Multi-agent scheduling models and methods for manufacturing as a service systems

Manufacturing as a Service (MaaS) systems facilitate collaboration, leading to more efficient resource utilisation, improved supply chain resilience, and increased competitiveness. Sectors such as machinery manufacturing, additive manufacturing, and automotive supply chains benefit from shared resources, allowing for greater flexibility and quicker adaptation to market and technological shifts. MaaS systems are multi-agent by nature, as each service provider and customer pursues their own objectives and therefore requires coordination of activities. This paper addresses this multi-agent scheduling challenge through scalable combinatorial optimisation formulations and solution methods. Novel exact Mixed-Integer Programming (MIP) and Constraint Programming (CP) models, together with a Logic-Based Benders Decomposition (LBBD) algorithm that exploits both models, are developed. State-of-the-art exact solvers are used for implementing and tuning the exact models and the LBBD algorithm, while a metaheuristic solver is employed for benchmarking. An extensive set of novel instances, including practical extensions arising from manufacturing and distribution processes, is generated. Computational experiments for benchmarking the developed models and methods, along with sensitivity analysis, demonstrate the applicability of the proposed solution methods to large-scale instances of the problem.