The food waste in grocery retail is a worldwide problem. Many mathematical inventory models for perishable items do not have a closing days constraint, although the age of perishable items also increases on closing days in grocery stores. We develop a new age-based inventory model with a closing days constraint. This stochastic multi-item inventory model includes total stock capacity constraints, a positive lead time, a periodic inventory control, a target customer service level and mixed FIFO and LIFO issuing policies for perishable items with a fixed lifetime under a non-stationary random demand. We show in a comparative simulation study under a rolling planning that the closing days constraint improves order decisions and reduces waste quantities and costs in grocery stores.