Distributionally robust scheduling of stochastic knapsack arrivals

This paper studies the discrete-time Stochastic Knapsack with Periodic Scheduled Arrivals (SKPSA). The goal is to find a schedule such that the capacity usage of the unconstrained cousin of the knapsack is as close as possible to a target utilization. We approximate the SKPSA with a Wasserstein distance based Distributionally Robust Optimization (DRO) model, resulting in the DRO-SKPSA. We present an algorithm that efficiently solves this model, and show that the DRO-SKPSA produces robust schedules. The problem arises in particular in healthcare settings in the development of Master Surgical Schedules (MSSs). We discuss managerial insights for MSSs with downstream capacity constraints.