  The Jobs shop Scheduling Problem (JSP) is a canonical combinatorial
optimization problem that is routinely solved for a variety of industrial
purposes. It models the optimal scheduling of multiple sequences of tasks, each
under a fixed order of operations, in which individual tasks require exclusive
access to a predetermined resource for a specified processing time. The problem
is NP-hard and computationally challenging even for medium-sized instances.
Motivated by the increased stochasticity in production chains, this paper
explores a deep learning approach to deliver efficient and accurate
approximations to the JSP. In particular, this paper proposes the design of a
deep neural network architecture to exploit the problem structure, its
integration with Lagrangian duality to capture the problem constraints, and a
post-processing optimization to guarantee solution feasibility.The resulting
method, called JSP-DNN, is evaluated on hard JSP instances from the JSPLIB
benchmark library. Computational results show that JSP-DNN can produce JSP
approximations of high quality at negligible computational costs.
