Senior Numerical Optimization Engineer

ABOUT THE TEAM

Maritime Digital Production (MDP) is the software and digital systems function within Anduril's Heavy Metal division. We build and deploy the full technology stack that powers Anduril's shipbuilding factories: the data infrastructure that makes every machine and sensor visible in real time, the manufacturing execution system (ArsenalOS) that workers and planners use every shift, the scheduling engine that replans production in minutes instead of days, and the AI systems that eliminate manual toil from both the shop floor and business operations.

MDP operates at the boundary between Operational Technology and Information Technology. Our systems live where factory-floor machines, edge compute, and OT networks meet enterprise platforms and cloud infrastructure. We incubate solutions close to the production line, validate them with real operators building real hardware, harden them for reliability and security, and then scale them across multiple sites. The environment is fast, physical, and consequential. When our systems go down, production stops. The output of our work is not a dashboard: it is a ship.

This is not a support function. It is a strategic investment by Anduril in the premise that digitizing the manufacturing lifecycle end-to-end, from engineering definition through scheduling through execution through field feedback, is how Heavy Metal will out-build, out-adapt, and out-scale the traditional defense industrial base. MDP is scaling from a founding team to 70+ engineers across multiple U.S. sites. You will be joining early, working on hard problems with real operational stakes, and shaping how manufacturing software is built at Anduril from the ground up.

ABOUT THE JOB

As a Senior Numerical Optimization Engineer on this unique initiative, you will own the scheduling optimization core that decides when and how ships get built. This project represents a shipyard's work as a graph of 100,000+ manufacturing operations carrying precedence, spatial, resource, and qualification constraints, then continuously replans as the factory changes. You will formulate that problem, build and benchmark the solvers that attack it, and keep them fast and trustworthy enough that a new plan can reach the floor within minutes of a disruption.

This is a research-grade problem with production consequences. Resource-constrained project scheduling at this scale is NP-hard, there is no ground truth to measure against, and a schedule has to be stable enough that the shop floor is not thrashed every time it changes. You will have the latitude to develop novel approaches and the obligation to ship them.

WHAT YOU'LL DO

• Formulate shipyard production scheduling as a mathematical optimization problem covering precedence with lag, disjunctive spatial exclusion, multi-resource capacity with qualification matching, calendars and shifts, and material availability.
• Own the solver-agnostic scheduling interface, integrate commercial and open-source solvers behind it, and benchmark them against each other on makespan, stability, resource utilization, and solve time.
• Build the two-tier replan path: fast local repair that returns a feasible schedule in seconds for a bounded affected subgraph, and background global re-solve that runs for minutes and swaps in when it beats the incumbent plan.
• Develop the stability objective that keeps a replan from needlessly moving work the factory has already staged, and the policy that decides when a better plan is worth the churn.
• Establish what "good enough" means when there is no ground truth: LP relaxation lower bounds, best-of-N ensemble upper bounds, quality ratios, and solution-quality regression tests that run on every change.
• Research and evaluate approaches beyond the V1 solver, including decomposition, metaheuristics, rolling-horizon methods, and non-traditional hardware (wafer-scale compute, quantum annealing) where they earn their place.
• Turn disruption events into replans: determine blast radius across the operation graph, scope the re-solve, merge the result into the live schedule, and resolve boundary conflicts.
• Build adaptive planning templates that generate recovery work (E.g. a damaged part that must be removed, replaced, and reinspected) by composing geometric queries with scheduling logic.
• Compose scheduled operations into work orders a manufacturing execution system can dispatch, and recompose them when the plan changes.
• Write production-quality code with comprehensive tests, participate in code review and architectural discussion, and instrument your systems so solution quality is observable, not just uptime.
• Partner with manufacturing engineers, planners, and factory operators to turn how the yard actually works into constraints and objectives.
• Work alongside the computational geometry engineer who derives geometric precedence from CAD, and the data engineers who supply the operation graph and the live factory event stream.
• Leverage AI tooling (coding assistants, automation) in your development workflow and contribute to team engineering practices.
• Join an on-call rotation supporting production scheduling systems.

REQUIRED QUALIFICATIONS

• 5+ years of experience building production software systems, ideally in a fast-paced environment.
• Deep expertise in numerical optimization, including linear programming, mixed-integer linear programming, constraint programming, combinatorial optimization, or metaheuristics.
• Demonstrated ability to take a real-world problem, formulate it as a mathematical model, and carry that model all the way into a system other people depend on.
• Hands-on experience with optimization solvers and libraries (E.g. Gurobi, CPLEX, OR-Tools, SCIP, PuLP, CVXPY, Pyomo), including the judgment to recognize when a given solver or formulation is the wrong tool.
• Expert proficiency in Python for scientific computing and robust software development, with strong foundations in numerical computing libraries (NumPy, SciPy, Pandas).
• Strong theoretical and practical grounding in graph algorithms, constraint satisfaction, and computational complexity analysis.
• Experience with scheduling or resource allocation at a scale where exact methods stop working, and the judgment to know when to stop optimizing.
• Experience building systems that operate reliably under real operational constraints such as high availability, latency budgets, or degraded inputs.
• Excellent written and verbal communication, including the ability to explain an optimization trade-off to a factory planner who does not care about duality gaps.
• Advanced degree in Operations Research, Applied Mathematics, Computer Science, Industrial Engineering, or a related quantitative field, or equivalent depth built in practice.
• U.S. Person status is required as this position needs to access export controlled data.

PREFERRED QUALIFICATIONS

• Ph.D. in Operations Research, Applied Mathematics, or a closely related field, with publications or production work in scheduling or large-scale optimization.
• Experience with resource-constrained project scheduling (RCPSP), job shop scheduling, or precedence-constrained scheduling in a production setting.
• Experience with dynamic or online rescheduling: replanning under uncertainty, schedule stability, and rolling-horizon methods.
• Experience benchmarking solvers or algorithms where no ground-truth optimum exists, using dual bounds, anytime curves, or ablation across constraint classes.
• Experience with metaheuristics (genetic algorithms, simulated annealing, tabu search, large neighborhood search) and decomposition methods (Benders, column generation, Lagrangian relaxation).
• Experience with performance-critical implementation in C++ or Rust for optimization kernels or hot-path graph traversal.
• Familiarity with graph databases or large in-memory graph representations at 100K+ nodes.
• Experience in manufacturing, industrial, or OT-adjacent domains, and familiarity with BOM structures, manufacturing routing, work centers, and MES, ERP, PLM, or APS systems.
• Exposure to traditional and non-traditional optimization hardware e.g. GPU-accelerated solvers, HPC, or quantum annealing and QUBO formulations.
• Experience in hyper-growth startup-like environments, with demonstrated success balancing speed, ambiguity, and long-term system health.
• Familiarity with frontier AI tooling, AI coding assistants, and AI-enabled software development workflows.
• Experience in shipbuilding, aerospace, or complex discrete manufacturing.
• Eligible to obtain and maintain a U.S. Secret security clearance.