In the max-min ki-partitioning problem, the task is to assign a set of jobs with positive integer processing times to a set of parallel machines – each having an associated machine-dependent cardinality limit ki on the maximal number of jobs that can be processed by machine i – so that the minimum machine completion time is maximized without exceeding the cardinality limits.
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References:
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Lawrinenko, A.; Schwerdfeger, S.; Walter, R. (2017): Reduction criteria, upper bounds, and a dynamic programming based heuristic for the max-min k_i-partitioning problem. Journal of Heuristics (online first, doi=10.1007/s10732-017-9362-9).