Scheduling and Routing in the Flexible Job Shop with Heterogeneous Transbots and Zoning: A Constraint Programming Approach

Coordinating production and material transfers is increasingly important in modern manufacturing systems equipped with mobile transfer robots, known as transbots. This study considers a flexible job shop environment in which heterogeneous transbots transport parts between machines. The shop floor is partitioned into zones, with each transbot assigned to a specific zone, and inter-zone movements are facilitated through designated handoff points. These zoning constraints, transbot heterogeneity, and inter-zone handoffs give rise to a challenging variant of the flexible job shop problem with embedded transbot-routing features, resulting in substantial computational complexity. Motivated by a real manufacturing setting, two constraint programming formulations that integrate production scheduling with transbot routing are proposed: an arc-based formulation that explicitly models machine-to-machine transfers, and an operation-embedded formulation that embeds transfer decisions directly within the operation scheduling structure, leading to tighter synchronization between production and transportation decisions. Both formulations capture machine flexibility, zoning restrictions, handoff coordination, and collision-free path planning. To efficiently solve the resulting problem, a book-and-release strategy is proposed. It coordinates transbot movements without enforcing rigid routing patterns. Computational experiments on case study-adapted benchmark-based demonstrate that the proposed formulations generate high-quality solutions with strong computational performance. The generation of instances is described in detail to support future work in this emerging area.