Conference Agenda

We study the problem of allocating scarce societal resources of different types (e.g., permanent housing, deceased donor kidneys for transplantation, ventilators) to heterogeneous allocatees on a waitlist (e.g., people experiencing homelessness, individuals suffering from end-stage renal disease, Covid-19 patients) based on their observed covariates. We leverage administrative data collected in deployment to design a policy that maximizes expected outcomes while satisfying budget constraints, in the long run. Our proposed policy waitlists each individual for the resource maximizing the difference between their estimated mean treatment outcome and the estimated resource dual-price or, roughly, the opportunity cost of using the resource. Resources are then allocated as they arrive, in a first-come first-serve fashion. We demonstrate that our data-driven policy almost surely asymptotically achieves the expected outcome of the optimal out-of-sample policy under mild technical assumptions. We extend our framework to incorporate various fairness constraints. We evaluate the performance of our approach on the problem of designing policies for allocating scarce housing resources to people experiencing homelessness in Los Angeles based on data from the homeless management information system. In particular, we show that our policies simultaneously improve exit rates from homelessness and enhance fairness compared to historical allocations.

We study decision problems under uncertainty, where the decision-maker has access to K data sources that carry biased information about the underlying risk factors. The biases are measured by the mismatch between the risk factor distribution and the K data-generating distributions with respect to an optimal transport distance. In this situation, the decision-maker can exploit the information contained in the biased samples by solving a distributionally robust optimization (DRO) problem, where the ambiguity set is defined as the intersection of K optimal transport neighborhoods, each of which is centered at the empirical distribution on the samples generated by a biased data source. We show that if the decision-maker has a prior belief about the biases, then the out-of-sample performance of the DRO solution can improve with K - irrespective of the magnitude of the biases. We also show that, under standard convexity assumptions, the proposed DRO problem is computationally tractable if either K or the dimension of the risk factors is kept constant.

Mechanism design with inspection has received increasing attention due to its applications in the field. For example, large warehouses such as those operated by Amazon have started to auction scarce capacity. This capacity shall be allocated in a way that maximizes the seller's revenue. In such mechanism design problems, the seller can inspect the true value of a buyer, his realized sales in the next period, without cost. Prior work on mechanism design with deferred inspection is based on the assumption of a common prior distribution. We design a mechanism with a deferred inspection that is distributionally robust. We assume a principal who is ambiguity-averse in the sense that she wants to maximize her worst-case payoff from the auction. We consider the single-agent setting and Markov ambiguity sets, which contain all distributions within a fixed support satisfying a constraint on expectation. When the lowest possible expected value is above some threshold, a relatively simple mechanism with a concave allocation rule and a linear payment rule achieves robust optimality. When the lowest possible expected value is under this threshold, we propose an approximate mechanism instead, as the calculation of a robustly optimal mechanism requires solving high-order polynomials.

Condition-based maintenance aims to proactively plan actions to prevent equipment failure while considering economic implications. In this study, we address the problem of a component that experiences degradation with independent stationary increments. Failure occurs when the degradation exceeds a threshold and the degradation is periodically inspected. During each inspection, a decision must be made whether or not to replace the component and an estimate of the remaining useful life can be made for spare part inventory planning. Although this problem has been extensively studied, computing optimal replacement policies requires dynamic programming, which is an obstacle to implementation in practice. To address these issues, we perform an asymptotic analysis of optimal replacement thresholds and cost rates, leading to the development of an efficient replacement heuristic with an asymptotic optimality guarantee. Our extensive numerical experiments show that the average optimality gap of our heuristic replacement policy is at most 0.01% when degradation increments follow a discrete distribution and 0.52% when the distribution is continuous. Notably, the heuristic outperforms the exact algorithm in terms of computational time by a factor of at least 1000. Furthermore, we are extending our analysis to situations where the parameters of the degradation increment distribution are unknown, necessitating a Bayesian learning approach.