LightGBM
Learns from the factory’s past sales: recent sales, lagged values, region, product and calendar patterns. Its latest design also learns how a weekly level is distributed across days.
Local training learns the factory’s sales patterns.
01 / The business problem
Predicting Water Demand More Accurately
Comparing LightGBM with Timestral to improve daily and weekly sales forecasting.
5 major Oman regions × 2 products = 10 sales series
For each region and bottle size (200ML or 330ML), we estimate the next 28 days of recorded sales. The factory can use that forward view to anticipate demand and reduce the risk of planning for too little.
Forecasts help planning. We cannot claim fewer actual stock-outs: historical stock records were not available.
The idea in one picture
02 / How the forecast is made
Two different ways to read sales history.
Both models start with past recorded sales and produce the next 28 daily estimates for each of the ten series. Neither gets to see future actual sales when making the forecast.
Timestral-209M
A pretrained time-series model. We pass in ten historical daily sales sequences together; its weights are not fine-tuned on our Oman data. One forecast cutoff produces 28 future days per series, including P50 and P60 estimates.
Frozen pretrained model, applied to our historical sales.
What Timestral actually receives
One batch × ten series × the available historical days. Nothing from after the forecast cutoff is included.
——days of context across matched origins
03 / From days to weeks
Forecast 28 days. Add them in groups of seven.
Days 1–7 become Week 1; Days 8–14 become Week 2; Days 15–21 become Week 3; Days 22–28 become Week 4. Each model predicts all 28 days from the same starting point.
One product in one region · 28 future days
Four rows × seven days = four weekly forecast totals. This happens separately for each of the ten region–product series.
Illustrative seven-day example
100 + 120 + 105 + 90 + 80 + 115 + 110 = 720 units
These teaching values are invented; the benchmark comparisons below use saved historical forecasts.
Why weekly error can be smaller
Actual 100 + 200; predicted 150 + 150. Daily errors total 100 units, but both weekly totals are 300: weekly error is zero. Opposite daily misses can cancel after aggregation.
04 / The matched comparison
Timestral makes the smaller absolute error.
Same actual sales, ten series and 13 non-overlapping historical 2024 forecast starts for each model. WAPE means total absolute forecast error divided by total recorded sales. Lower is better.
| Forecast | Daily WAPE ↓ | Weekly WAPE ↓ | Signed bias |
|---|
Daily forecasting error
Total daily absolute error ÷ total recorded sales
Weekly forecasting error
Sum seven days first; then measure weekly absolute error
—less weekly absolute error for Timestral P50 versus LightGBM; the relative reduction in daily error is —. These are reductions relative to LightGBM’s error, not percentage-point changes.
One real historical forecast · selected near the typical error level
Actual salesLightGBMTimestral P50
—
P60 keeps similar measured daily and weekly WAPE, but shifts the forecast upward. These are historical comparisons, not guaranteed future performance.
05 / Put the errors in business units
Imagine 1,000,000 actual sales units.
Scale the measured error rates to an easy-to-read, hypothetical volume. This is not a claim that the factory sold exactly one million units.
Absolute forecast error = actual sales × WAPE
Weekly absolute forecast error
LightGBM — · Timestral P50 —
— fewer error units
Cumulative absolute error measured after forecasts are added into weeks.
Daily absolute forecast error
LightGBM — · Timestral P50 —
— fewer error units
Cumulative absolute error measured before weekly aggregation.
Same illustrative sales volume · two different error resolutions
Bar lengths represent cumulative absolute forecast deviations in sales units. Weekly and daily errors are different ways of scoring the same forecasts, not volumes to add together.
What this does not mean. Fewer forecast-error units do not automatically equal saved inventory, avoided waste, extra sales or financial savings. Those claims require real stock and operating data.
06 / Choosing the right forecast level
P50 is central. P60 leans slightly higher.
P50 is the model’s median estimate, and the best central forecast here. P60 is its 60th percentile — not “60% more demand” — and trades fewer underforecast deviations for more overforecast deviations.
Timestral P50
Best central estimate
Net signed bias — · underforecast volume — · overforecast volume —.
Timestral P60
Optional modest upper estimate
Net signed bias — · underforecast volume — · overforecast volume —.
Signed bias · direction of net error
Left: forecast totals below recorded sales. Right: above. P60 crosses zero into mild net overforecasting.
At 1,000,000 illustrative sales units
—fewer units of cumulative underforecast error with P60 versus P50.
—additional units of cumulative overforecast error. Both are deviations from observed sales, not physical shortages or leftovers.
Where the error goes · illustrative one-million-unit scale
■ Underforecast ■ Overforecast. Divide either deviation total by actual sales to get its percentage. The percentages add to daily WAPE; their difference is signed bias. Near-zero bias does not guarantee low absolute error.
07 / The decision
Approve Timestral-209M v1 as the forecasting baseline.
It produced the best matched central daily and weekly results among the models compared. Keep the forecast separate from the eventual decision about how much to produce.
Default
P50 · expected sales view
Use the central 28-day forecast and its four weekly totals as the starting point for demand planning.
Optional
P60 · moderately higher view
Show alongside P50 when a higher estimate is useful, with its increased overforecast error made explicit. Both native levels come from the same supported Timestral inference.
The proposed planning flow
A forecast can support a planning decision. Determining an inventory-optimal production quantity requires operational information this research did not have.