Equilibrium-based Workload Balancing for Robust Emergency Response Operation

Khaled Abdelghany (), Parya Roustaee (), Ahmed Hassan (), Aline Karak () and Mohammad Khodayar ()
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Khaled Abdelghany: Southern Methodist University
Parya Roustaee: Southern Methodist University
Ahmed Hassan: Cairo University
Aline Karak: Southern Methodist University
Mohammad Khodayar: Southern Methodist University

Networks and Spatial Economics, 2023, vol. 23, issue 3, No 8, 715-753

Abstract: 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.

Keywords: Community Operational Research; Emergency Response; Workload Balancing; Non-linear Mathematical Programming; Frank-Wolfe Decomposition Algorithm (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11067-023-09589-w

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