Improved convolutional neural networks for the bullwhip effect in supply chains

The Bullwhip Effect (BWE) introduces significant challenges to production systems by amplifying demand and order oscillations. One of the most effective methods for predicting and modeling complex systems is Convolutional Neural Networks (CNNs). However, certain phenomena, such as the BWE in supply chains (SC), are difficult to predict and identify directly. The primary challenge for Machine Learning (ML) algorithms in this context lies in the training phase: the raw demand and order data are fed into the network, yet the desired training outcome is the oscillatory behavior of these data from the perspective of the BWE. Consequently, conventional max pooling, average pooling operators, kernels, and weighted linear combinations of data are insufficient for capturing this type of learning. To address this issue, in this paper, a novel structure containing new pooling operators and kernels of CNNs is proposed to tailor the unique characteristics of the BWE. Specifically: a) Considering the temporal propagation nature of the BWE, new filters and pooling operators were designed to enable CNNs to predict the BWE accurately. b) A tensor structure was also proposed for the time signal of demand as inputs of the CNNs to facilitate the analysis of all factors influencing the occurrence of the BWE. c) To capture the magnitude of the BWE among features, a novel combination of filters and pooling operators was proposed, enabling the CNNs to account for hidden but yet significant feature effects during training. The benefits of the proposed approach lie in its versatility, and it can be applied to train CNNs to model structured fluctuations like the BWE in various dynamic systems.