An Integer Programming Model for the Dynamic Location and Relocation of Emergency Vehicles: A Case Study

In this paper, we address the dynamic Emergency Medical Service (EMS) systems. A dynamic location model is presented that tries to locate and relocate the ambulances. The proposed model controls the movements and locations of ambulances in order to provide a better coverage of the demand points under different fluctuation patterns that may happen during a given period of time. Some numerical experiments have been carried out by using some real-world data sets that have been collected through the French EMS system.

💡 Research Summary

This paper addresses the problem of dynamically locating and relocating emergency medical service (EMS) vehicles in order to improve response times and coverage under fluctuating demand. Building on the well‑known dynamic relocation problem (t‑RP) introduced by Gendreau et al., the authors propose an extended integer programming model called t‑DRP (dynamic relocation problem with demand weighting). The key innovation is the introduction of two demand‑intensity parameters for each demand point i: 1ᵢᵈ, representing the average occurrence rate of ordinary (single) calls, and 2ᵢᵈ, representing the average occurrence rate of simultaneous (multiple) calls. These parameters are estimated from historical EMS call logs and allow the model to differentiate between locations where multiple emergencies are likely to occur at the same time and those where calls are typically isolated.

The decision variables are: yⱼₖ ∈ {0,1} indicating whether ambulance k is stationed at service centre j; x₁ᵢ and x₂ᵢ ∈ {0,1} indicating whether demand point i is covered within the short response time 1 r and the longer response time 2 r, respectively; and λᵢ ∈ {0,1,2} denoting how many times point i is covered. The objective function simultaneously maximizes weighted coverage and minimizes relocation costs:

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