Abstract
Interval capacity consistency tests consider the resource capacities available and required within certain time intervals. The goal of the tests is to draw conclusions that allow to rule out inadmissible activity start times or sequences. The tests can be effectively used to reduce the search space of difficult time- and resource-constrained scheduling problems. They have successfully been applied in algorithms for solving idealised problems such as the classical job shop scheduling problem (JSP) or the resource-constrained project scheduling problem (RCPSP) as well as for solving industrial scheduling problems. For instance, it seems fair to say that the advances in modern branch and bound algorithms for the JSP that have been made in the last decade can to a large extent be attributed to the effect of interval consistency tests, some of which are also known under the names of immediate selection, edge finding, and energetic reasoning. The tests can also serve to derive tight lower bounds for makespan minimisation problems.
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