  Healthcare systems are facing serious challenges in balancing their human
resources to cope with volatile service demand, while at the same time
providing necessary job satisfaction to the healthcare workers. We propose in
this paper a distributionally robust optimization formulation to generate a
task assignment plan that promotes the fairness in allocation, attained by
reducing the difference in the total working time among workers, under
uncertain service time. The proposed joint chance constraint model is
conservatively approximated by a worst-case Conditional Value-at-Risk, and we
devise a sequential algorithm to solve the finite-dimensional reformulations
which are linear (mixed-binary) optimization problems. We also provide explicit
formula in the situation where the support set of the random vectors is a
hyperrectangle. The experiment with synthetic data suggests promising results
for our approach.
