Fuzzy Hierarchical Queueing Models for the Location Set Covering Problem in Congested Systems

In hierarchical service networks, facilities at dierent levels provide dierent types of service. For
example, in health care systems, general centers provide low-level services, such as primary health
care, while specialized hospitals provide high-level services. Because of the demand congestion
at service networks, the location of servers and their allocation of demand nodes can have
a strong impact on the length of the queue at each server, as well as on the response time to
service calls. This study attempts to develop hierarchical location-allocation models for congested
systems by employing a queueing theory in a fuzzy framework. The parameters of each model
are approximately evaluated and stated as fuzzy-numbers. The coverage of demand nodes is
also considered in an approximate manner and is stated by the degree of membership. Using
queueing theory and fuzzy conditions, both referral and nested hierarchical models are developed
for the Location Set Covering Problem (LSCP). To demonstrate the performance of the proposed
models, a numerical example is solved in order to compare the results obtained from the existing
probabilistic models and the new fuzzy models developed in this paper.