Maximal Covering Location Problem: A Set Coverage Approach Using Dynamic Programming

The Maximal Covering Location Problem (MCLP) represents a fundamental optimization challenge in facility location theory, where the objective is to maximize demand coverage while operating under resource constraints. This paper presents a comprehensive analysis of MCLP using a set coverage methodology implemented through 0/1 knapsack dynamic programming. Our approach addresses the strategic placement of facilities to achieve optimal coverage of demand points within specified service distances. This research contributes to the understanding of facility location optimization by providing both theoretical foundations and practical algorithmic solutions for real-world applications in urban planning, emergency services, and supply chain management.