# Optimizing a Fuzzy Multi-Item Inventory System and Ordering Cost Depletion Contingent on Lead Time With Carbon Emission Cost

## Authors

• R. Vithyadevi Mother Teresa Women’s University, Kodaikanal, Tamilnadu 624101, India; Department of Mathematics, SSM Institute of Engineering and Technology, Dindigul, Tamilnadu 624002, India
• K. Annadurai PG and Research Department of Mathematics, M.V. Muthiah Government Arts College for Women, Dindigul, Tamilnadu 624001, India

## Keywords:

Fuzzy multi-item inventory model, Graded mean integration technique, Minimum integrated total cost for multi-item, Optimal order quantity for each item, Kuhn-Tucker method

## Abstract

Multi-item integrated inventory system and ordering cost depletion liable scheduled lead time with carbon emission cost is established in a fuzzy situation. Multiple items can considerably drop total inventory costs for hiring orders aimed at multiple items in single refill demand would drop ordering costs. Owing to the inaccuracy of various parameters and objective is imprecise in the environment. As the development of fuzzy objective is uncertain, the model is formulated as multi-item problems were confident/suspicious profit of the objective with some uncertainty. The model is solved via the graded mean technique with the addition of the Kuhn-Tucker method when the fuzzy equivalent of the problem remains available. An algorithm is established to attain optimal order quantity for each item and then find the minimum integrated total cost for a multi-item inventory system. The evaluation of a fuzzy multi-item inventory system through the crisp multi-item inventory system is completed over mathematical illustrations. Lastly, the graphical demonstration remains offered toward establishing the suggested system. An ending outcome demonstrates that this fuzzy multi-item system is perhaps moderately suitable defining optimal order quantity for each item and then the minimum integrated total cost for the multi-item technique when the lead time is assessed.

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16-04-2024
CITATION

## How to Cite

Vithyadevi, R., & Annadurai, K. (2024). Optimizing a Fuzzy Multi-Item Inventory System and Ordering Cost Depletion Contingent on Lead Time With Carbon Emission Cost. Communications in Mathematics and Applications, 14(5), 1693–1725. https://doi.org/10.26713/cma.v14i5.2272

Research Article