Max-Min Fair Restoration of Infrastructure Networks

Hamoud Sultan Bin Obaid (), Yasser Adel Almoghathawi and Mohammed Algafri
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Hamoud Sultan Bin Obaid: Department of Industrial Engineering, King Saud University, Riyadh 11421, Saudi Arabia
Yasser Adel Almoghathawi: Department of Industrial and Systems Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Mohammed Algafri: Department of Industrial and Systems Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

Mathematics, 2025, vol. 13, issue 19, 1-21

Abstract: Connectivity is one of the essential needs in today’s standards in many aspects of life, starting with personal relationships, education, and remote work and ending with the security and economy of countries. However, connectivity is susceptible to intentional and unintentional disruptions, leading to great impact on critical infrastructures. Hence, maintaining connectivity is a crucial task to sustain the continuous flow of life. The challenge is to find an optimal recovery plan to reconnect all demands as soon as possible after the disruptive event, ensuring fairness in the process of reallocating the remaining resources. In this paper, we present a post-disruption recovery framework for networked systems to optimize the recovery plan to reconnect the network demands as soon as possible. More specifically, we introduce an algorithmic approach using a mathematical programming model that optimally recovers the disrupted arcs of the network while ensuring the highest connectivity. The proposed approach considers both fairness and efficiency through finding the MMF (max-min fairness) resource allocation throughout the recovery process. The proposed approach is tested on a variety of benchmark networks under a set of disruption levels; then, the results are compared with the maximum-flow model.

Keywords: max-min fairness; the direct progressive-filling algorithm; load balancing; goal programming; fairness in resource allocation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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