This paper studies an industrial lot-sizing and scheduling problem coming from the food-industry that extends the multi-item capacitated lot-sizing and includes lost sales, overtimes, safety stock and non uniform sequence-dependent setups on parallel machines. We introduce two different formulations and adapt the well-known Relax-and-Fix and Fix-and-Optimize heuristics in order to quickly obtain feasible solutions on large industrial instances. The complexity of our problem prevents the procedure to obtain good solutions within the time allocated by practitioners on real-life cases, hence we propose to use a clustering approach to approximate the sequence-dependent setup times. The resulting problem is significantly smaller to solve and experimental results suggest that this transformation effectively improves the solutions found on industrial instances. In particular, the combination of this clustering method and Relax-and-Fix and Fix-and-Optimize procedure turns out to be a promising approach to obtain good solutions in the given time-limit.