  We proposed a mathematical model for designing the layout diagram of stand
locations at the Macao Food Festival. The optimal layout diagram may be defined
in such a way that, while requiring the distance between every pair of stands
should not be too far away from each other, the crowd control is well managed
so that people may patronize stands more effectively. More popular stands may
have larger patronage, resulting in higher pedestrian flow nearby. Therefore,
to avoid customers from packing shoulder to shoulder around more popular
stands, we may treat every stand as a charged particle carrying an effective
charge: the more popular a stand is, the higher the effective charge it
carries. Under this assumption, the problem is then converted to the
minimization problem of Coulomb electrostatic potential energy on a specific
configuration of charge locations, with which the global minimum may be found
by the Simulated Annealing and Metropolis Algorithm. Electrostatic energy
density is interpreted as density of customers, while electric field the
reversed crowd flow. Therefore, at a certain location we are able to predict
the customer density by calculating the energy density and the net crowd flow
with electric field lines. We also concluded that even though the required
computation time to obtain a configuration of stand locations with the energy
value close to the global minimum with a tolerable difference may be irrelevant
to the randomly generated initial configuration of stand locations, setting up
an appropriate initial configuration could be one of the key issues to find out
the actual global minimum.
