Abstract
ob-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. For
fast resolution of the problem, a promising direction is to formulate it
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 on ILP methods for existing ILP
formulations are high. In this paper, a novel ILP formulation is
presented. In the formulation, a set of binary indicator variables
indicating whether an operation begins at a time slot on a machine group
or not is selected as decision variables, and all constraints are
innovatively formulated based on this set of variables. 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.