Consumers today expect supermarkets to offer a wide variety of items at favourable prices and with consistent availability. These expectations lead to major capacity challenges for distribution centres responsible for replenishing goods since consumer demand fluctuates weekly. Therefore, we investigate an integrated warehouse design and product allocation problem for a distribution centre in the retail food industry. For this purpose, we formulate a multi-periodic mixed-integer program that reflects the flow of goods within the distribution centre and, thus, explicitly captures daily fluctuations in demand. The suitability of the approach is demonstrated using modified data from a distribution centre in Germany. The results show that a static approach violates the weekday-specific capacity restrictions and that only a multi-periodic approach can meet the requirements of practice. In analyzing the real-world case we selected, the trade-off between handling and transport costs reveals that the automated storage and retrieval system is fully utilized. Interestingly, it shows that, even considering 20,000 different items, the problem can be solved in seconds using the presented model formulation.