Implemented Two-Stage Heuristic Algorithm for Solving LRP Problem

This article presents an implemented two-stage heuristic algorithm designed to solve the Location-Routing Problem (LRP), which integrates the Clarke-Wright savings algorithm as a nested component. The LRP is commonly applied in route planning and logistics optimization scenarios. Our methodology enhances decision-making processes in these domains by implementing a sequential approach: the first stage handles facility location selection using combinatorial optimization techniques, while the second stage employs the embedded savings algorithm for vehicle routing optimization with route merging operations based on cost-saving calculations. The algorithm architecture emphasizes computational efficiency and solution quality through strategic problem decomposition. Key implementation features include distance matrix preprocessing, neighbor search mechanisms for facility allocation, and iterative route improvement procedures using savings value sorting. This approach maintains computational tractability while addressing complex constraints typical in supply chain applications. We demonstrate that this methodology provides practitioners in transportation, logistics, and traffic planning sectors with a robust tool for obtaining near-optimal LRP solutions. The algorithm's modular design allows for customization with domain-specific constraints, making it adaptable to various industrial applications requiring coordinated location and routing decisions.