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Inventory replenishment with product substitution using reinforcement learning in omnichannel retailing

Product substitution plays a critical role in omnichannel retailing and is becoming increasingly important due to capacity constraints and growing customer expectations for availability across multiple channels. We address the replenishment and fulfilment challenges faced by an omnichannel retailer within a capacitated retail network, selling products to a large region across a multi-period horizon. This horizon is partitioned into cycles, where replenishment occurs at the start of each cycle and fulfilment decisions regarding how much to replenish and allocate across sales channels take place in each time period. We consider three sales channels: walk-in, home delivery, and click-and-collect. For the online channels, the retailer can choose to substitute a product with another if the customer’s original choice is out of stock and the potential substitute has sufficient stock available. Our model aims to maximize the retailer’s expected total profit. Due to limited capacity, lost sales are often unavoidable; likewise, periodic replenishment leads to unavoidable holding costs. To address these challenges, we incorporate product substitution as a practical strategy to improve service levels and the profit. We formulate the problem as a Markov Decision Process (MDP) and propose a reinforcement learning method that scales to large networks. Within this framework, we develop a tailored algorithm to model and optimise product substitution decisions, enabling more adaptive and profitable fulfilment policies under uncertainty.