Distributionally Robust Resource Planning Under Binomial Demand Intakes

In this paper, we consider a distributionally robust resource planning model inspired by a real-world service industry problem in which 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 will complete on each day of the plan. Any jobs that are not completed by the end of their due date incur a cost and become due the following day. We present a distributionally robust optimisation (DRO) model where we treat the number of uncertain jobs due on each day as a binomial random variable with unknown parameters. We make use of theoretical properties of the binomial distribution to present a simple and fast algorithm for the two-day model. We present theoretical results regarding the near-optimality of this algorithm, namely that it finds the worst-case distribution for a subset of the solution space. For the multi-day model, we extend this algorithm and present two others, one based on the cutting surface algorithm commonly seen in the DRO literature, and one based on a probability-based reduction of the uncertainty set for the uncertain parameters. We test these algorithms on a number of different problem instances to establish their performance.