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

Authors Constantin Gaul, Sascha Kurz, Jörg Rambau

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Constantin Gaul
Sascha Kurz
Jörg Rambau

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Constantin Gaul, Sascha Kurz, and Jörg Rambau. The Combinatorics of (S,M,L,XL) or the best fitting delivery of T-shirts. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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.
  • Supply chain management
  • fashion retailer
  • integer linear programming
  • demand forecasting


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