GB527 Unit 9 Demand Forecast Example

Three Forecasts Tested on a Year They Never Saw: A Unit 9 Demand Forecast for Aftermarket Irrigation Valves

[Student Name]

Purdue University Global

GB527: Global Operations

Unit 9 Demand Forecast

[Instructor Name]

[Date]

The manufacturer, its dealers and every sales figure are composite and illustrative; the methods and sources cited are real.

The Data

Platte Valve Works sells replacement valves and regulators to irrigation dealers, separate from the valves it ships to pivot manufacturers. Monthly aftermarket sales over two years were:

Year one: 265, 395, 734, 732, 460, 345, 314, 390, 581, 440, 312 and 271, for 5,239 valves.

Year two: 276, 406, 735, 712, 472, 387, 338, 396, 607, 530, 395 and 352, for 5,606 valves.

Plotted, the series has two peaks each year. The larger, in March and April, comes as dealers repair systems before the irrigation season. The smaller, in September, comes as farmers order retrofits after harvest. Demand grew about 7 percent from year one to year two.

The Test

Year one was used to set up each method. Each method then forecast year two one month ahead, using actual sales up to the month before. Accuracy was measured by mean absolute deviation (MAD), the average size of the error in valves, and mean absolute percentage error (MAPE), the average error as a share of actual sales. Hyndman and Athanasopoulos (2021) recommend testing forecasting methods on data not used to build them, because a method that fits its own history well may forecast poorly.

Exhibit 1: The Error Table

Three-month moving average: MAD about 168 valves; MAPE about 35.3 percent.

Simple exponential smoothing, alpha 0.3: MAD about 134 valves; MAPE about 27.9 percent.

Seasonal index model: MAD about 30 valves; MAPE about 6.5 percent.

Why the First Two Methods Fail

The moving average and exponential smoothing both forecast the next month from recent months. Neither has any way to know that March is different from February. In March of year two, exponential smoothing forecast about 362 valves; dealers bought 735. The forecast missed by 373 valves, more than the whole of a typical January. The moving average missed the same peak by even more, then forecast high in summer because the spring peak was still in its average.

Both simple methods chase the season instead of anticipating it, so they are lowest just before the peak and highest just after it.

The Seasonal Index Model

The seasonal model divides each month of year one by year one's monthly average of about 437 to obtain an index. March and April each have an index of about 1.68, meaning they run 68 percent above an average month; January's is about 0.61. The model forecasts each month of year two as a level, set at year one's average raised by an assumed 4 percent growth, about 454 valves, multiplied by that month's index.

This model forecast March of year two at about 763 valves against actual sales of 735, an error of 28. Across the year its MAD of about 30 valves is less than a quarter of exponential smoothing's.

Exhibit 2: Catching the Seasonal Model Drifting

A low average error can hide a bias. A tracking signal shows whether the misses keep leaning one way: it is the cumulative signed error expressed in units of the MAD measured up to that month. Values beyond about plus or minus four are a common warning limit.

Errors by month (actual minus forecast): 0, minus 5, minus 28, minus 49, minus 6, 28, 11, minus 10, 3, 72, 71 and 70.

Tracking signal: it fell to about minus 4.0 in April and minus 5.0 in May, then recovered, and rose to about 3.4 in November and 5.3 in December.

Two biases appear. In spring, the model forecast too high: the 4 percent growth assumption overstated demand in a season when dealers bought about the same as the year before. From October, the model forecast too low by about 70 valves a month, three months running. The cause was in the business, not the data: Platte signed six new dealers in Mato Grosso and Kansas over the summer, and their autumn orders added demand the model had no way to know about.

What the Errors Cost

Forecast error is not only a statistic. Heizer et al. (2020) point out that forecasts drive scheduling, purchasing and staffing, so the cost of an error depends on what it causes. Under exponential smoothing, the March miss of 373 valves would have left dealers waiting in the busiest weeks of their year, and the summer over-forecasts would have built stock that sat until the next spring. Under the seasonal model, the autumn under-forecast of about 70 valves a month meant three months of tight stock and some expedited orders for the new dealers. At Platte's margins, an expedited shipment costs about $45 more than a planned one, so the autumn bias cost roughly $9,000 in freight alone, small next to what the simple methods would have cost but large enough to justify watching the tracking signal.

Recommendations

Use a seasonal method with updating. Move from fixed indices to a method that updates its level, trend and seasonal indices each month, such as Holt-Winters exponential smoothing, which Hyndman and Athanasopoulos (2021) describe for data with trend and seasonality.

Watch the tracking signal monthly. Treat a value beyond plus or minus four as a prompt to look for a cause, not only to adjust the numbers.

Add business information. Ask the sales team each month for changes in the dealer network and large known orders, and adjust the forecast for them. Chopra and Meindl (2019) recommend combining statistical forecasts with market intelligence, because a model can only project patterns already in its data.

Forecast in ranges. Report each month's forecast with a range based on recent errors, so that inventory and production planning can allow for uncertainty.

Use in Planning

A better aftermarket forecast feeds the seasonal reorder point from Unit 5 and the capacity planning from Unit 3. The March and April peak, now forecast within about 30 valves, should set the start of Saturday shifts and the timing of the higher reorder point for solenoid coils.

Limits

Two years of data provide only two observations of each month's seasonal pattern, so the indices are imprecise. A drought year or a sharp change in crop prices could shift the pattern in ways the history does not show. The forecast should be rebuilt each year with the added data, and the seasonal indices compared with the year before to see whether the pattern itself is shifting.

References

Chopra, S., & Meindl, P. (2019). Supply chain management: Strategy, planning, and operation (7th ed.). Pearson.

Heizer, J., Render, B., & Munson, C. (2020). Operations management: Sustainability and supply chain management (13th ed.). Pearson.

Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and practice (3rd ed.). OTexts.