Open and shared manufacturing factories typically dispose of a limited number of robots that should be properly allocated to tasks in time and space 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 and location of robots need to be determined at consecutive periods within a given time horizon and products can be anticipated or backordered related to the demand period. We consider a decentralized 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 centralized 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 decentralized approach based on the spillover effect that solves this NP-hard problem by distributing decisions in an intrinsically decentralized multi-agent system environment while protecting private and sensitive information. To the best of our knowledge, this is the first decentralized algorithm for the solution of the studied problem in intrinsically decentralized 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.