Two-stage stochastic days-off scheduling of multi-skilled analysts with training options

Motivated by a cybersecurity application, this paper studies a two-stage, stochastic days-off scheduling problem with (1) many types of jobs that require specialized training, (2) many multi-skilled analysts, (3) the ability to shape analyst skill sets through training decisions, and (4) a large number of possible future demand scenarios. We provide an integer linear program for this problem and show it can be solved with a direct feed into Gurobi with as many as 50 employees, 6 job types, and 50 demand scenarios per day without any decomposition techniques. In addition, we develop a matheuristicthat is, an integer-programming-based local search heuristicfor instances that are too large for a straightforward feed into a commercial solver. Computational results show our matheuristic can, on average, produce solutions within 4-7% of an upper bound of the optimal objective value.