An Approach for Solving Unconstrained and Constrained Neutrosophic Geometric Integer Programming Problems

Neutrosophic logic, introduced by Smarandache, offers a powerful framework for modeling uncertainty and inconsistency in real-world problems. This paper presents a novel approach for solving both unconstrained and constrained Neutrosophic Geometric Programming (NGP) problems with integer decision variables under a three-level framework of truth, indeterminacy, and falsity. By representing uncertain coefficients as triangular neutrosophic numbers, the proposed method translates the NGP model into a crisp equivalent using score and accuracy functions. Standard optimization techniques, including duality and normality conditions, are applied to derive optimal integer solutions. The approach addresses limitations in fuzzy and intuitionistic fuzzy systems by incorporating indeterminacy, thus providing a more robust solution framework. This method increases the degree of truth and minimizes indeterminacy and falsity, making it a viable tool for solving uncertainty problems within a neutrosophic environment. To validate the methodology's effectiveness and demonstrate the NGP's potential, numerical examples and a real-world case application were solved, showing its use in operations research, such as the Gravel Box Design Problem, and engineering optimization, such as supply chain management and truss structure design.