An enhanced application of Lotka-Volterra model to forecast the sales of two competing retail formats

- An enhanced application of LV-model for forecasting two competing retail formats.
- Revenues embedded with trend, competition, and seasonal components are compound data.
- Monthly revenues as input of LV-model may lead to unsatisfactory forecast accuracy.
- Accuracy substantially improved by input decomposed competition component to LV-model.
- Two retail formats form a predator-prey relationship; convenience-oriented format is predator.

This research develops a sales forecasting model that can analyze the interaction effects of two retail competing formats (convenience-oriented vs. budget-oriented formats). A traditional approach to making such a forecast is based on the Lotka-Volterra equations (also called the LV-model). The LV-model assumes that the population of each species is affected by its self-growth, internal interaction within the species, and external interaction with other species. Most prior studies in business applications directly use sales data as input to the LV-model. The prior approach may result in misleading conclusions when sales data are embedded with seasonal variation, because this variation is not addressed in the original development of the LV-model. Therefore, this study proposes a forecasting framework (an enhanced application of the LV-model). The sales data of each retail format is considered as a compound data, which is decomposed into three individual components: (1) aggregate, (2) competition, and (3) seasonal components. The LV-model is used to forecast the competition component; the other two components are forecasted by typical time series methods; and the data of three components are finally combined into one. Empirical study indicates that the proposed method substantially outperforms the prior approach in terms of forecasting errors (4.4% vs. 16.7% for convenience-oriented and 5.8% vs. 16.2% for budget-oriented). In addition, the proposed method reveals a more convincing predator-prey relationship between the two retail formats, which concludes that the convenience-oriented is the predator. To the opposite, the prior approach, concluding that the budget-oriented is the predator, is quite doubtful because the convenience-oriented shall be preferred while the GDP grows over time. This research makes a contribution in how to appropriately apply the LV-model in forecasting revenue and analyzing the interaction effects of two competing business species.