In semiconductor manufacturing, new technologies impose more and more time constraints in product routes, i.e. a maximum time between two (often non-consecutive) operations. The management of Time Constraint Tunnels (TCTs, combining multiple time constraints) in high-mix facilities is becoming more and more challenging. This paper first recalls an approach for estimating the probability that a lot at the entrance of a TCT will leave the TCT on time. This approach relies on a list scheduling algorithm using a dispatching policy with random components. Three dispatching policies are presented. Computational experiments on industrial data comparing these policies are discussed. Perspectives are drawn to extend the approach and support decision making.