2.1

Retail supply chain

Depending on the objective of the forecast, all demand forecasts in the retail sector depend on the degree of aggregation of products, locations, or periods. For the retail sector, forecasts are generated based on suppliers, distributors, retailers, individual product categories, and individual SKUs. While these different dimensions of forecasting share many of the same issues, such as seasonality and trends. However, the focus of their forecasts will differ depending on the subject of the forecast, they will have different objectives, and data characteristics.

2.1.1

Supplier Level Demand Forecasting.

Supplier level forecasts relate to the total sales of the entire business and the period for this level of forecasting can be monthly, quarterly, or annually. The supplier level is shown in Figure 1. To enable suppliers to plan and operate their retail business effectively at a strategic level, it is necessary to forecast demand at the supplier level⁸. Supplier level demand data shows strong trends and seasonal variations. Unlike at the supplier level, data at the distributor and retailer levels involve irregular observations over time and a large number of zero values.

Figure 1.

Supplier level.

2.2

DeepAR

DeepAR is a deep neural network model which builds a single global model⁹. Traditional time series forecasting methods (ARIMA, Holt-Winters) tend to model the single time series, and it is difficult to use extra features. By comparison, DeepAR models can easily take additional features into account. In the retail sector, for example, if future product sales probability distributions are known, the optimal purchasing volume for different business objectives can be derived using operations optimization methods to aid decision-making. DeepAR accepts as input the past series and its covariates. Let z_i,t denotes the value of the ith series at time step t, and x_i,t are covariates. The time point t₀ is used as the division time, indicating the start of the forecast. The objective of the model is to obtain the joint conditional probability distribution. As shown in Figure 2, DeepAR predicts the probability distribution of z_i,t based on an autoregressive recurrent neural network, denoted by the likelihood function l(z_i,t|θ_i,t). In turn, the parameters of the likelihood function are calculated θ_i,t = θ(h_i,t). Network parameters are updated by maximizing natural functions.

Figure 2.

DeepAR network architecture.

2.3

Tweedie loss

At the retailer level, some of the time series includes many zero values, whereas a Poisson or binomial distribution may underestimate the probability of a value of zero. To alleviate the problem of too many zero values in the time series, the Tweedie distribution¹⁰ is used as the target distribution in this paper. As shown in Table 1, p=1, Tweedie is the Poisson distribution, when p=2, Tweedie is the Poisson distribution. When 1< p <2, it becomes a composite distribution of Poisson and Gamma.

Table 1.

Tweedie distribution.

We use Poisson-Gamma distribution in this paper. The distribution is the sum of N independent identically distributed random variables sampled from the gamma distribution, where the number of samples to be added (N) is the Poisson distribution variable.

3.1

Dataset

In this paper, five consecutive years of sales records of a retailer are selected and aggregated at different levels to produce a time series of sales for each distributor and a time series of sales for the manufacturer.

As shown in Figure 3, the sales data show a clear trend and a certain seasonal pattern, with some randomness. The sales data is then extracted from the distributors and averaged over a 7-day window for the demand data and rolled up. The smoothed data shown in Figure 4 gives a visual indication of the trend.

Figure 3.

Inventory sale percentage by date.

Figure 4.

Rolling 7-day demand count by store.

As shown in Figure 5, there are a large number of zero values in the specific SKU sales data, reflecting the intermittent demand for that SKU.

Figure 5.

Sales data for an SKU.

3.2

AggDeepar model construction

After analyzing the data of this enterprise, this paper proposes the AggDeepar model by taking advantage of the gradient advancement model and the autoregressive neural network model for the data characteristics of different levels of data and the special situation of the retail industry. The hierarchy is divided into two levels according to the needs of different retailers at different levels. The first level is the sales of individual SKUs, as well as individual distributors, and the data at this level shows intermittent trends similar to counting. The second hierarchy is the manufacturer’s sales, where the data shows a continuous trend.

For the first level, we use an autoregressive neural network, modeled directly with a modified DeepAR, which uses a recursive prediction strategy in the forecasting process, i.e., samples drawn from the parametric distribution at the previous time step are considered as input to infer the distribution parameters at subsequent time steps. Based on the samples extracted from the parameterized distribution, the quantile of each time step in the prediction horizon was calculated. The target parameter distribution is the Tweedie distribution.

As shown is Figure 6, for the second level, to improve the forecast values, we trained a model, which was trained using Poisson loss, assuming that the retail data are close to a Poisson distribution. The predictions were combined with the deeper model.

Figure 6.

AggDeepar model.

3.3

Experiment

In this paper, we choose the RMSE as the criterion for evaluating the model.

The parameters of the model are set as shown in Table 2. To further verify the application performance of the AggDeepar aggregation model, Holt-winter, ARIMA model, LSTM model, and DeepAR (Gaussian) were used as the comparison models in this paper.

Table 2.

DeepAR (Gaussian) and DeepAR (Tweedie) model parameters.

As shown in Table 3 and Figure 7, the AggDeepar model has improved relative to the other models, indicating that the combined forecasting results of the model are relatively valid and more applicable than a single model in forecasting the sales of the business. Traditional statistical models do not predict multiple time series very well and do not capture the characteristics of the time series very well. Experiments have demonstrated that traditional models can only predict a single time series, and difficult to operate with a large number of time series. This proves that for retail sales forecasting, the traditional approach is no longer suitable and that AggDeepar, a deep learning model that learns a global model, is more practical. AggDeepar also fits similar products to new products based on their characteristics for the cold start problem.

Figure 7.

Forecast results for two commodities.

Table 3.

Experimental results.