What should we order today?

An offline experiment, not a browser model

Candidate forecasts are fitted in Python and exported as compact JSON. The static site and the visitor's browser never train a model. Deep-learning families such as N-HiTS or N-BEATS can be added later as further offline adapters; they are omitted here because a poorly trained network would be a label, not evidence.

Candidate models

Baseline: the mean of all 260 observations, with future weeks sampled independently from that history. Statistical: additive damped Holt–Winters with a 13-week season, plus Croston, Syntetos–Boylan approximation (SBA) and Teunter–Syntetos–Babai (TSB) with smoothing constants 0.1. ML: a direct multi-horizon histogram gradient-boosted tree. Each horizon is a separate prediction from features known at the origin only (lags 1, 2, 3, 4, 13 and 26; rolling means, standard deviations and occurrence rates over 4, 13 and 26 weeks; the target week's 13- and 26-week seasonal position). Every point forecast is truncated at zero.

Chronological validation and Recommended

Models are refitted at rolling origins using only y[:origin]. Calibration origins are every second week from 104 to 176; validation origins are every fourth week from 188 to 248. The primary score is pooled H1–H9 RMSE; MAE and MASE (in-sample naïve scale) are reported alongside. Recommended is the lowest validation RMSE, with the model id breaking exact ties. Statistical is the same rule restricted to Holt–Winters, Croston, SBA and TSB. Percentage errors are avoided because zero-demand weeks would make them undefined or misleading.

Forecast uncertainty

For the baseline, 20,000 nine-week futures are independent draws from the observed history. For every other model, whole out-of-sample error vectors from the calibration origins are resampled jointly and added to the current point forecast, then truncated at zero. That keeps horizon dependence and the model's observed bias. A zero point forecast can still have positive uncertainty. The path-mean can therefore differ from the raw point; both are exported. The weekly interval is the 10th–90th percentile of those paths. It is pointwise, not an 80% simultaneous band.

One simulation, consistent horizons

Each path is cumulatively summed: Dₕ = d₁ + … + dₕ. All horizons use prefixes of the same paths. Quantiles use NumPy's inverted-cdf definition. Nonnegative demand makes every path total nondecreasing with horizon.

The stock target uses a quantile of these cumulative totals, never a sum of weekly upper bounds. Expected protection-period demand is the sum of that model's simulated weekly path means.

The replenishment decision

H = L + R, with R = 1 week
S = quantile_α(D_H)
Expected demand = sum of simulated weekly path means over H
Uncertainty buffer = S − expected demand
IP = on hand + on order − backorders
Requirement = max(0, S − IP)
Q = 10 × ceil(requirement / 10)

This is a periodic-review order-up-to policy with fixed lead time, a fixed ten-unit pack and zero current backorders. Demand coverage plays the role of a one-sided planning service target. It is not a measured fill rate, observed cycle-service level or guarantee against stockout.

The existing receipt is due at the start of week 2. The new order arrives at the start of week L + 1. Both count towards inventory position, but they are posted to their own weeks in the expected-stock schedule. Today's order cannot resolve a shortage before its arrival. There is no expediting, cancellation, lost-sales model, capacity limit or cost optimisation.

How the synthetic histories are generated

Smooth: 42 + 0.08t + 8 sin(2πt/13) + N(0, 2), rounded to a positive integer. Erratic: a 13-week seasonal level with a mild trend, lognormal size noise (σ = 0.65) and a 6% chance of a threefold surge. Intermittent: occurrence probability 0.12 + 0.0004t, plus 0.22 if the previous week was positive; positive sizes 40 + 0.03t + N(0, 3). Lumpy: occurrence 0.10 + 0.0003t, plus 0.25 after a positive week; positive sizes follow a weak 26-week pattern times a lognormal(−0.5, 1) shock. Zeros are observed zero demand, not missing values.

Generator version 2 uses NumPy Generator seeds 20260910–20260913. Each model's simulation seed is the scenario seed plus 1000 plus the model's index. There is no promotion, actual SKU, supplier, price or stockout-censored sales data.

What the uncertainty leaves out

Resampled errors assume future residual structure resembles the calibration window. They exclude parameter uncertainty, regime change, supplier delay and unseen extremes. Twenty thousand simulations reduce sampling noise; they do not create twenty thousand weeks of evidence. No accuracy, service attainment or commercial performance is claimed.

This is an independent educational demonstration using standard public methods. It does not reproduce the Priory Direct forecasting/procurement system or expose proprietary KTP implementation.

Background: Forecasting: Principles and Practice — prediction intervals; Syntetos, Boylan and Croston, “On the categorisation of demand patterns”, JORS 56 (2005); MIT — probabilistic inventory policies (PDF).