Relax-and-fix heuristics applied to a real-world lot-sizing and scheduling problem in the personal care consumer goods industry

TL;DR

This paper develops relax-and-fix heuristics for a complex, real-world lot-sizing and scheduling problem in the personal care industry, demonstrating significant cost reductions over current solutions.

Contribution

It introduces novel relax-and-fix heuristics with hybrid partitioning strategies tailored for a complex, real-world, NP-hard lot-sizing and scheduling problem with unique constraints.

Findings

Heuristics significantly reduce costs compared to existing solutions.

The approach effectively manages inventory and machine allocation.

Results are validated on real-world and synthetic data.

Abstract

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.