Integrated demand forecasting and inventory replenishment in omni-channel retail with deep learning

The rise of omni-channel grocery retail presents new challenges for store-level inventory replenishment because retailers must coordinate online and offline demand within a shared physical store. This study formulates a daily, SKU-level replenishment problem in which the front store serves walk-in customers, the backroom primarily serves online fulfilment, and inventory can be shared between the two pools at asymmetric operational costs. To address this complexity, we develop and compare two decision frameworks: a Separated Forecasting–Optimization (SFO) approach based on a feature-driven bivariate probabilistic demand model and a decision-focused End-to-End Deep Learning (E2E) model that directly learns replenishment decisions by minimising empirical inventory cost. Using large-scale real-world data from five omni-channel grocery stores, our empirical results show that the E2E framework consistently achieves lower total costs and better demand–supply balance than the SFO approach and several simpler benchmarks across cost settings, promotion conditions, demand intermittency, and time periods. The results clarify when integrated learning is operationally valuable, demonstrate the importance of explicitly modelling costly inventory sharing between the front store and backroom.