Retail stores sell products to consumers. Their ability to sell depends upon the availability of the planned assortment, i.e. every item is on shelf so that the consumer can buy it. In particular, for fast moving consumer goods, like food, the consumer expects that each item is on stock. The retailer’s decisions on the length of replenishment cycles of stores, on the shelf-capacity allocated to each item, on the amount of inventory stored in the backroom of the store, on the minimum order quantity of each item, or on the case size affect the fill rate of the store.