network location problem for two congestible facilities considering impatient customers

in this paper, we study the network location problem for two congestible facilities, considering impatient customers. we suppose that when a customer arrives his/her corresponding facility and faces a queue with the size more than a predetermined threshold, the customer decides not to join the queue but to go to the closest facility to current facility. in the second facility, if the queue size is also more than the threshold, the customer gives up the service. since the impatience is the case for many real world situations, its consideration helps to construct more realistic mathematical models. the aim of the proposed mathematical model is to select two locations among a prespecified number of candidate locations and then to assign all customers in the network in such a way that the number of the lost customers is minimized. based on a new kind of hypercube queue models, the queue systems of the servicing facilities is analyzed and modeled as a mathematical programming model. in order to evaluate the performance of the proposed model, a numerical example is presented and solved using gams software.