Deterministic networking with end-to-end delay guarantees is becoming a must for a wide-range of Internet applications. In this context, dampers are used to guarantee deterministic end-to-end (E2E) delay and bounded jitter in Large Deterministic Networks (LDN). Here, we introduce the Admission Control problem in a Damper-based deterministic Networks (ACDN) to decide about flows' acceptance along with shaping patterns at ingress nodes and routing paths to satisfy ES2 delay requirements. To efficiently solve the ACDN, we propose a column generation algorithm and a rounding procedure. A branch-and-Price algorithm is currently being developed in order to solve to optimality the ACDN.