This paper addresses an integrated lot-sizing and scheduling problem in the
industry of consumer goods for personal care, a very competitive market in
which the good customer service level and the cost management show up in the
competition for the clients. In this research, a complex operational
environment composed of unrelated parallel machines with limited production
capacity and sequence-dependent setup times and costs is studied. There is also
a limited finished-goods storage capacity, a characteristic not found in the
literature. Backordering is allowed but it is extremely undesirable. The
problem is described through a mixed integer linear programming formulation.
Since the problem is NP-hard, relax-and-fix heuristics with hybrid partitioning
strategies are investigated. Computational experiments with randomly generated
and also with real-world instances are presented. The results show the efficacy
and efficiency of the proposed approaches. Compared to current solutions used
by the company, the best proposed strategies yield results with substantially
lower costs, primarily from the reduction in inventory levels and better
allocation of production batches on the machines