We consider applications where decisions affect multiple beneficiaries, and the decision maker aims to ensure that the impact is distributed equitably among them. Our focus is on stochastic environments, where there is uncertainty in the system.
We first present a robust programming approach that seeks to maximize system efficiency while ensuring an equitable outcome allocation, even in the worst-case scenario. We derive tractable formulations by leveraging results on the properties of highly unfair allocations. We demonstrate the approach through applications in project selection and shelter allocation.
We then turn to chemotherapy scheduling and propose a metric for quantifying efficiency and fairness concerns in patient waiting times. To optimize this metric, we formulate a two-stage stochastic mixed-integer nonlinear programming model. We introduce a binary search-based algorithm that incorporates scenario set reduction and augmentation techniques to improve computational performance. We illustrate the applicability of the approach using data from a major oncology hospital.