Goal programming model with the deployment of ATMs machines random demand

We all have experienced the discomfort of waiting in a queue. Unfortunately, this phenomenon is becoming increasingly common in urban societies with increasing population. One of the problems of ATM machines is the long queue in front of these machines which results in customer dissatisfaction. Therefore, banks should attempt to solve this huge problem, so that they could prevent distrust to electronic banking and its tools including ATMs. So, nonlinear queuing model was suggested by Passandideh and Niaki (2010) with two objectives of minimizing customer waiting time and percentage of idle time for ATM. In the present research, alinear approximation of this model is investigated to obtain a simpler and more accurate solution. This linear model has been examined with 13 numerical examples, solved by GAMS software. It was found that the process time is far less than the previous non-linear model. Based on this model and using these examples a goal programming model was introduced. Solving this linear model (by software GAMS) resulted in more optimized solutions than the previous linear model which showed improvements compared to Passandideh-Niaki model.