  To handle the detrimental effects brought by leakage of radioactive gases at
nuclear power station, we propose a bus based evacuation optimization problem.
The proposed model incorporates the following four constraints, 1) the maximum
dose of radiation per evacuee, 2) the limitation of bus capacity, 3) the number
of evacuees at demand node (bus pickup stop), 4) evacuees balance at demand and
shelter nodes, which is formulated as a mixed integer nonlinear programming
(MINLP) problem. Then, to eliminate the difficulties of choosing a proper M
value in Big-M method, a Big-M free method is employed to linearize the
nonlinear terms of the MINLP problem. Finally, the resultant mixed integer
linear program (MILP) problem is solvable with efficient commercial solvers
such as CPLEX or Gurobi, which guarantees the optimal evacuation plan obtained.
To evaluate the effectiveness of proposed evacuation model, we test our model
on two different scenarios (a random one and a practical scenario). For both
scenarios, our model attains executable evacuation plan within given 3600
seconds computation time.
