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The progress of digitization makes the integration of online and offline sales channels increasingly necessary for retailers. Multichannel and omnichannel multi-echelon networks are gradually more common in responding to customer demands, but their complexity makes the optimization of replenishment and item allocation policies among different channels challenging, especially if products have a short shelf life, as in the case of food retailers, where customer behavior (e.g., first-/last- in-first-out selection) also plays a role. It is not always possible to solve this problem exactly and heuristics are required. We propose a dynamic model and jointly optimize allocation and replenishment policies in the case of perishable goods with stochastic demand, uncertainty in customer selection preferences, and fixed lead times. We study complexity and structure of optimal policies. Furthermore, we explore several intuitive generalizations of base-stock policies over multi-echelon networks, analyzing the effect that potential correlations and imbalances in demand volumes across channels generate on the heuristics and identifying the pros and cons of such solutions. Results show that inventory-pooling effects in multi-echelon models for perishable items are often combined with the allocation of fresher products to offline channels. Generalizations of the well-known constant-order or base-stock policies can be a viable solution that generates benefits and increases system flexibility. They advantageously leverage negative channel correlation, but in the case of unbalanced demand distributions, increased offline demand can impoverish the quality of some heuristics.
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