Better Propagation for Non-preemptive Single-Resource Constraint Problems

Overload checking, forbidden regions, edge finding, and not-first/not-last detection are well-known propagation rules to prune the start times of activities which have to be processed without any interruption and overlapping on an exclusively available resource, i.e. machine. These rules are extendible by two other rules which take the number of activities into account which are at most executable after or before another activity. To our knowledge, these rules are based on approximations of the (minimal) earliest completion times and the (maximal) latest start times of sets of activities. In this paper, the precise definitions of these time values as well as an efficient procedure for their calculations are given. Based on the resulting time values the rules are re-formulated and applied to a well-known job shop scheduling benchmark.