High-frequency forecasting for grocery point-of-sales: intervention in practice and theoretical implications for operational design


Food waste in grocery supply chains may exceed one third of the total volume, depending on the category. To address this problem effectively, grocery retailers are introducing automated systems for more efficient store replenishment and dynamic pricing. The stock keeping unit (SKU) and store level forecast is pivotal in these operations management solutions, but operationally challenging. Large grocery retailers have millions of SKU-store combinations that depending on the operational application would need to be forecasted on a weekly, daily, hourly, or even 15-min frequency. However, in grocery it is challenging to account for demand variation at high frequencies without introducing manual decisions into the process of forecast model configuration. To investigate the limits of current practice and explore opportunities of technology-enabled change, we explore how an advanced forecasting method for electricity demand, called TBATS, can automate daily forecasting for grocery store replenishment. Adopting an interventionist approach, we explore the implications for the design of the operational process in the operational setting provided by the case company. We find that TBATS can produce high frequency base forecasts for the SKU-store level accurately for a period exceeding 3 months. This finding points to the opportunity of shifting operational focus from recalculating forecasts to monitoring forecast errors. Introducing variable, even indefinite re-training frequencies for forecasting models is a significant change of the forecasting process for situations where monitoring requires less computation than retraining, potentially reducing the time and cost associated with increasing the forecast frequency.

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  1. 1.

    On the retail supply chain level, van Donselaar et al. (2006) investigated daily replenishment, but not forecasting, of perishables in six supermarkets. Daily forecasting of aggregate replenishment orders placed to the distribution center using different types of demand signals (Narayanan et al. 2019) and different types of demand representations (Sillanpää and Liesiö 2018) was recently investigated. Note that daily forecasting of aggregate replenishment orders is different by an order of magnitude from daily forecasting in individual supermarkets.

  2. 2.

    See Pulkka (2020) for a further description of the components and functionality of the Bayesian Regression Model applied in the context of grocery retailing.


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Appendix 1

BATS and TBATS models

De Livera et al. (2011) introduced both BATS and TBATS models. BATS cannot handle non-integer seasonality, which is why TBATS was created. TBATS uses Fourier terms to represent seasonal components in a trigonometric manner, thus allowing for non-integer seasonality. The components of both models are explained in Table 8.

Table 8 Description BATS and TBATS model components

Comparison of approaches for high frequency forecasting

Table 9 Summary of the comparison between selected high frequency forecasting models

Appendix 2

Evaluation criteria

The case company noted the importance of highlighting measures that show that a forecasting model(s) has reduced large forecast errors/ biases significantly when compared to another model, as this is crucial in practice. Due to the occurrence of zero sales, we disregard scale independent measures as they become undefined in the presence of zeros. We also calculate the forecast bias separately because even though some amount of bias is permissible, it is necessary to escalate extreme biases to management to be dealt with manually. We use four measures overall (explained in detail in Table 10):

  • Root Mean Square Error (RMSE) and Mean Absolute Error (MAE): for forecast accuracy

  • Mean Error (ME) and bias coefficient: for forecast bias

RMSE, MAE and ME are well established in literature while the bias coefficient was proposed recently by Kourentzes, Trapero, Svetunkov (2014). We use the bias coefficient to calculate the number of SKU-stores showing extremely high biases (the value of ‘extreme bias’ can be decided based on the industry and products in question). Since they most highlight/ penalize large errors, we pay special consideration to the RMSE as the primary measure of forecast accuracy and extremely high bias as the primary measure of forecast bias.

Table 10 Measures of forecast accuracy and bias

Aggregation and presentation of results

It is necessary to aggregate forecast errors for ease of evaluation and comparison between solutions. We chose the entire forecast period (126 days) and product category as aggregation levels for all four measures.

Some additional steps are also needed for the RMSE, MAE and ME. Since different products can have vastly different sales volumes even within the same product category, these forecast errors should be weighted based on product volume. We also present these results relative to the current solution for increased readability (since the original numbers are quite small). This process is summarized in Table 11.

Table 11 Methods of aggregation for forecast measures

Level of automation

Automation eliminates user involvement and thus reduces effort. However, computational efficiency is likely to decrease when complex methods are fully automated. Therefore, the feasibility of automating such methods and whether other aspects such as increased accuracy can be used as tradeoffs have to be discussed before they are used practically. When measuring the performance of the new solution, we calculated the time taken to create the forecasting model(s) and forecast as a measure of computational efficiency. These numbers were discussed with case company representatives to understand their practical relevance. We also calculated the time to forecast using an assumed model (in place of the case company’s current solution) in order to perform a more direct comparison.

Transparency and ease of usage

Forecasting models are not used by researchers or statisticians in business contexts, but usually by nonprofessionals in the fields of statistics and numerical modeling. Therefore, the new solution must ideally be intuitive and easy to use. We discussed and compared the new solution’s complexity with the current solution, with feedback from the case company. It was also necessary to consider if there are justifiable tradeoffs for decreased transparency, which we reasonably expect with a more intricate forecasting model such as TBATS.

Appendix 3

Monthly box plots

Fig. 3

Category 1 product sales per month

Fig. 4

Category 2 product sales per month

Fig. 5

Category 3 product sales per month

Fig. 6

Category 4 product sales per month

Daily box plots

Fig. 7

Category 1 product sales per day

Fig. 8

Category 2 product sales per day

Fig. 9

Category 3 product sales per day

Fig. 10

Category 4 product sales per day

Appendix 4

Practicalities in using the intervention

Since the new solution is fully automatic, a user simply has to have the sales data in a format that can be read by RStudio. Data can be imported into RStudio in a variety of formats including csv, xls and xlsx. This solution currently cannot be used for new product forecasting; therefore, it is recommended to have at least a few weeks of sales data to train the TBATS model.

The user can change certain parameters easily, such as the frequencies considered when training the TBATS model(s), training period for the TBATS model(s), the number of forecasts produced, whether a single or multiple SKUs are forecasted etc. Currently, the unified and segmented approaches are run separately (the user can choose which approach to use). However, this can easily be modified so that the approach is chosen automatically based on some criteria (for e.g. the product category). Rolling forecasts and long forecasts are also separately calculated based on the user’s choice, but this too can be modified in a similar manner.

It is also possible to modify the technical parameters of the TBATS model, such as:

  • Whether or not to use the Box-Cox transform, trend, damping parameter for the trend and ARMA errors

  • The lower and upper limits for the Box-Cox transform

  • The values (p and q) for ARMA errors

However, this is generally unnecessary since all such possible scenarios are automatically tried out and the best options are chosen to train the TBATS model. Modifying these parameters could be useful, for e.g. if it is clear that the time series in question does not need any transform because it is linear (Box-Cox transform is then set to NULL). Setting unnecessary parameters to NULL makes the forecasting process faster, however this requires the user to have expertise in this area.

The produced forecasts are automatically exported to an xlsx file (this can be changed if the user prefers some other format). This xlsx file shows both the dates and corresponding forecasts for the chosen forecast horizon. If multiple SKUs are forecasted at the same time, these results will be displayed in the same file (in separate columns or sheets, as can be chosen by the user).

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Dharmawardane, C., Sillanpää, V. & Holmström, J. High-frequency forecasting for grocery point-of-sales: intervention in practice and theoretical implications for operational design. Oper Manag Res (2021). https://doi.org/10.1007/s12063-020-00176-7

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  • Grocery retail operations
  • Automatic store replenishment
  • High frequency forecasting
  • Retraining frequency
  • Error monitoring