In this work, we focus on a non-preemptive unrelated parallel machines scheduling problem with a common server and job-sequence dependent setup times. This problem arises when planning the production of some mechanical parts of automobile, hydraulic and electrical sectors. It's well known to be NP-Hard. We first propose new mixed integer linear programming formulations for the problem. We then compare them with the only state-of-the-art formulation for the same problem. Based on these results, we devise a Branch-and-Cut algorithm along with computational results are presented to evaluate the performance of our approach. Moreover, we provide a warm starting algorithm for the problem, and further show its influence on boosting the Branch-and-Cut algorithm.