In this work, we delve into a real-life scheduling problem involving the production of off-road vehicles, subject to precedence, machines, and resource constraints. This scheduling problem shares characteristics with many others, but also comprises less investigated aspects like a specific precedence structure and a resource constraint limiting the number of simultaneously active machines. We formally present the problem and devise two lower bounds. To solve the problem, we propose a Constraint Programming model and compare it with a Mathematical Programming one. Our findings reveal the superiority of the Constraint Programming approach in both real-life and synthetic instances, and validate the quality of the proposed lower bounds.