Overload-Checking and Edge-Finding for Robust Cumulative Scheduling

Scheduling frameworks are not necessarily stable. The aim is to introduce schedules resistant to disruptions such as when resources become unavailable, the supply chain for them breaks down, etc. A schedule is robust if it absorbs some level of unforeseen events when at most a certain number of activities are delayed. Taking advantage of constraint programming, we present two new filtering algorithms for a constraint that models cumulative scheduling problems in robust contexts where up to $r$ out of $n$ tasks can be concurrently delayed while keeping the schedule valid. We adapt the overload-checking and edge-finding filtering rules for this framework. We show that our robust versions of these algorithms run in $\mathrm{\Theta }(r^{2}n\log (n))$ and $O(r^{2}zn\log (n))$, respectively, where $z$ denotes the number of distinct capacities of all tasks. This achievement implies that the complexities of the state-of-the-art algorithms for these techniques are invariable when $r$ is constant. Experiments illustrate that our algorithms scale, with respect to $n$ and $r$. As a practical application, the experimental results on a special case of crane assignment problem also verify a stronger filtering for these methods in terms of backtrack numbers as well as computation times when used in conjunction with time tabling. Finally, in order to show that our CP-based algorithms improve to solve a robust scheduling problem, we make a comparison against temporal protection as an external robust scheduling approach.

History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete.

Funding: H. Fahimi received funding from Shahid Chamran University of Ahvaz with [Grant number SCU.MC1402.44132]. C.-G. Quimper was funded by a NSERC Discovery Grant from Canada.

Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2021.0138.