We formulate a problem where an entrepreneur is engaging in a simultaneous search process and hypothesis testing on whether the profit of a given venture exceeds a desired threshold. At each stage, the entrepreneur can stop and conclude, or choose an experiment from a set of strategic and operational options, implements it and observes the resulting profit. We utilize tools from machine learning to model the search process, use tools from sequential hypothesis testing to model the testing procedure and analytically solve for the optimal solution.

We present a novel and tractable Bayesian decision-theoretical framework on multi-period adaptive clinical design. Our framework builds on the sequential hypothesis testing paradigm in which the clinical trial designer can either choose among different experiments with different information, or to terminate the trial. We show that the log-likelihood ratio (LLR) converges to a diffusion process via a limiting approximation and the optimal solution to the resulting stochastic control problem is analytically solved. The insight is to use more informative controls when the belief is more certain, and to use less informative ones otherwise. We demonstrate using real world clinical trial data that our model performs considerably better than existing policies in terms of overall expected economic benefits.

We model the creation of a new venture with a novel diffusion control framework with the state of the venture captured by a diffusion process. The entrepreneur chooses between costly controls that determine both the process's drift and the variance. When the process reaches an upper boundary (i.e. milestone), the venture succeeds and when it reaches a lower boundary (i.e. bankrupt), the venture fails. The entrepreneur's aim is to maximizes the expected profit. We derive the optimal policy and we prove that it switches between the two controls at most once.

We develop a Machine Learning model to optimally select and test samples by predicting their probative-ness, using data from the San Francisco Police Department. We showed that the Machine Learning model performed considerably better compared to existing testing procedure or full testing in terms of both CODIS (Combined DNA Index System) yield and cost-effectiveness. In particular, using the Machine Learning model as a prediction tool could turn every one dollar of testing into 130 dollars of future benefits.

We studied the impact of COVID-19 pandemic on Operating Room (OR) management, where a much longer patient recovery and cleanup times were becoming the norm. We simulated 20,000 work days of workload in an ambulance surgical suite, where the distributions of events in a day were learnt from historical data, and showed that performing online resequencing of surgical cases using Machine Learning could lead to a 6% increase in productivity. We also showed that it was sufficient for the OR manger to decide whether to implement re-sequencing procedure just based on whether the OR with the least estimated workload exceeded 8 hours.

We developed dispatch models to improve efficiency for ride-sharing companies. We proposed a two-stage framework to study short-term repositioning policy, provided an optimization formulation of ride dispatch for any region having a connective network and evaluated the performance of our framework in a set of numerical experiments utilizing actual data from a ride-sharing platform.