Time series data is ubiquitous, with forecasting applications spanning from finance to healthcare. Beyond popular deterministic methods, generative models are gaining attention due to advancements in areas like image synthesis and video generation, as well as their inherent ability to provide probabilistic predictions. However, existing generative approaches mostly involve recurrent generative operations or repeated denoising steps, making the prediction laborious, particularly for long-term forecasting. Most of them only conduct experiments for relatively short-term forecasting, with limited comparison to deterministic methods in long-term forecasting, leaving their practical advantages unclear. This paper presents TARFVAE, a novel generative framework that combines the Transformer-based autoregressive flow (TARFLOW) and variational autoencoder (VAE) for efficient one-step generative time series forecasting. Inspired by the rethinking that complex architectures for extracting time series representations might not be necessary, we add a flow module, TARFLOW, to VAE to promote spontaneous learning of latent variables that benefit predictions. TARFLOW enhances VAE's posterior estimation by breaking the Gaussian assumption, thereby enabling a more informative latent space. TARFVAE uses only the forward process of TARFLOW, avoiding autoregressive inverse operations and thus ensuring fast generation. During generation, it samples from the prior latent space and directly generates full-horizon forecasts via the VAE decoder. With simple MLP modules, TARFVAE achieves superior performance over state-of-the-art deterministic and generative models across different forecast horizons on benchmark datasets while maintaining efficient prediction speed, demonstrating its effectiveness as an efficient and powerful solution for generative time series forecasting. Our code is available at https://github.com/Gavine77/TARFVAE.

Accurate prediction of Order Fulfillment Cycle Time (OFCT) is essential for improving customer satisfaction and operational efficiency within the domain of on-demand grocery retailing (OGR). OGR platforms typically rely on Front Distribution Centers (FDCs) to manage inventory and deploy dedicated fleets for last-mile delivery to fulfill customer demands. Orders are processed at FDCs initially and then dispatched to delivery fleets. OFCT is influenced by a multitude of factors such as order volume, processing capabilities, delivery capacities, and dispatching strategies. These factors pose significant challenges to refining OFCT prediction accuracy. This paper presents an innovative deep learning model informed by a detailed comprehension of the order fulfillment process, with the objective of significantly enhancing OFCT prediction precision. We employ Recurrent Neural Network (RNN) blocks to dynamically evaluate the workload across processing and delivery stages. To address the interactions among orders and the impact of latent courier dynamics on order prioritization, we incorporate a suite of specialized attention modules into our framework. Our approach further employs Deep Bayesian Multi-Target Learning (DBMTL) to discern the sequential interactions between various stages of order fulfillment, thereby elucidating the influence of earlier stages on subsequent ones. Through online experiments on Meituan-Maicai, one of the biggest OGR platforms in China, our model demonstrates its superiority by outperforming well-acknowledged and advanced baselines. Furthermore, we assess the contributions of specific designs in our model through ablation studies. Our research presents a notable advancement in OFCT prediction, providing valuable insights for OGR platforms seeking to optimize their fulfillment operations and enhance customer experiences.

We propose two recommendation algorithms for e-commerce with supply limits, a scenario that has not been intensively studied in the literature. One algorithm is a linear programming-based algorithm that uses historical data to approximate customer arrival patterns and generate shadow prices for inventories. The price of inventory can be introduced to existing recommendation algorithms to obtain adjusted rankings for recommendation. The other algorithm balances expected revenue and inventory consumption, and it uses a simple penalty function to reduce the chance of recommending low-inventory-level products. Both algorithms are suitable for online recommendation systems for grocery stores with both online and offline channels, and can incorporate the features of perishable products, which need to be sold within limited time. Both algorithms are tested in a simulation using estimated parameters from Freshippo, a supermarket owned by the Alibaba Group. The numerical results show that both algorithms can generate higher sales volume and higher revenue.