated with fuzzy total cost and fuzzy optimal order quantity. Findings: The results of our discussion represent that the solution obtained from fuzzy by using two methods is slightly the same as the solution found from the crisp model. But since five parameters with ambiguous nature are solved under fuzzy by considering them in the form of a hexagonal fuzzy number, uncertainty is faced here. To show the applicability of the proposed model, numerical examples are given. Novelty: Implementation of obsolescence cost and its emissions in a green inventory system and the process of considering and solving parameters under fuzzy is a unique and important feature of our study. It helps sectors to know the effects of obsolete inventory, the need to include it, and also to rectify vagueness in their specified data. Hence this study is novel in the sense it discusses the above criteria under two fuzzy techniques. 2020 Mathematics Subject Classification: 90B05 Keywords: Hexagonal fuzzy numbers, Centroid method, Graded mean integration representation method, Obsolescence cost, Greenhouse gas emissions