Coordination of the decentralized concurrent open-shop

In a concurrent open-shop, several jobs have to be completed, where each job consists of multiple components that are processed simultaneously by different dedicated machines. We assume that the components are sequenced on each machine in a decentralized manner, and analyze the resulting coordination problem under the objective of minimizing the weighted sum of disutility of completion times. The decentralized system is modeled as a non-cooperative game for two environments: (i) local completion times, where each machine considers only the completion times of their components, disregarding the other machines; and (ii) global completion times, where each machine considers the job completion times from the perspective of the system, i.e., when all components of each job are completed. Tight bounds are provided on the inefficiency that might occur in the decentralized system, showing potentially severe efficiency loss in both environments. We propose and investigate scheduling based, coordinating job weighting mechanisms that use concise information, showing impossibility in the local completion times environment and possibility using the related weights mechanism in the global completion times environment. These results extend to a setting with incomplete information in which only the distribution of the processing times is commonly known, and each machine is additionally informed about their own processing times.