Spillover Algorithm: A decentralised coordination approach for multi-robot production planning in open shared factories

Open and shared manufacturing factories typically dispose of a limited number of industrial robots and/or other production resources that should be properly allocated to tasks in time for an effective and efficient system performance. In particular, we deal with the dynamic capacitated production planning problem with sequence independent setup costs where quantities of products to manufacture need to be determined at consecutive periods within a given time horizon and products can be anticipated or back-ordered related to the demand period. We consider a decentralised multi-agent variant of this problem in an open factory setting with multiple owners of robots as well as different owners of the items to be produced, both considered self-interested and individually rational. Existing solution approaches to the classic constrained lot-sizing problem are centralised exact methods that require sharing of global knowledge of all the participants' private and sensitive information and are not applicable in the described multi-agent context. Therefore, we propose a computationally efficient decentralised approach based on the spillover effect that solves this NP-hard problem by distributing decisions in an intrinsically decentralised multi-agent system environment while protecting private and sensitive information. To the best of our knowledge, this is the first decentralised algorithm for the solution of the studied problem in intrinsically decentralised environments where production resources and/or products are owned by multiple stakeholders with possibly conflicting objectives. To show its efficiency, the performance of the Spillover Algorithm is benchmarked against state-of-the-art commercial solver CPLEX 12.8.