Integrated Optimization and Simulation Framework for Large-Scale Crowd Management Application

This paper introduces an integrated optimization–simulation framework for the formation, scheduling, and path assignment of groups at large-scale, organized events. The framework consists of network analysis, optimization, and simulation components. The first component finds sets of shortest paths for each origin in the network. The optimization component determines the group size, the departure time, and the path under capacity constraints. The objective is minimization of the travel time and matching of the preferred arrival time distribution of different demand units. The simulation component simulates each person in the network according to that person’s path and departure time determined by the previous components. The network performance characteristics supplied by the simulation inform the network analysis and optimization components for the next iteration. The framework is applied to the Jamarat process during the Hajj season in the Kingdom of Saudi Arabia to provide a schedule for 1.5 million people in a given day. The convergence of travel times, demand satisfaction, and level of service is achieved after several iterations.