[Paper Review] Algorithm for Resource Redistribution Required for Recovery of Society after Large Scale Disasters

Vasily Lubashevskiy, Taro Kanno+1 more|arXiv (Cornell University)|Oct 2, 2013

Ecosystem dynamics and resilience3 citations

TL;DR

This paper proposes a decentralized, cooperative algorithm for semi-optimal resource redistribution to accelerate short-term recovery after large-scale disasters. By prioritizing cities based on resource deficit and population, and modeling dynamic supply constraints via temporal capacity limits, the algorithm reduces recovery time—especially through cooperative effects that scale efficiently with damage extent.

ABSTRACT

The recovery of society after a large scale disaster generally consists of two phases, short- and long-term recoveries. The problem of short-term recovery is rather close to the problem of resilience in their goal, namely, bouncing the damaged system back to the operating standards. The present paper proposes an algorithm for the vital resource redistribution required for implementation of the short-term recovery. The developed model is based on the cooperative interaction of cities during the resource redistribution, ordering the cities according to their priority in resource delivery, and a generating a semi-optimal plan for the desired redistribution. Nonlinear effects caused by the city limit capacities are taken into account. Two types of systems, "uniform" and "centralized", are studied numerically. In particular it is demonstrated that the cooperation effects are able to shorten substantially the duration of the process required for its implementation.

Motivation & Objective

• Address the urgent need for rapid short-term recovery of vital life-support systems after large-scale disasters.
• Overcome limitations of pre-planned, centralized logistics by enabling real-time, adaptive resource redistribution.
• Model the dynamic nature of supply networks where cities temporarily become unavailable after sending resource quanta.
• Investigate how cooperation among cities and capacity constraints affect recovery duration and efficiency.
• Develop a semi-optimal algorithm that balances decentralization with centralized coordination for timely response.

Proposed method

• Prioritize cities for resource delivery using the metric $ S_i = \theta_i N_i $, where $ \theta_i = \frac{Q_i - Q_{ci}}{Q_{ci}} $, to reflect relative deficit and population impact.
• Model resource delivery as a stepwise process: prepare quantum → send → wait for next preparation, introducing temporal exclusion.
• Simulate dynamic network effects by applying temporal renormalization of inter-city distances to reflect finite preparation times.
• Use two system configurations: 'uniform' (many small cities) and 'centralized' (four large hubs) for comparative analysis.
• Incorporate city-specific limit capacities to model nonlinear supply dynamics and prevent overloading.
• Conduct numerical simulations to evaluate recovery duration, regional involvement, and system resilience under varying damage and capacity levels.

Experimental results

Research questions

• RQ1 How does decentralized, cooperative resource redistribution compare to centralized models in reducing recovery time after large-scale disasters?
• RQ2 To what extent do cooperative effects reduce recovery duration as the number of affected cities increases?
• RQ3 How do finite city preparation capacities influence the dynamics and efficiency of resource redistribution?
• RQ4 What is the optimal size of administrative units for effective disaster recovery, based on recovery duration and regional involvement?
• RQ5 How does the failure of a central hub affect recovery time in a centralized supply model compared to a distributed one?

Key findings

• Cooperative resource redistribution significantly shortens recovery time, especially as damage spreads across more cities, due to increased participation.
• In the 'uniform' system, recovery duration increases only weakly with higher damage levels, indicating strong cooperative scaling effects.
• The 'centralized' system exhibits longer recovery times and is highly vulnerable—failure of one hub causes a drastic increase in recovery duration.
• When both central hubs and satellites are damaged, recovery completion times become nearly synchronized across cities, indicating system-wide resilience.
• Recovery duration saturates with increasing numbers of participating cities, suggesting a practical upper limit for optimal administrative unit size.
• The algorithm produces a semi-optimal plan that balances decentralization for speed with centralized coordination for information and planning.