Solving the 2-stage outsourcing flowshop problem through a MILP-heuristic

Outsourcing is a commonly used business tactic to increase production capacity without the need for additional investments in manufacturing facilities. Typically, decision makers use outsourcing to manage temporary spikes in demand or to improve specific performance metrics (such as delivery times) quickly and without making modifications to the manufacturing site. This study focuses on minimizing the total system makespan in a 2-stage flowshop setting where initial operation can be outsourced. The problem is formulated using Mixed Integer Linear Programming (MILP) and a heuristic based on the branch and check strategy is proposed. Although traditional MILP approaches are computationally intensive for various scheduling problems, the proposed branch and check approach presents interesting results in surpassing existing benchmarks in the literature and emerges as a practical strategy for real-world applications.