Inspect the mechanism.

NPV = sum of cash flow at t divided by (1 + r)^t, with initial cash at t = 0. NPV sign is evaluated as an exact rational from the canonical decimal representation of the validated JSON numbers. The JSON export retains the exact fraction and a rounded forty-significant-digit decimal; charts use its Number approximation. IRRs are the distinct positive roots of the exact canonical-decimal cash-flow polynomial in x = 1 / (1 + r). Square-free reduction and a BigInt Sturm chain certify the count; rational intervals isolate each root before nearest-even Number rate conversion. DSCR = CFADS / debt service for periods with positive debt service. Sensitivity holds every cash flow constant while moving the discount rate; the operating stress changes future cash flows and CFADS by 20%. First undiscounted recovery uses exact canonical decimal cumulative cash balances and within-period interpolation. Later deficits do not erase the first recovery.

Find the cash-flow structure that survives a hurdle rate and debt-service stress.

Effective stage capacity = nominal capacity × availability. Serial throughput = minimum of demand and effective stage capacities. Chain unit cost = sum of variable cost + sum of annual fixed cost / actual annual throughput. USDm divided by Mt gives USD/t. Each expansion case increases one nominal capacity by 20%; availability stress reduces every stage by 10 percentage points. Capacity products, throughput, demand gaps and constraint membership use exact rational arithmetic for each canonical decimal input; plotted quantities and costs use numeric approximations.

Locate the binding stage, expose stranded expansion and price the whole chain.

Weights are normalised to sum to one. Cost and risk are minimised, impact and readiness maximised. Each raw criterion maps linearly to 0 to 1 over the current alternative set; equal values receive 0.5. Weighted score = 100 × sum of normalised weight × normalised criterion value. A Pareto alternative is not weakly dominated on all four raw criteria with strict dominance on at least one. Sensitivity shifts each normalised weight by ±20 percentage points, capped at 0 or 100%, and scales other weights proportionally. Canonical decimal normalisation, contributions, ranking and sensitivity redistribution use exact rational arithmetic. Released weight follows positive supplied weights; equal-thirds redistribution is used only when every other weight is exactly zero. Tied exact scores use literal name order independent of browser language for consistent display; the model displays every equal leading alternative and implies no strict preference.

Make preferences visible, inspect the efficient frontier and test ranking fragility.

PV lifecycle cost includes acquisition at t = 0, replacements at each service-life multiple strictly before the horizon, annual opex, escalated energy and downtime, less supplied horizon residual. Energy price in year 1 equals the input price, then compounds annually. Equivalent annual cost divides lifecycle PV by the ordinary annuity present-value factor. Savings hurdle divides incremental fixed lifecycle PV (acquisition, replacements and residual) by the annuity factor. Positive values require that much annual operating saving. Bid totals are ordered by their computed lifecycle present value. A tie warning applies only to the same computed value, with a stable name ordering. Equal computed costs use literal name order independent of browser language for consistent display; no economic superiority is implied by that order.

Compare like-for-like lifecycle costs, replacement burdens and negotiation hurdles.

Expected value = prior × success payoff + (1 − prior) × failure payoff. Bayes updates the prior separately after a positive and negative test. Branches of probability zero have no posterior. EVSI = expected best payoff after the imperfect test − best payoff before it. EVPI is the analogous value of perfect state knowledge. Net information value = EVSI − test cost. Payoffs are assumed to exclude this test cost. Joint signal-state masses, action rankings, EVSI, EVPI and the net-value sign use exact rational arithmetic for canonical decimal inputs. Only an exact zero is labelled break-even. Tied action values use literal name order independent of browser language for consistent display; this ordering does not establish a strict payoff advantage.

Discover whether an imperfect test changes the preferred action enough to pay for itself.

PERT mean = (optimistic + 4 × most likely + pessimistic) / 6. Variance = ((pessimistic − optimistic) / 6)^2. Forward CPM gives earliest start/finish; backward CPM gives latest start/finish; total float = latest start − earliest start. Every critical path is a start-to-finish path of zero-float activities with contiguous earliest times. At most 50 are displayed. Deadline probability uses a normal approximation with variance summed on the first displayed critical path. PERT means, CPM dates, float and path membership use exact rational arithmetic for canonical decimal inputs. Positive float remains positive at every supported scale.

Expose precedence, schedule float and the assumptions behind a completion estimate.

Each measure reduces remaining energy demand, adds any new demand, then adds renewable supply. Renewable use is capped at demand; excess supply is curtailed. State updates use the canonical decimal input values before numeric display conversion. Annual emissions = grid MWh × grid factor + renewable MWh × renewable factor. The balance is evaluated before numeric display conversion; separately displayed totals can hide a small genuine reduction. Annualised capex = capex / annuity present-value factor. Incremental annual cost = annualised capex + measure opex − incremental energy-cost saving. Marginal abatement cost = incremental annual cost / positive incremental annual emissions reduction. Sequence determines the attribution. Marginal abatement cost is evaluated for each strictly positive canonical decimal emissions reduction, including small positive values, without an absolute floor. A zero or negative reduction has no defined abatement denominator. The reversed-order physical diagnostic compares the canonical decimal annual emissions balances exactly before numeric display conversion. It reports a genuine order effect without an absolute emissions floor or floating-point allowance.

Reconcile energy before pricing abatement, then expose the effect of sequence and factor choice.

Adjusted annual benefit = stated annual benefit × confidence × readiness. These are explicit judgement multipliers, not measured probabilities. For each candidate, compute the unselected prerequisite closure, cost, effort and adjusted annual benefit. Choose the affordable closure with highest marginal annual benefit / investment cost; ties resolve by ID. Repeat with the remaining budget and effort. Selected sequence follows dependencies. Zero-cost positive-benefit bundles take precedence, subject to effort. Budget and effort admission compare exact sums of the canonical decimal input numbers, without an absolute feasibility allowance. JSON resourceEvaluation retains the exact decimal capacity, used and remaining accounts. Tied bundle ratios use literal identifier order independent of browser language for consistent selection; this remains the declared heuristic rather than proof of an optimum.

Make prerequisite bundles, constrained capacity and benefit assumptions explicit.

Gross expected loss = probability × event impact. Controls share one Bernoulli availability state. Residual expected loss = gross expected loss × [(1 − reliability) + reliability × (1 − prevention) × (1 − mitigation)]. Expected avoided loss = gross expected loss × shared availability × (prevention + mitigation − prevention × mitigation). Net control value = avoided expected loss − annual control cost. Stress changes gross probability and impact and reduces control reliability; probabilities cap at one with an explicit warning. Residual event probability is a marginal; severity is conditional on an event. Break-even availability = annual control cost / [gross expected loss × (prevention + mitigation − prevention × mitigation)], if attainable. Event-conditional severity is unavailable when the marginal event probability is zero. A zero monetary severity remains meaningful when the event population exists. Complements, stress clipping, control-value sums and break-even comparisons use exact rational arithmetic for canonical decimal input numbers. JSON exports retain numerator, denominator and a forty-significant-digit decimal; metrics and charts use numeric approximations. Equal exact residual losses use literal name order independent of browser language for consistent display; this name order is not a causal risk distinction.

Connect event mechanisms to control reliability and challenge expected-loss resilience.

Expected new customers each month = acquisition spend / CAC. Acquisition occurs at the beginning of the month, with first revenue in that month. For cohort age a: active customers = cohort size × (1 − churn)^a; price = initial price × (1 + expansion)^a. Contribution = revenue − active customers × variable cost. Monthly operating profit subtracts acquisition spend and fixed costs. Working capital = revenue × receivable days / 30 + variable cost total × (inventory days − payable days) / 30. Cash flow = operating profit − change in working capital. Finite-horizon contribution LTV discounts one customer’s expected contributions at ages 0 to horizon − 1. CAC payback uses undiscounted cohort contribution. Its first recovery crossing is evaluated from exact canonical JSON-number decimals, without a numerical tolerance.

Reconcile acquisition cohorts, contribution and working-capital cash before celebrating revenue.