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We consider the problem of approximating the branch and size dependent demandof a fashion discounter with many branches by a distributing process beingbased on the branch delivery restricted to integral multiples of lots from asmall set of available lot-types. We propose a formalized model which arisesfrom a practical cooperation with an industry partner. Besides an integerlinear programming formulation and a primal heuristic for this problem we alsoconsider a more abstract version which we relate to several other classicaloptimization problems like the p-median problem, the facility location problemor the matching problem.

Lotsize optimization leading to a $p$-median problem with cardinalities