Computing for Isotope-Supply Logistics

Planning production, decay, storage, and delivery of isotopes whose inventory changes on its own over time.

The moving-inventory problem

Isotopes are unusual logistics items: they decay. A stock of tritium shrinks with a 12.3-year half-life whether or not it is used, so an inventory plan must account for time itself as a sink. Supply logistics for isotopes therefore combines ordinary scheduling with radioactive-decay bookkeeping.

What is modeled

• Production rate versus demand over time
• Decay of stored inventory between production and delivery
• Storage capacity and safety limits
• Lead times and the buffer needed to absorb variability

The decay term

Any inventory model for a decaying isotope carries an exponential loss term. Stock at a future time equals stock now times the decay factor, plus production, minus withdrawals. Over long storage the decay term dominates planning: hoarding a short-lived isotope is self-defeating.

import math

def inventory(I0, half_life, days, produced_per_day, used_per_day):
    lam = math.log(2)/half_life
    I = I0
    for _ in range(days):
        I = I*math.exp(-lam) + produced_per_day - used_per_day
    return max(I, 0.0)

Why it matters at Kronos

The Hyperion breeder produces tritium as part of closing its own fuel cycle, and the isotope platform is a strategic dimension of the program. Logistics computing keeps the tritium bookkeeping honest across production, storage, and use, and separates the bankable near-term picture from longer-horizon isotope roles. This is inventory and scheduling analysis; it deliberately carries no economics.

Uncertainty

Production and demand are uncertain, so plans are stress-tested against ranges rather than single forecasts. The output is a buffer policy that stays feasible across scenarios, not a brittle just-in-time schedule.