The Combinatorics of (S,M,L,XL) or the best fitting delivery of T-shirts

A fashion discounter supplies its branches with apparel in various sizes. Apparel is ordered in pre-packs three months in advance from overseas: replenishment impossible. Thus, the supply in each size and branch must be consistent with the demand right away. We present new ILP-models for the resulting lot-type design problem: For each branch, find lot types and delivery volumes so that the demand is met best. Our vision is an integrated price-and-size optimization model that takes the mark-down process into account when placing the orders. The results are applied by a german fashion discounter with over 1000 branches