A Position-Based Propagator for the Open-Shop Problem

The Open-Shop Problem is a hard problem that can be solved using Constraint Programming or Operation Research methods. Existing techniques are efficient at reducing the search tree but they usually do not consider the absolute ordering of the tasks. In this work, we develop a new propagator for the One-Machine Non-Preemptive Problem, the basic constraint for the Open-Shop Problem. This propagator takes this additional information into account allowing, in most cases, a reduction of the search tree. The underlying principle is to use shaving on the positions. Our propagator applies on one machine or one job and its time complexity is in O(N logN), where N is either the number of jobs or machines. Experiments on the Open-Shop Problem show that the propagator adds pruning to state-of-the-art constraint satisfaction techniques to solve this problem.