Coverage Optimization with Balanced Capacitated Fragmentation

Milos Seda () and Pavel Seda ()
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Milos Seda: Institute of Automation and Computer Science, Brno University of Technology, Technicka 2, 623 00 Brno, Czech Republic
Pavel Seda: Department of Telecommunications, Brno University of Technology, Technicka 12, 616 00 Brno, Czech Republic

Mathematics, 2025, vol. 13, issue 5, 1-24

Abstract: This paper investigates a specialized variant of the set covering problem, addressing the optimal allocation of service centers to ensure that all customers (or larger entities, such as urban areas) have access to specialized services within a predefined acceptable distance, referred to as the threshold. In addition to minimizing the number of service centers required or their total cost, this study emphasizes the critical importance of balancing capacity fragmentation—defined as the uneven distribution of service demand across facilities—to enhance accessibility and ensure equitable service delivery for customers. We propose an innovative mathematical model with additional practical constraints related to service deployment and designed to optimize both coverage and capacity fragmentation within a defined region. The model is validated through simulations implemented in GAMS, which document that this software tool is capable of solving even large problem instances in a reasonable amount of time. The results demonstrate the model’s effectiveness in addressing real-world challenges associated with equitable and efficient service allocation.

Keywords: set covering; threshold; reachability matrix; GAMS (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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