Industry: Environmental Product: ModelRisk Application: Waste-stream volume against processing capacity and the statutory diversion target
A regional waste authority sized a new processing line at 520,000 tonnes a year of permitted throughput against a current arisings figure of 470 kt — a comfortable 50 kt of headroom on paper. The deterministic plan also showed a recycling programme running at 62%, safely clear of the 60% statutory diversion target. Both conclusions were point estimates, and both were wrong about the thing that mattered. Run forward over the planning horizon with uncertain economic activity and growth, the mean arisings climb to 511 kt, the probability of exceeding the 520 kt capacity in a given year is 42%, and the chance of actually meeting the 60% diversion target is barely a coin-flip at 52%.
Waste arisings are not a constant. They have a seasonal shape — summer green waste and a December festive peak — and, more importantly, they ride a macroeconomic tide: a boom year lifts consumption and packaging across every month at once, and five years of compounding growth can shift the whole distribution before the new line is even commissioned.
We built annual arisings month-by-month: a baseline seasonal profile, multiplied by a shared per-year economic-activity factor (LogNormal, sigma_log 0.10), a five-year growth multiplier from an uncertain annual growth rate (Normal, mean 1.5%, sd 1.2%), and a small per-month idiosyncratic LogNormal(0, 0.06) weather-and-events noise. The shared economic factor is the crux. Because it scales all twelve months together, the months of a year are not independent — the correlation between January and July arisings across simulated years is 0.79. That single design choice keeps the annual total's coefficient of variation at 11.7%, against the 3.8% an independent-month model would have produced by the central-limit theorem. An i.i.d. model would have made the annual figure look three times more certain than it is and would have priced the capacity breach as a rounding error.
Read off the utilization curve: the median year runs the line at 98% of permitted capacity and the P90 year at 113% — meaning one year in ten, arisings exceed the permit by more than a tenth. The probability of running over 100% capacity in any single year is 42%. A deterministic 470-kt-versus-520-kt comparison reports "8% spare capacity"; the simulation reports a line that is effectively full in the median year and over-permit in nearly half of them, with the overflow forced to landfill or costly merchant export.
Diversion is a fraction, so it is modelled as a Beta programme-effectiveness draw (mean ~62%), then coupled to the same economic factor — boom years dilute the capture of clean recyclables — and penalised when arisings spill over capacity and get landfilled at zero diversion. The result: a mean achieved diversion of 60.3%, but a P10 of 46.0% and a P90 of 74.3%, and only a 52% probability of meeting the 60% target. The same boom year that breaches capacity also pushes diversion down, because more waste arrives than the recycling streams can cleanly absorb — a coupling that two separate point estimates would never reveal.
Against the 42% baseline breach probability, the multi-year growth-rate uncertainty is the largest lever (±5.5 points) — unsurprising, since a small error in the assumed growth rate compounds over five years into a large error in commissioning-year volume. The shared economic-activity factor is second. The permitted-capacity headroom is third — which quantifies exactly how much extra permit the authority would need to buy down the breach risk. Seasonal amplitude and per-month weather noise barely register, confirming that the risk lives in the year-level common factors, not in month-to-month wobble.
Sizing a waste line to a single arisings number assumes the future is one number; the diversion target and the capacity limit are both breached by the same boom year, and only a model that lets one economic factor move every month at once can show how often that year arrives.