Simulation of a multi-layered facility location model by cosidering queueing theory

In multi-layered facility location models, customers receive different services at different layers. When the customer enters the system, he must receive all services at different layers; in fact, the customer will not leave the system in the middle layers. In this study, we are seeking to provide a facility location model with multiple service layers respect to the density of the system. The proposed model is a nonlinear integer programming model and it is in the field of highly complex problems. In order to solve the mathematical model, discrete event simulation approach has been used to increase efficiency. Interactions and complexities of the system, makes it difficult or impossible to predict the performance. Simulation models are able to show variability, interactions and complexities of the system. In this regard, the demand has considered as random and objective functions consist of minimization of customer’s travel time to desired facility, customer’s waiting time in queue and the possibility of unemployment of a facility which has the highest rate of unemployment. According to the results of simulation and testing 4 different scenarios, it can be stated that in scenario (4), only by adding 1 source to each available facility in the fourth layer, which is totally increasing 4 source, costumers wait time in queue will be improved about 46%.