Setting production capacities for production agents making selfish routing decisions

Traditionally, the capacity dimensioning step within the manufacturing system design process takes a known and fixed distribution of production flow across path alternatives to derive capacity demand based on a desired target utilisation rate. Setting target rates for machine utilisation provides limits on throughput times and allows to provide capacity buffers against changes in the production mix. In this contribution, we transfer this rationale into the world of Industry 4.0, where Cyber-Physical Systems can make autonomous and selfish routing decisions. Under this new framework, non-cooperative agents make decisions based on the capacity allocation and the decisions of all other agents, thus creating a feedback between flow and capacity distribution that makes existing methods for capacity dimensioning inapplicable. We use methods and insight from algorithmic game theory and operations research to investigate the capacity dimensioning process in this context. We prove properties of the throughput-time optimal allocation of production capacity under fixed target utilisation rates for important queue classes. Our findings not only provide a quantitative, easy to operationalise tool for production system designers, but also explore a trade-off between cost and flexibility that arises naturally in this regime.