Fuzzy Hierarchical Location-Allocation Models for Congested Systems

There exist various service systems that have hierarchical structure. In hierarchical service networks, facilities at different levels provide different types of services. For example, in health care systems, general centers provide low-level services such as primary health care services, while the specialized hospitals provide high-level services. Because of demand congestion in service networks, location of servers and allocation of demand nodes have a strong impact on the length of queues at servers as well as on the response times to service calls. The thrust of this article is the development of hierarchical location-allocation models for congested systems by employing queueing theory in a fuzzy framework. The new models allow partial coverage of demand nodes and approximate determination of parameters. Using queueing theory and fuzzy conditions, both referral and nested hierarchical models are developed for the maximal covering location problem (MCLP). An example is solved for both an existing probabilistic model and the new fuzzy models and the results are compared.