In this paper, the evacuation process is modeled as a Dynamic Traffic Assignment (DTA) problem with the objective of achieving fair evacuation outcomes. To address the nonconvex nature of the resulting Mixed-Integer Linear Programming (MILP) formulation, an iterative algorithm is proposed to determine the Min-Max Fair (MMF) evacuation times among evacuees. For benchmarking purposes, the proposed algorithm is also applied to a convex Linear Programming (LP) version of the model obtained by fixing the binary decision variables. The proposed framework seeks to bridge the gap between traditional static traffic assignment approaches and more realistic dynamic traffic assignment models by explicitly incorporating temporal traffic dynamics and fairness considerations. The model and solution methodology are first demonstrated on a small illustrative network and subsequently evaluated on a benchmark evacuation network commonly used in the literature. To assess the effectiveness of the proposed approach, several alternative objectives are considered for comparison, including Network Clearance Time (NCT), Average Evacuation Time (AET), Average Evacuation Time subject to Network Clearance Time ( ), and Average Evacuation Time under Equal Demand assumptions ( ). Fairness is quantified using the Sum of Absolute Deviations (SAD) of evacuees’ evacuation times, enabling a direct comparison between efficiency-oriented and fairness-oriented evacuation strategies.

Keywords

Evacuation planning, disaster management, fairness, mixed integer linear programming.