Global Estimations for Multiprocessor Job-Shop

Classical job-shop scheduling problem (JSP) is one of the heaviest (strongly) NP-hard scheduling problems, which is very difficult to solve in practice. No approximation algorithms with a guaranteed performance exist. We deal with a natural generalization of this problem allowing parallel processors instead of each single processor in JSP, and an arbitrary task graph (without cycles) instead of a serial-parallel task graph in JSP. Parallel processors might be identical, uniform or unrelated. The whole feasible solution space grows drastically compared to JSP. However, as it turned out, parallel processors can also be used to reduce the solution space to a subspace, which is essentially smaller than even the corresponding solution space for JSP. For large problem instances, this space still may remain too big. Here we propose different global estimations which allow us to reduce it further. By applying our bounds to the reduced solution space, a class of exact and approximation algorithms are obtained. We are in the process of the implementation of our reduction algorithm and the bounds. Then we aim to carry out the experimental study comparing the behavior and the efficiency of the proposed bounds in practice