Ambulance Deployment With Relocation Through Robust Optimization

Abstract

This paper investigates the deployment issue of an emergency medical service (EMS) system to maintain the preferred service coverages under different considerations. Specifically, two coverage levels are introduced to reflect the requirements under the regular situation and the situation with ambulance unavailable. We propose the two-stage robust optimization (RO) models to design a reliable ambulance system subject to unavailability of the ambulances, with and without the ambulance relocation. For the RO problem with mixed-integer recourse for relocation, we customize the column and constraint generation method with an approximation strategy to handle the computational challenge. Our numerical study: 1) demonstrates that our RO formulations have a strong modeling capacity on designing the EMS system; 2) shows that our approximation algorithm performs very well; and 3) provides a quantitative evaluation of, including, relocation operations on the system performance. Note to Practitioners —This paper presents the novel optimization models to help ambulance deployment. Due to ambulance unavailability and relocation operations, traditional optimization formulations might not be sufficient for modeling or might be hard for computation. In this paper, we provide an uncertainty set-based approach to capture ambulance unavailability and to build the robust optimization models (with relocation recourse decisions). Also, efficient algorithms are designed to support practical instances. Numerical results are very supportive to our new models and computational methods.