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Rescue Craft Allocation in Tidal Waters of the North and Baltic Sea

Tom Mucke, Alexander Renneke, Finn Seesemann, Felix Engelhardt

TL;DR

The paper addresses reducing average naval rescue response times in the North and Baltic Seas by optimally allocating rescue crafts to stations under tide-induced operability constraints. It develops a tide-aware RCAP model with a two-part solution (fleet-station assignment and incident-zone-tide dispatch rules), proves NP-hardness, and formulates an Integer Program, complemented by practical simplifications that aggregate tide states and cluster zones. A comprehensive computational study using DGzRS-like data demonstrates that tide- and zone-clustering simplifications yield substantial gains in scalability with little loss in solution quality, while a full tide-aware formulation (best-tidal) is often computationally prohibitive. The work provides actionable guidance for real-world SAR planning, and points to enhancements in robustness, workload balancing, routing, and seasonal reallocation as promising future paths.

Abstract

This paper aims to improve the average response time for naval accidents in the North and Baltic Sea. To do this we optimize the strategic distribution of the vessel fleet used by the Deutsche Gesellschaft zur Rettung Schiffbrüchiger (German Maritime Search and Rescue Service) (DGzRS) across several home stations. Based on these locations, in case of an incoming distress call the vessel with the lowest response time is dispatched. A particularity of the region considered is the fact that due to low tide, at predictable times some vessels and stations are not operational. In our work, we build a corresponding mathematical model for the allocation of rescue crafts to multiple stations. Thereafter, we show that the problem is NP-hard. Next, we provide an Integer Programming (IP) formulation. Finally, we propose several methods of simplifying the model and do a case study to compare their effectiveness. For this, we generate test instances based on real-world data.

Rescue Craft Allocation in Tidal Waters of the North and Baltic Sea

TL;DR

The paper addresses reducing average naval rescue response times in the North and Baltic Seas by optimally allocating rescue crafts to stations under tide-induced operability constraints. It develops a tide-aware RCAP model with a two-part solution (fleet-station assignment and incident-zone-tide dispatch rules), proves NP-hardness, and formulates an Integer Program, complemented by practical simplifications that aggregate tide states and cluster zones. A comprehensive computational study using DGzRS-like data demonstrates that tide- and zone-clustering simplifications yield substantial gains in scalability with little loss in solution quality, while a full tide-aware formulation (best-tidal) is often computationally prohibitive. The work provides actionable guidance for real-world SAR planning, and points to enhancements in robustness, workload balancing, routing, and seasonal reallocation as promising future paths.

Abstract

This paper aims to improve the average response time for naval accidents in the North and Baltic Sea. To do this we optimize the strategic distribution of the vessel fleet used by the Deutsche Gesellschaft zur Rettung Schiffbrüchiger (German Maritime Search and Rescue Service) (DGzRS) across several home stations. Based on these locations, in case of an incoming distress call the vessel with the lowest response time is dispatched. A particularity of the region considered is the fact that due to low tide, at predictable times some vessels and stations are not operational. In our work, we build a corresponding mathematical model for the allocation of rescue crafts to multiple stations. Thereafter, we show that the problem is NP-hard. Next, we provide an Integer Programming (IP) formulation. Finally, we propose several methods of simplifying the model and do a case study to compare their effectiveness. For this, we generate test instances based on real-world data.
Paper Structure (22 sections, 5 theorems, 11 equations, 6 figures, 1 table)

This paper contains 22 sections, 5 theorems, 11 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model
  4. Parameters
  5. Feasible Solutions
  6. Objective Function
  7. Complexity
  8. Integer Program for rcap
  9. Corrected water levels for Stations and Vessels
  10. Corrected water levels for Stations
  11. Computational Study
  12. Available data
  13. Data on vessel types, stations and incidence types
  14. Geographical data
  15. Generation of zones
  16. ...and 7 more sections

Key Result

Lemma 2

The frcap is in $\mathcal{NP}$.

Figures (6)

  • Figure 1: The red triangles show the positions of the $55$dgzrs-stations in the Northern and Baltic Sea.
  • Figure 2: Incident generation across North and Baltic Sea. Yellow dots represent zones generated (amount: $1000$). Red dots represent clusters of zones (amount: $10$).
  • Figure 3: Locations of the gauges used to determine the water levels
  • Figure 4: Time required to build the Gurobi Models and cluster the zones.
  • Figure 5: Memory usage of the complete instances with $1000$ zones and the complete tidal information. The $x$-axis is $\log$ scaled for better readability.
  • ...and 1 more figures

Theorems & Definitions (11)

  • Definition 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 4
  • proof
  • Corollary 5
  • proof
  • Corollary 6
  • ...and 1 more