  This paper presents two stochastic optimization approaches for simultaneous
project scheduling and personnel planning, extending a deterministic model
previously developed by Heimerl and Kolisch. For the problem of assigning work
packages to multi-skilled human resources with heterogeneous skills, the
uncertainty on work package processing times is addressed. In the case where
the required capacity exceeds the available capacity of internal resources,
external human resources are used. The objective is to minimize the expected
external costs. The first solution approach is a 'matheuristic' based on a
decomposition of the problem into a project scheduling subproblem and a
staffing subproblem. An iterated local search procedure determines the project
schedules, while the staffing subproblem is solved by means of the Frank-Wolfe
algorithm for convex optimization. The second solution approach is Sample
Average Approximation where, based on sampled scenarios, the deterministic
equivalent problem is solved through mixed integer programming. Experimental
results for synthetically generated test instances inspired by a real-world
situation are provided, and some managerial insights are derived.
