  Logistics network is expected that opened facilities work continuously for a
long time horizon without any failure, but in real world problems, facilities
may face disruptions. This paper studies a reliable joint inventory location
problem to optimize the cost of facility locations, customers assignment, and
inventory management decisions when facilities face failure risks and do not
work. In our model we assume when a facility is out of work, its customers may
be reassigned to other operational facilities otherwise they must endure high
penalty costs associated with losing service. For defining the model closer to
real world problems, the model is proposed based on pmedian problem and the
facilities are considered to have limited capacities. We define a new binary
variable for showing that customers are not assigned to any facilities. Our
problem involves a biobjective model, the first one minimizes the sum of
facility construction costs and expected inventory holding costs, the second
one function that mentions for the first one is minimized maximum expected
customer costs under normal and failure scenarios. For solving this model we
use NSGAII and MOSS algorithms have been applied to find the Pareto archive
solution. Also, Response Surface Methodology (RSM) is applied for optimizing
the NSGAII Algorithm Parameters. We compare the performance of two algorithms
with three metrics and the results show NSGAII is more suitable for our model.
