Abstract: This paper provides a framework in order to
incorporate reliability issue as a sign of disruption in distribution
systems and partial covering theory as a response to limitation in
coverage radios and economical preferences, simultaneously into the
traditional literatures of capacitated facility location problems. As a
result we develop a bi-objective model based on the discrete
scenarios for expected cost minimization and demands coverage
maximization through a three echelon supply chain network by
facilitating multi-capacity levels for provider side layers and
imposing gradual coverage function for distribution centers (DCs).
Additionally, in spite of objectives aggregation for solving the model
through LINGO software, a branch of LP-Metric method called Min-
Max approach is proposed and different aspects of corresponds
model will be explored.