The forecasting consists of taking historical data as inputs then using them to predict future observations, thus determining future trends. Demand prediction is a crucial component in the supply chain’s process that allows each member to enhance its performance and its profit. Nevertheless, because of demand uncertainty supply chains usually suffer from many problems such as the bullwhip effect. As a solution to those logistics issues, this paper presents a comparative analysis of four time series demand forecasting models; namely, the autoregressive integrated moving Average (ARIMA) a statistical model, the multi-layer perceptron (MLP) a feedforward neural network, the long short-term memory model (LSTM) a recurrent neural network and the convolutional neural network (CNN or ConvNet) a deep learning model. The experimentations are carried out using a real-life dataset provided by a supermarket in Morocco. The results clearly show that the convolutional neural network gives slightly better forecasting results than the Long short-term memory network.

No abstract

No abstract

The saturation assumption is widely used in a posteriori error analysis of finite element methods. It asserts, in its simplest form, that the solution can be approximated asymptotically better with quadratic than with linear finite elements. In this article, we show that a simple modification of this "hypothesis" is valid, and the proof of many authors can be made rigorous with this simple modification. We prove also the robustness of the estimator for a singularly perturbed problem.

No abstract