Technical Summary: Optimal Resource Allocation for Multiple Wildfires Considering Critical Infrastructure Interdependencies

Problem Definition

The paper addresses the complex challenge of allocating and scheduling firefighting resources during multiple simultaneous wildfire incidents. Unlike traditional single-fire scenarios, this problem involves distributing limited, heterogeneous resources (aerial, machinery, and ground personnel) across several active fires that may have different propagation speeds, directions, and behaviors.

A critical aspect of the problem is the interdependency of Critical Infrastructure (CI). Wildfires do not only threaten natural landscapes but also disrupt essential systems such as electrical grids, water distribution, transportation, telecommunications, and healthcare. The disruption of one infrastructure often cascades to others, amplifying the total socioeconomic impact. The objective is to determine an optimal resource deployment strategy that minimizes the total system cost, defined as the sum of:

1. Operational costs: Expenses related to deploying and using firefighting resources.
2. Damage costs: Costs associated with infrastructure repair and service disruptions, which are dynamically influenced by the interdependencies between systems.

The problem is further complicated by dynamic constraints, including:

• Resource constraints: Limited availability, travel times between bases and fire sites, and maximum working periods (influenced by rest and training levels).
• Fire dynamics: Fires may merge over time, altering perimeter sizes and containment requirements.
• Temporal constraints: Decisions must be made online as the fire evolves, with a planning horizon typically covering a 6-hour window (36 time steps of 10 minutes each).

Methodology

The authors propose an online optimization framework that integrates a Mixed-Integer Linear Programming (MILP) model with a simulation tool called i2SIM (Infrastructure Interdependencies Simulator).

1. The i2SIM Simulator

To quantify the financial impact of wildfires on interconnected infrastructure, the study utilizes i2SIM. This tool models the flow of resources between systems using Human Readable Tables (HRTs).

• Mechanism: HRTs define the input-output relationships for each infrastructure (e.g., a hospital's patient capacity depends on electricity, water, staff, and physical integrity).
• Logic: At each time step, the operating level of an infrastructure is determined by its most limiting input (the "bottleneck"). If a wildfire damages a power plant, the resulting power outage reduces the hospital's capacity, which in turn increases service disruption costs.
• Scope: The framework models six key infrastructures: electrical networks, gas pumps, transportation routes, water distribution, telecommunication towers, and healthcare.

2. The MILP Optimization Model

The core decision-making engine is a MILP model designed to minimize the total cost over the planning horizon.

• Objective Function: Minimize the sum of Net Value Change (NVC) costs (damage and service disruption) and resource operational costs.
• Decision Variables: The model determines the location and status of each resource $i$ at each time step $t$, including:
  • Whether a resource is at a specific fire location or base.
  • Whether a resource is moving between locations.
  • Whether a resource is actively containing a fire.
• Constraints:
  • Fire Dynamics: Models the remaining perimeter of fires, accounting for natural spread rates and the reduction in perimeter due to containment efforts.
  • Resource Flow: Ensures resources move realistically based on travel times ($\tau$) and cannot be at two locations simultaneously.
  • Operational Limits: Enforces maximum working periods ($WP_i$) for ground crews based on rest-efficiency and training multipliers.
  • Fire Merging: The model dynamically handles scenarios where separate fires merge into a single larger fire, recalculating perimeters and resource requirements.
• Time Step: The model operates on a discrete-time framework with a 10-minute time step.

3. Experimental Setup

The framework was tested using:

• Base Case: A single specific scenario modeled after the 2024 Jasper City wildfires, involving three fires that progressively merge.
• Large-Scale Simulations: 50 distinct scenarios with varying fire perimeters, spread rates, and spatial configurations.
• Benchmark: A priority-based heuristic was used for comparison. This heuristic assigns all available resources to the single fire with the highest immediate damage cost, ignoring trade-offs and future dynamics.
• Solver: Gurobi Optimizer (v13.0.0) with a 600-second time limit per run.

Key Contributions

1. Integrated Framework: The paper introduces a novel coupling of a fire containment MILP with the i2SIM simulator. This allows for a socioeconomic cost analysis that explicitly accounts for the cascading failures of critical infrastructure, moving beyond simple "area burned" metrics.
2. Dynamic Resource Scheduling: The model handles online decision-making where fire conditions (merging, spreading) and resource constraints (travel time, fatigue) evolve in real-time.
3. Handling Fire Merging: The formulation explicitly addresses the non-linear dynamics of fire merging, where the combined perimeter is less than the sum of individual perimeters, requiring adaptive re-optimization.
4. Operational Realism: The model incorporates realistic human factors, such as rest-efficiency and training levels, to calculate effective working periods for ground crews.

Results

• Cost Reduction: The proposed optimization framework significantly outperformed the priority-based heuristic. Across the 50 large-scale wildfire scenarios, the optimization model reduced total costs by 6.6% to 45.1%.
• Diminishing Returns: The study found that adding more resources does not linearly reduce losses. The marginal benefit of additional resources decreases as availability increases.
• Resource Sensitivity:
  • Aerial Resources: Increasing the availability of aerial resources (particularly helicopters) yielded the most significant reduction in damage costs due to their high containment efficiency and rapid deployment.
  • Travel Time: Early deployment of high-capacity resources is critical. Delays in arrival times significantly increased total costs, highlighting the importance of accessibility.
• Computational Efficiency: The MILP approach proved computationally feasible. Only 2.78% of instances reached the 600-second time limit without proving optimality, and even in those cases, the MIP-Gap was minimal (0.02%), indicating high-quality near-optimal solutions were found quickly.

Significance and Claims

The paper claims that its primary significance lies in providing a computationally feasible, online decision-support tool for emergency managers facing multiple simultaneous wildfires. By integrating infrastructure interdependencies, the framework offers a more accurate representation of the true cost of wildfires, enabling strategies that minimize not just the fire's physical spread, but the broader societal and economic disruption.

The authors emphasize that while traditional methods often rely on static or single-fire assumptions, their approach captures the dynamic, interdependent nature of modern wildfire emergencies. The findings suggest that strategic prioritization—specifically the early deployment of aerial assets and the dynamic re-allocation of resources as fires merge—is essential for effective emergency management. The paper concludes that predictive simulation combined with optimization is a vital advancement for planning dynamic wildfire containment under changing conditions.