  The Flexible Job-shop Scheduling Problem (FJSP) is an important combinatorial
optimization problem that arises in manufacturing and service settings. FJSP is
composed of two subproblems, an assignment problem that assigns tasks to
machines, and a scheduling problem that determines the starting times of tasks
on their chosen machines. Solving FJSP instances of realistic size and
composition is an ongoing challenge even under simplified, deterministic
assumptions. Motivated by the inevitable randomness and uncertainties in supply
chains, manufacturing, and service operations, this paper investigates the
potential of using a deep learning framework to generate fast and accurate
approximations for FJSP. In particular, this paper proposes a two-stage
learning framework 2SLFJSP that explicitly models the hierarchical nature of
FJSP decisions, uses a confidence-aware branching scheme to generate
appropriate instances for the scheduling stage from the assignment predictions
and leverages a novel symmetry-breaking formulation to improve learnability.
2SL-FJSP is evaluated on instances from the FJSP benchmark library. Results
show that 2SL-FJSP can generate high-quality solutions in milliseconds,
outperforming a state-of-the-art reinforcement learning approach recently
proposed in the literature, and other heuristics commonly used in practice.
