Minimising total production time in the additive or layered manufacturing is a critical concern, and in this respect, the idea of balancing assembly time and build time is rapidly gaining research attention. The proposed work intends to provide benefit in terms of reduced lead time to customers in a collaborative environment with simultaneous part printing. This paper formulates a mixed-integer non-linear programming (MINLP) model to evaluate the near optimal threshold area and support material allocation while segregating parts for a single material additive manufacturing set-up. The resulting time minimisation model is finitely bounded with respect to support material volume, total production time and total assembly cost constraints. A novel swarm intelligence-based part segregation procedure is proposed to determine the number of part assemblies and part division scheme that adheres to cross-sectional shape, cross-sectional area, and height restrictions. The proposed approach is illustrated and evaluated for objects with regular as well as free-form surfaces using two different hypothetically simulated real size 3D models. Results indicate that the proposed approach is able to reduce the total amount of manufacturing time in comparison with single part build time for all the tested cases. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.