###### Abstract  
In reverse logistics, the accurate prediction of waste electrical and electronic equipment (WEEE) return amount is of great significance to guide electronic enterprises to formulate a reasonable recycling plan, remanufacturing production plan and inventory plan. However, due to the uncertainty of WEEE return, it is a challenge to accurately predict the WEEE return amount of recycling sites. Differently from the existing research methods aiming at the spatial correlation of the recycling amount of recycling sites, a spatial mathematical model based on Kriging method is proposed by this paper to predict the return amount of WEEE in reverse logistics. Based on the second-order randomness of the return amount, the spatial structure of the return amount of the recycling network is analyzed. According to the principle of unbiased prediction and minimum variance, the Kriging space mathematical model of WEEE return amount is derived, and the calculation process of three variograms is given. The results of Monte Carlo simulation and the case study on ] company in Shanghai show that it is effective to utilize the Kriging method-based spatial mathematical model to predict the WEEE return of reverse logistics and analyze the spatial correlation structure of each recycling site. The proposed model can accurately predict the WEEE return amounts of unknown sites as well as those of the whole area through the known site data, which provides a novel analysis method and theoretical basis for the prediction of reverse logistics return amount. reverse logistics; return prediction; waste electrical and electronic equipment; kriging method 202113536. [[https://doi.org/10.3390/app1108356](https://doi.org/10.3390/app1108356)]([https://doi.org/10.3390/app1108356](https://doi.org/10.3390/app1108356))  
25 March 202114 April 202115 April  
There are also prediction models based on the regression equation: [PERSON] et al. studied the prediction of reverse logistics return volume [23]. They assumed that the product return volume was a function of product sales volume and return volume in the past, and built a return prediction model based on sales and recycling historical data. [PERSON] et al. used a spatial autoregressive regression (SARX) model to characterize the roundness of a manufactured product [24]. [PERSON] and [PERSON] established a logistic regression model to predict the trend of waste computers [25]. The polynomial regression analysis is good at fitting the trend of polynomials in a data series but the highest idempotent of polynomials mainly depends on human choice, especially the power of polynomial items is assumed to be integers, which will lead to model errors. In terms of prediction models based on neural network, based on the back propagation (BP) neural network prediction method, [PERSON] and [PERSON] constructed a combined forecasting model of return neural network to predict the product return [26]. [PERSON] et al. proposed a reverse logistics forecasting model based on the neural network method after analyzing the disadvantages of common prediction methods such as moving average method, exponential smoothing method and causal analysis method [27]. The modeling process is mainly reflected in two aspects: one is the representation structure of the prediction network, and the other one is the number of nodes in the input/output layer, hidden layer and output layer of the network. The input layer is the factor affecting the return amount, the intermediate layer is the neuron set by the user according to the actual problem, and the output layer is the return amount on the time series to be predicted. Neural network is a modeling tool which has developed rapidly in the past 20 years [28; 29; 30]. It can be used for regression modeling and autoregressive modeling when it is used to predict the return amount based on time series.