Bayzhan Mukatay

Heart allocation is complex - there are blood type matching, distance rules, status priorities, and a bunch of other factors. When UNOS changes the rules, it's hard to predict the impact. This tool lets you test new policies against real historical data before implementing them.

This simulator takes real transplant data (candidates, donors, transplants) from SRTR and replays a year of heart allocation under whatever policy you want to test. It's basically a "what if" machine for transplant policy. The process involves many steps, including:

1. De-transplantation and generating hypothetical histories for people who were transplanted in real life but not under the tested policy. (this can be done using Higher Order Markov Chains or Sampling Techniques)

2. Making an event log and handlers for each case: candidate & donor arrival/removal, frequent status changes, etc.

3. Allocating hearts to candidates based on the policy.

4. Analyzing, visualizing, and reporting the results of the allocation.

This simulation models the complex dynamics of the kidney transplant waiting list using continuous-time Markov chains. Patients arrive, receive transplants, experience graft failures, and some die—all while the system continuously evolves. Each patient transition is treated as a probabilistic event occurring at rates determined by real-world data.

The key question: What happens if we introduce xenotransplantation as an option for high-cPRA patients? We partition patients by their calculated panel reactive antibody (cPRA) level—a measure of how difficult it is to find a compatible donor. Patients with cPRA ≥ 85% face significantly longer wait times and higher mortality rates, making them ideal candidates for xenotransplantation.

I identified a recurring struggle of Rice students—conflicting exam schedules.

I approached the chair of our department to mentor me in solving this problem.

Generating an exam schedule for 4,000 students was a large-scale problem, and the infeasibility of directly matching classes with classrooms made it even more exciting.

I designed a two-phase algorithm using distinct Mixed Integer Programs (MIPs): the first MIP chooses which classes to split into multiple subsections, thereby making it feasible for the second MIP to timetable the exams.

This reduced conflicts by 90% while respecting university constraints and preferences of students.

Built a web messaging app with features including authentication, workspace/channel management, and real-time threaded message interactions using TypeScript, HTML, CSS, and utilizing JSON schema validation.

Developed a Go-based network-accessible NoSQL database API, designing concurrency with Go routines for parallel execution, concurrent data structures for safe data sharing, and server-sent events (SSE) for real-time updates.

Lagrangian Relaxation: Implemented the dual approach for handling complex constraints by moving them into the objective function with Lagrange multipliers, enabling decomposition of difficult problems into manageable subproblems.

Dantzig-Wolfe Decomposition: Developed the master-subproblem framework for solving large linear programs with block structure, using column generation to iteratively improve the solution by adding promising variables.

Benders' Decomposition: Created the "divide and conquer" approach for mixed-integer programs, separating complicating variables and using cutting planes to iteratively refine the solution space.

L-Shaped Method: Implemented the specialized Benders' approach for two-stage stochastic programming, handling uncertainty through scenario-based decomposition and optimality/feasibility cuts.

I designed a simulation-based optimization algorithm that searches for a kidney allocation policy that is equitable yet most effective in terms of post-transplant outcomes. Each policy was tested by simulating an allocation of roughly 12,000 kidneys for 90,000 waitlist candidates—a computationally heavy task. I implemented a parallel program that automatically designs and self-schedules new simulations and later gave a presentation covering our results at our center.

I founded and served as President of Rice's first undergraduate INFORMS chapter, creating a thriving community of students passionate about Operations Research.

We organized numerous events with experts from industry & academia, including guest lectures, workshops, and networking sessions.

Our flagship program, DecisionLab, was a semester-long project-based initiative where over two years, 70+ students developed OR projects addressing real challenges faced by other students.

Projects included roommate matching platform, dining hall schedule optimization, staff scheduling, and many more. Along with my teammates, we created a wholesome OR community at Rice, and our efforts were recognized with Magna Cum Laude at the Student Chapter Awards ceremony at the largest INFORMS Conference in Seattle. This experience taught me the importance of building bridges between theory and practice, and how collaborative environments can accelerate learning and innovation.