Managing perishable goods for grocery retailing: Optimal inventory policy under freshness-based substitution

Grocery retailers often face the decision of whether to allow freshness-based demand substitution by offering the same product with differing shelf lives. Offering both “new” and “old” units simultaneously enhances market penetration but also cannibalizes demand for new units, as old units are typically sold at a discount. This paper develops an analytical framework that extends the classical Economic Order Quantity (EOQ) model to explicitly capture intra-cycle competition between old and new units of a perishable product with a fixed shelf life (e.g., a carton of milk). We derive optimal policies under single-batch (no competition) and double-batch (competition within each cycle) replenishment strategies and characterize the conditions under which each policy is profit-maximizing. Accordingly, there exists a shelf-life threshold below which the single-batch policy is optimal, whereas a longer shelf life may justify adopting the double-batch policy. Interestingly, under the double-batch policy, both the optimal cycle length and order quantity are smaller, implying that a longer shelf life does not necessarily increase inventory levels. Partial competition, where intra-cycle competition is shorter than the cycle length, is rarely optimal and yields marginal profit improvement. We further extend the model by proposing a pricing-EOQ formulation, where markdown depth is endogenously determined, to assess the robustness of the findings and highlight the role of markdowns. The central findings remain true and the firm makes a deep markdown only when market expansion is limited. Our results identify when freshness-based competition should be avoided or strategically embraced. • We extend the traditional EOQ model to explicitly capture intra-cycle competition between old and new units of a perishable product with a fixed shelf life (e.g., a carton of milk). • There exists a shelf-life threshold below which the single-batch policy is optimal, whereas a longer shelf life may justify adopting the double-batch policy. • Under the double-batch policy, both the optimal cycle length and order quantity are smaller, implying that a longer shelf life does not necessarily increase inventory levels. • Partial competition, where intra-cycle competition is shorter than the cycle length, is rarely optimal and yields marginal profit improvement. • Our results identify when freshness-based competition should be avoided or strategically embraced.