Demand forecasting for planning

Saffron Wharf Supply (a fictional household-goods distributor) sells water heaters to retailers. Demand peaks every winter, and the January order has to be confirmed with the regional assembler in the last week of December, when the year's figures are complete. Last winter the warehouse ran short in January, and the year before it carried hundreds of unsold heaters through the summer.

The head of supply planning has asked you — the company's analyst — to replace the current rule of thumb (“order what we sold in the same month last year”) with a forecasting process that is tested, explained and honest about uncertainty. Your work will be reviewed by:

• The head of supply planning, who owns the January order and wants one number plus a defensible range;
• The finance controller, who sees unsold stock as tied-up working capital (for this scenario, assume SAR 70 to carry one unsold heater to the next winter: storage, handling and the cost of capital);
• The sales director, who sees every stock-out as lost margin (assume about SAR 260 of gross margin per heater a retailer could not get).

Both costs are planning assumptions for a fictional company, not industry figures.

Questions. (1) What do the data look like and can they be trusted as they are? (2) Which forecasting method actually forecasts best on data it has not seen? (3) How uncertain is the forecast, and are the usual prediction intervals believable here? (4) How many heaters should be ordered for January 2025, and why?

Constraints. The planning team has the lab's forecasting tools (benchmarks, exponential smoothing, Holt–Winters) and a spreadsheet; no bespoke software. The method must be re-run every month by someone who is not a statistician, so simpler wins unless a complex method is clearly better.

The data. monthly_demand has 288 rows: 96 months (January 2017 – December 2024) of units ordered by retailers for each of three product lines, in long format. You will work mainly with the water-heater series. The dataset is synthetic: it was generated to behave like real demand data (trend, seasonality, noise and one structural change), but it describes no real company and is not evidence about any real market.