Abstract: This paper proposes a bi-objective model for the
facility location problem under a congestion system. The idea of the
model is motivated by applications of locating servers in bank
automated teller machines (ATMS), communication networks, and so
on. This model can be specifically considered for situations in which
fixed service facilities are congested by stochastic demand within
queueing framework. We formulate this model with two perspectives
simultaneously: (i) customers and (ii) service provider. The
objectives of the model are to minimize (i) the total expected
travelling and waiting time and (ii) the average facility idle-time.
This model represents a mixed-integer nonlinear programming
problem which belongs to the class of NP-hard problems. In addition,
to solve the model, two metaheuristic algorithms including nondominated
sorting genetic algorithms (NSGA-II) and non-dominated
ranking genetic algorithms (NRGA) are proposed. Besides, to
evaluate the performance of the two algorithms some numerical
examples are produced and analyzed with some metrics to determine
which algorithm works better.