Stochastic Programming and Distributionally Robust Optimization Approaches for Location and Inventory Prepositioning of Disaster Relief Supplies

In this paper, we study the problem of disaster relief inventory prepositioning under uncertainty. Specifically, we aim to determine where to open warehouses and how much relief item inventory to preposition in each, pre-disaster. During the post-disaster phase, prepositioned items are distributed to demand nodes, and additional items are procured and distributed as needed. There is uncertainty in the (1) disaster level, (2) locations of affected areas, (3) demand of relief items, (4) usable fraction of prepositioned items post-disaster, (5) procurement quantity, and (6) arc capacity. We propose and analyze two-stage stochastic programming (SP) and distributionally robust optimization (DRO) models, assuming known and unknown uncertainty distributions, respectively. The first and second stages correspond to pre- and post-disaster phases, respectively. We propose a Monte Carlo Optimization procedure to solve the SP and a decomposition algorithm to solve the DRO model. To illustrate potential applications of our approaches, we conduct extensive experiments using a hurricane season and an earthquake as case studies. Our results demonstrate the (1) the robustness and superior post-disaster operational performance of the DRO decisions under various distributions compared to SP decisions, especially under misspecified distributions and high variability, (2) the trade-off between considering distributional ambiguity and following distributional belief, and (3) computational efficiency of our approaches

Stochastic Optimization Approaches for Outpatient Appointment Scheduling under Uncertainty

Outpatient clinics (OPCs) are quickly growing as a central component of the healthcare system. OPCs offer a variety of medical services, with benefits such as avoiding inpatient hospitalization, improving patient safety, and reducing costs of care. However, they also introduce new challenges for appointment planning and scheduling, primarily due to the heterogeneity and variability in patient characteristics, multiple competing performance criteria, and the need to deliver care within a tight time window. Ignoring uncertainty, especially when designing appointment schedules, may have adverse outcomes such as patient delays and clinic overtime. Conversely, accounting for uncertainty when scheduling has the potential to create more efficient schedules that mitigate these adverse outcomes. However, many challenges arise when attempting to account for uncertainty in appointment scheduling problems. In this dissertation, we propose new stochastic optimization models and approaches to address some of these challenges. Specifically, we study three stochastic outpatient scheduling problems with broader applications within and outside of healthcare and propose models and methods for solving them. We first consider the problem of sequencing a set of outpatient procedures for a single provider (where each procedure has a known type and a random duration that follows a known probability distribution), minimizing a weighted sum of waiting, idle time, and overtime. We elaborate on the challenges of solving this complex stochastic, combinatorial, and multi-criteria optimization problem and propose a new stochastic mixed-integer programming model that overcomes these challenges in contrast to the existing models in the literature. In doing so, we show the art of, and the practical need for, good mathematical formulations in solving real-world scheduling problems. Second, we study a stochastic adaptive outpatient scheduling problem which incorporates the patients’ random arrival and service times. Finding a provably-optimal solution to this problem requires solving a MSMIP, which in turn must optimize a scheduling problem over each random arrival and service time for each stage. Given that this MSMIP is intractable, we present two approximation based on two-stage stochastic mixed-integer models and a Monte Carlo Optimization approach. In a series of numerical experiments, we demonstrate the near-optimality of the appointment order (AO) rescheduling policy, which requires that patients are served in the order of their scheduled appointments, in many parameter settings. We also identify parameter settings under which the AO policy is suboptimal. Accordingly, we propose an alternative swap-based policy that improves the solution of such instances. Finally, we consider the outpatient colonoscopy scheduling problem, recognizing the impact of pre-procedure bowel preparation (prep) quality on the variability of colonoscopy duration. Data from a large OPC indicates that colonoscopy durations are bimodal, i.e., depending on the prep quality they can follow two different probability distributions, one for those with adequate prep and the other for those with inadequate prep. We define a distributionally robust outpatient colonoscopy scheduling (DRCOS) problem that seeks optimal appointment sequence and schedule to minimize the worst-case weighted expected sum of patient waiting, provider idling, and provider overtime, where the worst-case is taken over an ambiguity set characterized through the known mean and support of the prep quality and durations. We derive an equivalent mixed-integer linear programming formulation to solve DRCOS. Finally, we present a case study based on extensive numerical experiments in which we draw several managerial insights into colonoscopy scheduling.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/151727/1/ksheha_1.pdfDescription of ksheha_1.pdf : Restricted to UM users only