# Sales Forecasting for Fashion Products Considering Lost Sales
## 1 Introduction  
Sales forecasting is a critically important task in the fashion retail industry. It is an integral component of many core fashion retail processes, including the functional areas of pricing and inventory management, marketing and production purchasing, as well as finance and accounting [1, 2]. Forecasts on sales also provide the basis for regional distribution and replenishment plans [3]. Therefore, the ability to estimate the probable sales quantity could lead to improved customer satisfaction, reduced waste, increased sales revenue and more effective and efficient production plans as after-sales services [4]. Generally, accurate sales forecasting is a prerequisite to competing efficaciously in the fashion world [5]. A number of methods have been developed over the past two decades. Statistical methods are widely used in forecasting fashion products, including traditional time series techniques and discrete choice models such as tie multinomial logistic model and Bayesian analysis [6, 7]. Another popular method in sales forecasting is machine learning, such as artificial neural networks (ANN), evolutionary neural networks (ENN) and extreme learning machines (ELM) [8, 9, 10]. Despite the extensive research on the sales forecasting problem in fashion retail industry, there remain some practical issues that need consideration. Fashion products have the characteristic of short product life cycles [11]. Therefore, fashion products usually have a low inventory strategy in general, and every brick-and-mortar store has a low stock level, which leads to a serious problem with demand censoring [12, 13]. Censored demand increases the difficulty of forecasting and the impact of inventory, and censored demand tosales are unignorable in the fashion retail industry. Research on the total sales forecasting problem for fashion products with censored demand is relatively rare, which motivates us to design a new model to alleviate the impact of censored demand on sales considering the lost sales phenomenon. The objective of this paper is to improve the total sales forecast accuracy for fashion products and provide helpful guidance on decision-making for fashion industry managers. In this paper, a two layers (TLs) model for forecasting the total sales of new products is proposed, considering not only the actual demand but also the effect of censored demand in brick-and-mortar stores. In the first layer, the demand is estimated by traditional linear regression (LR), while in the second layer, the sales are modeled as a function of not only the demand but also the inventory. We incorporate two key parameters in this model, with one describing a product's basic conversion rate of one inventory to sales and another one describing the customers' preference for products. To solve the model, the gradient-boosting decision tree (GBDT) method is applied for feature selection. Considering the heterogeneity, products are clustered by a mixed k-mean clustering algorithm, and parameter estimation is conducted separately in each cluster by a genetic algorithm (GA). Collaborating with a multinational fashion retailer in Singapore, experiments are conducted based on real-world data of shoes and belts. The results of experiments are compared based on different models, including our TLs model, LR, GBDT, support vector regression (SVR) and ANN. The results show that our method outperforms other sales forecasting methods in most cases. For further conclusions, we analyze the results obtained by the TLs model and define the average conversion rate when the inventory level is equal to demand as one indicator to measure product competitiveness. We also involve the marginal conversion rate as another indicator for managers to make proper inventory decisions. Generally, our contribution is summarized in three points: (1) A TLs sales forecasting model is proposed based on the relationship between sales, inventory and demand and incorporates two parameters to describe the conversion rate of inventory to sales.