Dynamic Hybrid Lunar Logistics Optimization

MCM 2026 · Problem B · Team 2630693

Modeling and programming lead · Finalist (top 1%)

How should a 100,000-person lunar colony receive 100 million metric tons of construction material? Our model compares a space elevator, reusable ground rockets, and a dynamic hybrid strategy that changes as lunar resource production matures.

Workflow comparing the space-elevator, reusable-rocket, and dynamic hybrid lunar logistics systems — Three candidate logistics systems: a low-cost space elevator, a faster reusable-rocket fleet, and a dynamic hybrid that bridges the elevator's early capacity gap.

The modeling idea

The elevator is inexpensive per kilogram but initially bottlenecked by immature In-Situ Resource Utilization (ISRU). Ground rockets deliver cargo sooner and can later join the apex fleet, but relying on them throughout the mission is costly and carbon intensive. We therefore let the allocation between both systems evolve over time.

StrategyTimeCost

Space elevator382 years$17.21T

Ground rockets334 years$31.88T

Dynamic hybrid366 years$20.16T

Optimization and robustness

I led the mathematical modeling and programming. The final workflow combined nonlinear simulation, Differential Evolution, a 5,000-run Monte Carlo reliability study, and sensitivity analysis. The optimized hybrid policy shifts through rocket-dominant, transition, and elevator-dominant phases as ISRU matures.

Differential Evolution search, convergence, and cost-time trade-off plots for the lunar logistics model — Differential Evolution explored 1,301 candidate policies and converged on a three-phase hybrid allocation.

Three-phase cargo allocation in the optimized hybrid logistics strategy — The optimized allocation changes with ISRU maturity instead of using a fixed split.

Cost-time trade-off frontier comparing lunar logistics strategies — The selected policy balances the low cost of the elevator with the speed of rockets.

Sensitivity tornado chart for the hybrid model — Sensitivity analysis identifies maximum elevator allocation as the dominant decision variable.

The hybrid plan saves about $12 trillion relative to a rockets-only strategy and shows only 3.2% time and 2.1% cost degradation under modeled failures. The submission received the MCM Finalist Award, placing in the top 1%.