Manufacturing plays a significant role in promoting 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 the order being shipped late.
In addition, complex manufacturing scheduling becomes much more challenging
when the above uncertainties are present. Motivated by the presence of
uncertainties as well as combinatorial complexity, this paper addresses the
challenge illustrated through a case study of stochastic job-shop scheduling
problems arising within low-volume high-variety manufacturing. 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 step-sizing
formula thereby leading to fast convergence. Numerical testing demonstrates
that the new method is more than two orders of magnitude faster as compared to
commercial solvers