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We proposed a mathematical model for designing the layout diagram of standlocations at the Macao Food Festival. The optimal layout diagram may be definedin such a way that, while requiring the distance between every pair of standsshould not be too far away from each other, the crowd control is well managedso that people may patronize stands more effectively. More popular stands mayhave larger patronage, resulting in higher pedestrian flow nearby. Therefore,to avoid customers from packing shoulder to shoulder around more popularstands, we may treat every stand as a charged particle carrying an effectivecharge: the more popular a stand is, the higher the effective charge itcarries. Under this assumption, the problem is then converted to theminimization problem of Coulomb electrostatic potential energy on a specificconfiguration of charge locations, with which the global minimum may be foundby the Simulated Annealing and Metropolis Algorithm. Electrostatic energydensity is interpreted as density of customers, while electric field thereversed crowd flow. Therefore, at a certain location we are able to predictthe customer density by calculating the energy density and the net crowd flowwith electric field lines. We also concluded that even though the requiredcomputation time to obtain a configuration of stand locations with the energyvalue close to the global minimum with a tolerable difference may be irrelevantto the randomly generated initial configuration of stand locations, setting upan appropriate initial configuration could be one of the key issues to find outthe actual global minimum.

Optimal Layout Plan of Stands at the Macao Food Festival via Minimizing  the Electrostatic Potential Energy with the Effective Charge as Popularity of  Stands