Hybrid Optimization with Integer Constraints: Modeling and Solving Problems Using Simplex Techniques

Abstract

This paper presents a hybrid optimization framework for solving linear integer programming (LIP) problems using Simplex-based techniques. Building on the classical Simplex method and integrating it with branch-and-bound, cutting-plane, and heuristic approaches, the proposed methodology addresses the complexity of integer-constrained decision-making in areas such as scheduling, logistics, and resource allocation. A brief historical overview of the Simplex method and its evolution into LIP solutions is provided, along with theoretical insights into feasibility, constraint preservation, and solution structure. The effectiveness of the hybrid approach is demonstrated through a real-world application at Innoson Vehicle Manufacturing, showcasing how the integrated method improves solution accuracy and computational efficiency in practical settings. This study contributes to the broader field of optimization by offering a unified, adaptable approach for modeling and solving complex integer programming problems.