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We study the multi-level bottleneck assignment problem (MBA), which hasimportant applications in scheduling and quantitative finance. Given a weightmatrix, the task is to rearrange entries in each column such that the maximumsum of values in each row is as small as possible. We analyze the complexity ofthis problem in a generalized setting, where there are restrictions in howvalues in columns can be permuted. We present a lower bound on itsapproximability by giving a non-trivial gap reduction from three-dimensionalmatching to MBA.  To solve MBA, a greedy method has been used in the literature. We present newsolution methods based on an extension of the greedy method, an integerprogramming formulation, and a column generation heuristic. In computationalexperiments we show that it is possible to outperform the standard greedyapproach by around 10% on random instances.

The Multi-level Bottleneck Assignment Problem: Complexity and Solution Methods