Resource Allocation Problem in Emergency Rescue Decision-Making

Resource Allocation Problem in Emergency Rescue Decision-Making

Problem Description
Assume you are a decision-maker at an emergency command center. Two disasters occur simultaneously in a region: At location A, a bus has overturned with 20 passengers trapped. The rescue difficulty is estimated to be moderate, requiring 4 rescue units (e.g., ambulances, firefighting teams) to complete the rescue within 1 hour. At location B, an old residential building is on fire with 10 people trapped. The fire is spreading rapidly, and the rescue difficulty is estimated to be high, requiring 6 rescue units to control the fire and rescue people within 40 minutes. However, only 8 rescue units are immediately available for dispatch. As the decision-maker, how would you allocate these 8 units? Please explain your decision logic and trade-off process.

Step-by-Step Explanation of the Problem-Solving Process

Step 1: Clarify the Core Problem — Resource Constraints and Conflicting Objectives

  1. Identify Constraints:
    • Limited total resources: Only 8 rescue units available.
    • Conflicting task demands:
      • Location A needs 4 units (to complete rescue in 1 hour);
      • Location B needs 6 units (to control fire in 40 minutes).
    • Insufficient resources may lead to extended rescue time or reduced success rates.
  2. Define Decision Objectives:
    • The core is to maximize total survival probability or minimize total loss, rather than simply pursuing "fairness."
    • Judgment must be based on a comprehensive assessment of time urgency, rescue success rates, and potential risks.

Step 2: Analyze Key Variables — Quantifying the Relationship Between Time and Success Rate

  1. Time Sensitivity Analysis:
    • The fire at location B shows clear time urgency: Fire spread may lead to structural collapse or suffocation risks, making delayed rescue consequences more severe.
    • While the accident at location A carries no immediate explosion risk, victims may deteriorate due to blood loss or worsening injuries over time.
  2. Resource-Efficiency Function (Simplified Model):
    • Assume a nonlinear relationship between rescue success rate, resource input, and time:
      • With insufficient resources, rescue time extends and success rate declines;
      • For example: If location B receives only 4 units, it may take 80 minutes to control the fire, significantly reducing the survival probability of trapped individuals.

Step 3: Develop Allocation Plans and Assess Consequences
Plan 1: Prioritize meeting the needs at location B (6 units) + Allocate the remainder to location A (2 units)

  • Location B: Receives 6 units, can control the fire within 40 minutes, resulting in a relatively high survival probability for the 10 individuals.
  • Location A: Receives only 2 units, falling short of the 4-unit requirement. Rescue time may extend to 2 hours, potentially worsening the condition of some casualties due to delay.
  • Potential total loss: Risk at location B is manageable, but location A may suffer additional casualties due to resource shortage.

Plan 2: Equal allocation (4 units each)

  • Location B: 4 units are insufficient, extending fire control time to over 60 minutes and reducing the survival probability of trapped individuals.
  • Location A: 4 units meet the requirement, enabling rescue completion within 1 hour.
  • Potential total loss: Delay at location B may cause greater casualties. While location A achieves optimal results, overall risk may be higher.

Plan 3: Dynamic adjustment (e.g., initially concentrate resources on location B, then support location A)

  • Phase 1: Dispatch 6 units to location B. After controlling the fire in 40 minutes, some units can be transferred to support location A.
  • Phase 2: Location A initially receives only 2 units for basic rescue efforts, receiving reinforcements after 40 minutes.
  • Advantage: May reduce immediate risk at location B, but transfer time must be considered (e.g., 20 minutes for units to move from B to A).

Step 4: Introduce Decision Principles — Trade-off Between Ethics and Efficiency

  1. Utilitarian Principle:
    • Choose the plan that saves the most lives. Considering 20 people at location A vs. 10 at location B, prioritizing location A might save more. However, this should be adjusted to "weighted survival probability" (e.g., individuals at location B face higher immediate risk, giving them greater weight).
  2. Risk Minimization Principle:
    • Compare the expected number of deaths under different plans. For example:
      • Plan 1: Expected deaths at location B ≈ 0, at location A ≈ 2 due to delay → Total expected loss: 2 people;
      • Plan 2: Expected deaths at location B ≈ 3, at location A ≈ 0 → Total expected loss: 3 people;
      • Plan 1 is preferable (requires estimation based on real data).
  3. Emergency Management Conventions:
    • Prioritize events that "may cause cascading effects" (e.g., fire spreading to endanger surrounding buildings) or tasks with "extremely narrow time windows" (e.g., the golden hour for rescue).

Step 5: Comprehensive Decision and Implementation Details

  • Recommended Plans: Plan 1 (prioritize location B) or Plan 3 (dynamic adjustment), due to the higher irreversible risk of fire.
  • Supplementary Measures:
    1. Immediately request additional resources from neighboring regions;
    2. Use the 2 units at location A for basic stabilization (e.g.,止血, stabilizing the vehicle) while awaiting support;
    3. Utilize real-time data to monitor risk changes and adjust allocation flexibly.

Core Logic Summary:
In emergency resource allocation, "time urgency" and "resource utility thresholds" should be key metrics. Decisions should involve dynamic trade-offs through quantified risk assessment, rather than mechanically pursuing superficial fairness.