Abstract
This paper presents an equilibrium-based modeling framework for emergency response (ER) workload balancing for robust operations in metropolitan areas. The problem is formulated as a non-linear mathematical program (NLP), which determines the optimal maximum workload for each ER station such that the weighted sum of the area-wide expected response time and its variation is minimized. The concept of Marginal Cost of Uncertainty (MCU) is introduced to measure the impact of a station's workload increase on the robustness of the area-wide service performance. The solution of the NLP is proved to be equivalent to a state of equilibrium in which all stations have a minimum MCU. An iterative solution methodology is developed, which adopts a modified version of the Frank-Wolfe decomposition algorithm for convex optimization. The workload is iteratively balanced among adjacent stations until the state of equilibrium is achieved. At equilibrium, no station can reduce its MCU value by unilaterally shifting a part of its workload to any other station(s) in the area. The developed framework is applied to determine the optimal workload balancing strategy for 58 fire stations serving the City of Dallas. The framework is shown to enhance the robustness of the ER service performance especially in situations with imbalanced workloads.
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Data Availability
The data that support the findings of this study are available from Dallas Fire Rescue Department (DFRD) but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of DFRD.
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Acknowledgements
The authors would like to acknowledge Chief Daniel Salazar, Chief Jeff Wallis and Chief James Thornton with the Dallas Fire Rescue Department for their valuable feedback and for providing the data used in this research.
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This research is supported by the National Institute of Standards and Technology (NIST), US Department of Commerce under Award No. 60NANB17D180.
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Abdelghany, K., Roustaee, P., Hassan, A. et al. Equilibrium-based Workload Balancing for Robust Emergency Response Operation. Netw Spat Econ 23, 715–753 (2023). https://doi.org/10.1007/s11067-023-09589-w
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DOI: https://doi.org/10.1007/s11067-023-09589-w