Robust decision trees for the multi-mode project scheduling problem with a resource investment objective and uncertain activity duration

In this paper, we advocate the use of robust decision trees for a multi-mode resource constrained project scheduling problem with uncertain activity duration and a resource investment objective, coming from an industrial assembly line scheduling application. This work takes place in the context of multi-stage optimization where uncertainty is revealed progressively across a succession of decision time points. In a robust decision tree, a node represents a robust partial schedule from the time origin to a specific decision time point. At this point, the decision maker has access to some information, which partitions the uncertainty scenario set, yielding for each scenario subset a child node and an associated extended partial robust schedule up to the next decision point. Considering that the level of uncertainty is lowered, the new partial schedule is less conservative and improves the robustness guarantee. However, since all accessible information may not be relevant, we turned the information selection part into an optimization problem. An algorithm is proposed to solve the robust decision tree problem. Experimentation is provided to study the influence of decision tree parameters as well as highlighted recommendations. The interest of the decision tree is shown through an experimental comparison with classical approaches of the literature on benchmark instances and industrial instances.