Temporal decomposition approach and characterisation of feasible solutions for the single machine scheduling problem

We propose a temporal decomposition approach for the one-machine scheduling problem with ready times and due dates. A set of feasible schedules is characterized by means of constraint-based analysis rules. They permit the determination of the feasible locations of each task in a sequence, represented by rank intervals. A decomposition procedure based on comparisons of rank intervals is developed in order to group tasks to be sequenced in the neighbourhood of each other in a feasible solution. Computational results are reported so that the capability of our approach to prepare the problem for a solution computation, achieved either by a human operator or by an automatic solving procedure, can be evaluated.