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arxiv: 2605.05421 · v1 · submitted 2026-05-06 · 🧮 math.OC

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Policies for the Operation of an Ambulance Fleet under Uncertainty based on a New Preparedness Metric

Vincent Guigues , Anton Kleywegt , Victor Hugo Nascimento
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Pith reviewed 2026-05-08 16:12 UTC · model grok-4.3

classification 🧮 math.OC
keywords ambulance fleet managementpreparedness metricoptimization under uncertaintyemergency medical servicesdispatch decisionsreassignment policiesdynamic resource allocation
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The pith

A new preparedness metric quantifies ambulance fleet readiness for unknown future emergencies and guides dispatch decisions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a preparedness metric that measures how well an emergency medical service can respond to future calls whose locations and timings are unknown at decision time. This metric is embedded in a tractable optimization problem solved each time an ambulance must be selected for a new call or reassigned after finishing service. The resulting policies are evaluated against nine methods from the literature using historical data from a real large-city emergency medical service. A sympathetic reader would care because the metric offers a concrete way to make current choices that preserve overall system capacity without requiring forecasts of exact future demand.

Core claim

We propose a new preparedness metric that quantifies the ability of the emergency medical service to respond to future emergencies. The preparedness metric can be used to make ambulance selection decisions and ambulance reassignment decisions by solving a tractable optimization problem each time that a decision has to be made. We compare the performance of the resulting method with 9 methods that have been proposed in the literature, based on data from a real emergency medical service for a large city.

What carries the argument

The preparedness metric, which evaluates the effect of current ambulance locations and assignments on the fleet's capacity to cover potential future emergency sites under uncertainty, and is maximized via repeated solution of a tractable optimization problem.

Load-bearing premise

The preparedness metric correctly captures how current decisions affect the ability to respond to unknown future emergencies, and optimizing it produces decisions superior in practice to the nine comparison methods.

What would settle it

If the optimization-based decisions do not produce statistically better response performance than the best of the nine benchmark methods when both are applied to the same historical large-city data set, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.05421 by Anton Kleywegt, Victor Hugo Nascimento, Vincent Guigues.

Figure 1
Figure 1. Figure 1: Simulated mean allocation costs for the policies, using great circle distances and view at source ↗
Figure 2
Figure 2. Figure 2: Simulated mean response times for the policies, using great circle distances and view at source ↗
Figure 3
Figure 3. Figure 3: Simulated mean allocation costs for the policies, using great circle distances and view at source ↗
Figure 4
Figure 4. Figure 4: Simulated mean response times for the policies, using great circle distances and view at source ↗
Figure 5
Figure 5. Figure 5: Simulated mean allocation costs for the policies, using rectangular discretization and view at source ↗
Figure 6
Figure 6. Figure 6: Simulated mean response times for the policies, using rectangular discretization and view at source ↗
Figure 7
Figure 7. Figure 7: Simulated mean allocation costs for the policies, using hexagonal discretization and view at source ↗
Figure 8
Figure 8. Figure 8: Simulated mean response times for the policies, using hexagonal discretization and view at source ↗
Figure 9
Figure 9. Figure 9: Simulated mean extra response times for each emergency type, relative to a target of view at source ↗
read the original abstract

Two important decisions in the management of an ambulance fleet are ambulance selection decisions and ambulance reassignment decisions. Ambulance selection decisions determine what to do when an emergency call arrives (such as choosing what ambulance to dispatch to the emergency or putting the emergency in a queue of emergencies waiting for an ambulance to be dispatched). Ambulance reassignment decisions determine where to send an ambulance next when it has finished service for an emergency. Making good ambulance selection decisions and ambulance reassignment decisions is challenging because a decision made at a point in time affects the ability of the emergency medical service to respond to future emergencies (that are typically not known when the decision is made). We propose a new preparedness metric that quantifies the ability of the emergency medical service to respond to future emergencies. The preparedness metric can be used to make ambulance selection decisions and ambulance reassignment decisions by solving a tractable optimization problem each time that a decision has to be made. We compare the performance of the resulting method with 9 methods that have been proposed in the literature, based on data from a real emergency medical service for a large city.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a new preparedness metric that quantifies an EMS fleet's ability to respond to unknown future emergencies. This metric is embedded in a tractable optimization problem solved at each decision epoch to guide ambulance selection (dispatch or queueing) and reassignment decisions. The resulting policy is benchmarked against nine existing methods from the literature using historical data from a real EMS serving a large city, with performance assessed via simulation.

Significance. If the preparedness metric demonstrably improves decisions by correctly capturing the downstream effects of current actions on future response capability, the work could advance dynamic resource allocation in emergency services. The comparison to nine baselines on real data is a positive step toward practical relevance, but the single-city, in-sample simulation design limits claims of general superiority.

major comments (2)
  1. [Evaluation] Evaluation section: the reported superiority rests on a simulation whose arrival, travel-time, and service distributions are fitted to the same historical dataset used for testing, without temporal hold-out periods, cross-validation, or perturbation of the underlying processes. This setup leaves open the possibility that gains arise from alignment with dataset-specific statistics rather than from a general property of the metric.
  2. [Introduction and Evaluation] The central claim that the metric 'quantifies the ability ... to respond to future emergencies' and yields superior decisions requires evidence that it is not circular or overfit; the current single-region evaluation does not provide a falsifiable test of robustness to data shifts or new regions.
minor comments (2)
  1. [Abstract] The abstract states that the method was compared on real data but provides no definition of the metric, no formulation of the optimization problem, and no performance numbers or statistical details; these should be summarized with key equations and tables even in the abstract for clarity.
  2. [Metric Definition] Notation for the preparedness metric and the optimization objective should be introduced with explicit definitions and assumptions about uncertainty modeling to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive and detailed feedback. The points raised regarding the evaluation design are important, and we address them point by point below while proposing targeted revisions to the manuscript.

read point-by-point responses

  1. Referee: [Evaluation] Evaluation section: the reported superiority rests on a simulation whose arrival, travel-time, and service distributions are fitted to the same historical dataset used for testing, without temporal hold-out periods, cross-validation, or perturbation of the underlying processes. This setup leaves open the possibility that gains arise from alignment with dataset-specific statistics rather than from a general property of the metric.

    Authors: We agree that the simulation uses distributions fitted to the full historical dataset without temporal hold-out or cross-validation, which represents a limitation for establishing robustness. This setup aligns with common practice in the EMS operations literature, where operational datasets are often limited in scale and duration. In the revised manuscript we will add a new subsection on sensitivity analysis that perturbs the fitted parameters (e.g., arrival rates and travel-time means varied by ±15–25 %) and reports how the relative performance of the preparedness metric changes. We will also insert an explicit limitations paragraph in the Evaluation section acknowledging the in-sample character of the tests. These changes directly respond to the concern by providing evidence that performance advantages are not solely an artifact of exact distributional alignment. revision: yes

  2. Referee: [Introduction and Evaluation] The central claim that the metric 'quantifies the ability ... to respond to future emergencies' and yields superior decisions requires evidence that it is not circular or overfit; the current single-region evaluation does not provide a falsifiable test of robustness to data shifts or new regions.

    Authors: The preparedness metric is constructed from an explicit probabilistic model of future emergency locations, times, and service requirements; it is not estimated from the realized calls used in the simulation, so the formulation itself is not circular. The optimization then uses this forward-looking metric to select actions. We nevertheless accept that the single-city, in-sample simulation does not constitute a strong falsification test against distributional shifts. In the revision we will qualify the central claims in the Introduction and Abstract to reflect the tested setting, and we will add a dedicated paragraph in the Discussion section on the desirability of multi-region validation. We cannot supply results from additional cities because we lack access to comparable operational datasets from other EMS providers. revision: partial

standing simulated objections not resolved
  • We do not have access to emergency medical service data from other cities or regions and therefore cannot perform direct validation on new regions or under data shifts.

Circularity Check

0 steps flagged

No significant circularity; metric and policies derived independently of evaluation data.

full rationale

The paper defines a new preparedness metric to quantify response capability under uncertainty and embeds it in a per-decision optimization problem for ambulance selection and reassignment. Performance is then assessed by comparing the resulting policies against nine literature baselines on historical data from one city via simulation. No equations or steps reduce the metric or its optimality claims to fitted parameters, self-referential definitions, or prior self-citations by construction. The derivation chain remains self-contained: the metric is proposed from first principles as a quantification tool, the optimization is tractable by design, and empirical superiority is tested externally rather than presupposed. This aligns with the default expectation that most papers exhibit no circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit equations or definitions, so no free parameters, axioms, or invented entities can be identified; the preparedness metric itself likely rests on modeling assumptions about future demand that are not detailed here.

pith-pipeline@v0.9.0 · 5493 in / 1129 out tokens · 33831 ms · 2026-05-08T16:12:31.426549+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

6 extracted references · 2 canonical work pages

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