Automated Teller Machines (ATMs) are one of the most important cash distribution channels for the banks. Banks are expanding their ATM network to satisfy customer demand and are facing operating costs. This work focuses on the inventory management for optimizing the replenishment policy of the Automated Teller Machine (ATM) network. We introduce a multi-period strategy that helps to minimize the total cost of ATMs replenishment. In addition, the paper discusses how to obtain the shortest tour to replenish ATMs. We formulate the problem as a Mixed Integer Nonlinear Programming (MINLP) model and solve it using GAMS solver BARON, to minimize the total cost associated with replenishing ATMs. Then, we linearize the MINLP and compare the results of both models.