Fuzzy queuing location-allocation models for congested systems

Since in the emergency service networks the length of time to attend to call is of utmost importance, it is imperative to observe guidelines in locating the service centers within a service network and allocating the demand nodes to them in a manner that service can be provided within a reasonably short period of time. So far both qualitative and quantitative models have been developed to tackle these problems. The latest models, which assume a probabilistic orientation, use queuing theory notions to achieve a more suitable solution. This article attempts to apply both queuing theory and fuzzy theory to the location-allocation problem in hope of analyzing the problem in a more realistic environment. The models developed, consider fuzzified constraints, fuzzified objective functions and fuzzified sets of nodes covered by each service center. As such, each demand node is not served by just one server. In fact, each node can call for service from several servers according to its degree of membership. The developed fuzzy models are then transformed to mixed integer programming models which can be solved by the exact methods. An example problem is solved and presented along with results.