Investigation of a Fuzzy Production Inventory Model with Carbon Emission using Sign Distance Method

^1,2,3 Department of Mathematics, S.G.R.R. (P.G) College, Dehradun, India
⁴ Department of Mathematics, Graphic Era Deemed University, Dehradun, India
⁵ Department of Mathematics, SBAS, K.R Mangalam University, Gurugram, India
⁶ Lovely Professional University, Phagwara, Punjab, India

^* Corresponding author: yogendrarajo@gmail.com

Abstract

Reducing costs associated with inventory is the primary goal of conventional inventory models like the models of economic order quantity and economic production quantity. However, these models fall short of addressing defective goods or revising them. Imperfections in the manufacturing process result in flawed products alongside the final goods. To convert these flawed components into finished goods, rework is necessary. In manufacturing and reworking process produces carbon emissions which are harmful for the earth. To determine the optimal quantity for a single product manufactured in a single-stage manufacturing system that yields partially defective products that are reworked in the same cycle, is determined in real-life situations, where the inventory characteristics and objectives are not exact. Such a type of uncertainty may be characterized by fuzzy numbers. A pentagonal fuzzy number has been used to define the cost parameters. Due to fuzzy parameters, the model becomes a fuzzy quantity, and it is defuzzied by the sign distance method. this article formulates a model of manufacturing inventories with planned backorders. Furthermore, a closed form for the inventory’s system total cost is determined, and a range of actual values for defective products for which an appropriate method exists is also provided. A proper mathematical model is created to accomplish the goal, and the manufacturing lot size that reduces the overall cost is determined. The ideal amount of a production batch to reduce total cost is established in to attain this goal using an appropriate mathematical model. While formulating and solving the relevant model, the necessary and sufficient conditions for a single globally optimal solution have been determined. Examples used as visualizations are given and confirmed by data.