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Resource Allocation Based on Past Incident Patterns

M. N. M. van Lieshout

TL;DR

This paper tackles capacity planning for emergency response by minimizing the worst-case per-resource risk across spatial catchments. It combines adaptive kernel-based estimation of the incident intensity $\lambda$ to obtain $\Lambda(s)$ with minimax resource-allocation, solved via greedy algorithms for allocating vehicles and crews to stations, supported by a formal optimality framework. The approach is demonstrated on Twente Fire Brigade data, delivering explicit allocation rules and practical insights into how resources should be distributed by local risk. It provides a scalable, implementable framework that can be extended to heterogeneous resources and scheduling constraints in real-world settings.

Abstract

We formulate and solve two resource allocation problems motivated by a preparedness question of emergency response services. First, we consider the assignment of vehicles to stations, and, in a second step, assign crews to vehicles. In both cases, we work in a minimax framework and define the objective function for a spatial catchment area as the total risk in this area per resource unit allocated to it. The solutions are explicit and can be calculated in practice by a greedy algorithm that successively allocates a resource unit to an area having maximal relative risk, with suitable tie breaker rules. The approach is illustrated on a data set of incidents reported to the Twente Fire Brigade.

Resource Allocation Based on Past Incident Patterns

TL;DR

This paper tackles capacity planning for emergency response by minimizing the worst-case per-resource risk across spatial catchments. It combines adaptive kernel-based estimation of the incident intensity to obtain with minimax resource-allocation, solved via greedy algorithms for allocating vehicles and crews to stations, supported by a formal optimality framework. The approach is demonstrated on Twente Fire Brigade data, delivering explicit allocation rules and practical insights into how resources should be distributed by local risk. It provides a scalable, implementable framework that can be extended to heterogeneous resources and scheduling constraints in real-world settings.

Abstract

We formulate and solve two resource allocation problems motivated by a preparedness question of emergency response services. First, we consider the assignment of vehicles to stations, and, in a second step, assign crews to vehicles. In both cases, we work in a minimax framework and define the objective function for a spatial catchment area as the total risk in this area per resource unit allocated to it. The solutions are explicit and can be calculated in practice by a greedy algorithm that successively allocates a resource unit to an area having maximal relative risk, with suitable tie breaker rules. The approach is illustrated on a data set of incidents reported to the Twente Fire Brigade.
Paper Structure (7 sections, 2 theorems, 41 equations, 1 figure, 2 tables, 2 algorithms)

This paper contains 7 sections, 2 theorems, 41 equations, 1 figure, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Estimating the incident intensity function
  3. Resource allocation
  4. Allocation of vehicles
  5. Personnel allocation
  6. Capacity planning for fire services in Twente
  7. Discussion

Key Result

Theorem 4.1

Suppose that $K \geq |\mathcal{S}|$ and that $\Lambda(s) > 0$ for all $s\in \mathcal{S}$. Then, Algorithm A:pumper with $k=K$ returns a decision rule $n(s)$, $s\in \mathcal{S}$, that minimises the maximal average risk (e:vehicles) and that satisfies the constraints $1\leq n(s)$ for all $s$ and $\sum

Figures (1)

  • Figure 1: Left: Voronoi cells around $29$ fire stations in Twente coloured by risk. Right: mapped incidents that occurred in the year 2004.

Theorems & Definitions (3)

  • Theorem 4.1
  • Remark 5.1
  • Theorem 5.1