Optimize-via-Predict: Realizing out-of-sample optimality in data-driven optimization

We examine a stochastic formulation for data-driven optimization wherein the decision-maker is not privy to the true distribution, but has knowledge that it lies in some hypothesis set and possesses a historical data set, from which information about it can be gleaned. We define a prescriptive solution as a decision rule mapping such a data set to decisions. As there does not exist prescriptive solutions that are generalizable over the entire hypothesis set, we define out-of-sample optimality as a local average over a neighbourhood of hypotheses, and averaged over the sampling distribution. We prove sufficient conditions for local out-of-sample optimality, which reduces to functions of the sufficient statistic of the hypothesis family. We present an optimization problem that would solve for such an out-of-sample optimal solution, and does so efficiently by a combination of sampling and bisection search algorithms. Finally, we illustrate our model on the newsvendor model, and find strong performance when compared against alternatives in the literature. There are potential implications of our research on end-to-end learning and Bayesian optimization.Comment: 28 page

OPTIMIZATION IN PUBLIC POLICY - A RISK-BASED MULTI-PERIOD APPROACH

Ph.DDOCTOR OF PHILOSOPH

Strategic Workforce Planning Under Uncertainty

A new study in the INFORMS journal Operations Research proposes a data-driven model for conducting strategic workforce planning in organizations. The model optimizes for recruitment and promotions by balancing the risks of not meeting headcount, budget, and productivity constraints, while keeping within a prescribed organizational structure. Analysis using the model indicates that there are increased workforce risks faced by organizations that are not in a state of growth or organizations that face limitations to organizational renewal (such as bureaucracies). </jats:p

The Analytics of Bed Shortages:Coherent Metric, Prediction, and Optimization

Bed shortages in hospitals usually have a negative impact on patient satisfaction and medical outcomes. In practice, healthcare managers often use bed occupancy rates (BORs) as a metric to understand bed utilization, which is insufficient in capturing the risk of bed shortages. We propose the bed shortage index (BSI) to capture more facets of bed shortage risk than traditional metrics such as the occupancy rate, the probability of shortages, and expected shortages. The BSI is based on the riskiness index by Aumann and Serrano, and it is calibrated to coincide with BORs when the daily arrivals in the hospital unit are Poisson distributed. Our metric can be tractably computed and does not require additional assumptions or approximations. As such, it can be consistently used across the descriptive, predictive, and prescriptive analytical approaches. We also propose optimization models to plan for bed capacity via this metric. These models can be efficiently solved on a large scale via a sequence of linear optimization problems. The first maximizes total elective throughput while managing the metric under a specified threshold. The second determines the optimal scheduling policy by lexicographically minimizing the steady-state daily BSI for a given number of scheduled admissions. We validate these models using real data from a hospital and test them against data-driven simulations. We apply these models to study the real-world problem of long stayers to predict the impact of transferring them to community hospitals as a result of an aging population.</p

Inventory-Responsive Donor-Management Policy:A Tandem Queueing Network Model

Problem definition: In the blood-donor-management problem, the blood bank incentivizes donors to donate, given blood inventory levels. We propose a model to optimize such incentivization schemes under the context of random demand, blood perishability, observation period between donations, and variability in donor arrivals and dropouts. Methodology/results: We propose an optimization model that simultaneously accounts for the dynamics in the blood inventory and the donor’s donation process, as a coupled queueing network. We adopt the Pipeline Queue paradigm, which leads us to a tractable convex reformulation. The coupled setting requires new methodologies to be developed upon the existing Pipeline Queue framework. Numerical results demonstrate the advantages of the optimal policy by comparing it with the commonly adopted and studied threshold policy. Our optimal policy can effectively reduce both shortages and wastage. Managerial implications: Our model is the first to operationalize a dynamic donor-incentivization scheme, by determining the optimal number of donors of different donation responsiveness to receive each type of incentive. It can serve as a decision-support tool that incorporates practical features of blood supply-chain management not addressed thus far, to the best of our knowledge. Simulations on existing policies indicate the dangers of myopic approaches and justify the need for smoother and forward-looking donor-incentivization schedules that can hedge against future demand variation. Our model also has potential wider applications in supply chains with perishable inventory.</p

Intraday Scheduling with Patient Re-entries and Variability in Behaviours

Problem definition: We consider the intraday scheduling problem in a group of orthopaedic clinics where the planner schedules appointment times, given a sequence of appointments. We consider patient re-entry—where patients may be required to go for an x-ray examination, returning to the same doctor they have seen—and variability in patient behaviours such as walk-ins, earliness, and no-shows, which leads to inefficiency such as long patient waiting time and physician overtime. Academic/practical relevance: In our data set, 25% of the patients are required to go for x-ray examination. We also found significant variability in patient behaviours. Hence, patient re-entry and variability in behaviours are common, but we found little in the literature that could handle them. Methodology: We formulate the problem as a two-stage optimization problem, where scheduling decisions are made in the first stage. Queue dynamics in the second stage are modeled under a P-Queue paradigm, which minimizes a risk index representing the chance of violating performance targets, such as patient waiting times. The model reduces to a sequence of mixed-integer linear-optimization problems. Results: Our model achieves significant reductions, in comparative studies against a sample average approximation (SAA) model, on patient waiting times, while keeping server overtime constant. Our simulations further characterize the types of uncertainties under which SAA performs poorly. Managerial insights: We present an optimization model that is easy to implement in practice and tractable to compute. Our simulations indicate that not accounting for patient re-entry or variability in patient behaviours will lead to suboptimal policies, especially when they have specific structure that should be considered

Inventory-responsive donor-management policy: A tandem queueing network model

Ministry of Education, Singapore under its Academic Research Funding Tier