Discrete optimization algorithms for distributed bi-agent flowshop scheduling with release dates

The globalization of production has accelerated the growth of contract manufacturing, as brand firms increasingly outsource production to specialized manufacturers to reduce costs and improve efficiency. To meet rising production demands, contract manufacturers establish production facilities across global regions, leveraging localized advantages in labor costs, raw material access, and logistics infrastructure. Contract manufacturers in distributed assembly-line systems face the critical challenge of dynamically coordinating order allocation across decentralized facilities to satisfy multi-client requirements. This study introduces a distributed bi-agent permutation flowshop scheduling for minimizing the makespans of both agents while considering release dates to simulate real-world production scenarios. An exact branch-and-bound algorithm is proposed for optimizing the weighted sum of two objectives. A novel Q-learning-based artificial bee colony algorithm is presented to construct high-quality Pareto frontiers for the bi-objective optimization problem. The effectiveness of the proposed algorithms is validated through a comprehensive set of numerical experiments.