In this work, we deal with a dynamic problem arising from outpatient healthcare facility systems. Patients in need of service arrive during the day at the facility. Their requests are expected to be satisfied within a given target time, otherwise a tardiness is incurred. The facil- ity has multiple identical servers that operate simultaneously and are in charge of providing the patients with the requested services. Each server can provide only a finite subset of services, and each subset is called a configuration. The objective is to assign to each server a configuration selected from a set of predefined configurations, aiming at minimizing the total tardiness. Assignments are not fixed statically, but they can be dy- namically changed over time to better cope with the requested services. As the problem nature is dynamic, we propose a re-optimization algo- rithm that periodically optimizes the assignments with a Reduced Vari- able Neighborhood Search (RVNS). The RVNS works on neighborhood structures based on changing the assignments of one or more servers. The RVNS has been extensively tested on realistic instances. The results prove its efficiency in reaching low-tardiness solutions under low computational time.