In this paper, we consider a new scheduling problem, which occurs in the context of the automobile industry. Given a set of machines, and a set of jobs, we seek a fixed configuration for each machine (i.e. a set of values for different parameters), and an assignment of jobs to machines along the time horizon that respects compatibility constraints between jobs and machine configurations. Two objectives are optimized lexicographically: the number of late jobs, and the number of machines used. First we prove that even finding a feasible solution for the problem is NP-hard, and characterize the cases where compatibility constraints amount to ensuring that only pairwise compatible jobs are assigned to each machine. Then we propose a mathematical model for this problem, and a reformulation into a path-flow formulation. We use a refined labelling algorithm embedded in a column-and-row generation algorithm to produce primal and dual bounds from this formulation. We conducted computational experiments with industrial data from Renault, and compared our results with those obtained by solving a constraint programming model provided by the company. Our approach finds better solutions than those obtained by the company, and proves the optimality for all instances of our benchmark for the first objective function. We also obtain small optimality gaps for the second objective function.< Leer menos