  In this paper, we consider a distributionally robust resource planning model
inspired by a real-world service industry problem. In this problem, there is a
mixture of known demand and uncertain future demand. Prior to having full
knowledge of the demand, we must decide upon how many jobs we plan to complete
on each day in the planning horizon. Any jobs that are not completed by the end
of their due date incur a cost and become due the following day. We present two
distributionally robust optimisation (DRO) models for this problem. The first
is a non-parametric model with a phi-divergence based ambiguity set. The second
is a parametric model, where we treat the number of uncertain jobs due on each
day as a binomial random variable with an unknown success probability. We
reformulate the parametric model as a mixed integer program and find that it
scales poorly with the sizes of the ambiguity and uncertainty sets. Hence, we
make use of theoretical properties of the binomial distribution to derive fast
heuristics based on dimension reduction. One is based on cutting surface
algorithms commonly seen in the DRO literature. The other operates on a small
subset of the uncertainty set for the future demand. We perform extensive
computational experiments to establish the performance of our algorithms. We
compare decisions from the parametric and non-parametric models, to assess the
benefit of including the binomial information.
