  Manufacturing plays a significant role in economic development, production,
exports, and job creation, which ultimately contribute to improving the quality
of life. The presence of manufacturing defects is, however, inevitable leading
to products being discarded, i.e. scrapped. In some cases, defective products
can be repaired through rework. Scrap and rework cause a longer completion
time, which can contribute to orders being shipped late. Moreover, the presence
of uncertainties and combinatorial complexity significantly increases the
difficulty of complex manufacturing scheduling. This paper tackles this
challenge, exemplified by a case study on stochastic job-shop scheduling in
low-volume, high-variety manufacturing contexts. To ensure on-time delivery,
high-quality solutions are required, and near-optimal solutions must be
obtained within strict time constraints to ensure smooth operations on the
job-shop floor. To efficiently solve the stochastic job-shop scheduling (JSS)
problem, a recently-developed Surrogate "Level-Based" Lagrangian Relaxation is
used to reduce computational effort while efficiently exploiting the geometric
convergence potential inherent to Polyak's stepsizing formula thereby leading
to fast convergence. Numerical testing demonstrates that the new method is two
orders of magnitude faster as compared to commercial solvers.
