Abstract
Job-shop scheduling is an important but difficult problem arising in
low-volume high-variety manufacturing. It is usually solved at the
beginning of each shift with strict computational time requirements. To
obtain near-optimal solutions with quantifiable quality within strict
time limits, a direction is to formulate them in an Integer Linear
Programming (ILP) form so as to take advantages of widely available ILP
methods such as Branch-and-Cut (B&C). Nevertheless, computational
requirements for ILP methods on existing ILP formulations are high. In
this paper, a novel ILP formulation for minimizing total weighted
tardiness is presented. The new formulation has much fewer decision
variables and constraints, and is proven to be tighter as compared to
our previous formulation. For fast resolution of large problems, our
recent decomposition-and-coordination method “Surrogate Absolute-Value
Lagrangian Relaxation” (SAVLR) is enhanced by using a 3-segment
piecewise linear penalty function, which more accurately approximates a
quadratic penalty function as compared to an absolute-value function.
Testing results demonstrate that our new formulation drastically reduces
the computational requirements of B&C as compared to our previous
formulation. For large problems where B&C has difficulties,
near-optimal solutions are efficiently obtained by using the enhanced
SAVLR under the new formulation.