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

Algebra & Discrete Mathematics

Speaker: Joerg Rambau, U. Bayreuth
Location: 3106 MSB
Start time: Fri, Mar 14 2008, 2:10PM

A fashion discounter has to supply hundreds of branches with apparel in various sizes. In order to save work in the stock turn-over, apparel is ordered in pre-packs containing several sizes of the product. Since discount apparel is ordered three months in advance from overseas, there is no replenishment. Thus, the number of pieces delivered in each size and branch should be consistent with the demand for sizes in that branch. This leads to the task of pre-pack optimization: find assortments of sizes (Lot Types) and delivery volumes for each branch (in Lots of a Lot Type) so that the demand is met best. We present an Integer Linear Programming model for pre-pack optimization that is a generalization of the classical p-median problem. Moreover, we developed a fast heuristics that is suitable for the use in the field. Allthough, for the purpose of this talk, we take the demand forecast for granted, we briefly remark on the special difficulties involved.