George L. Nemhauser

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Let N be a finite set and z be a real-valued function defined on the set of subsets of N that satisfies z(S)+z(T)>-z(SUT)+z(SnT) for all S, T in N. Such a function is called submodular. We consider the problem maXscN {z(S): IS[ <-K, z(S) submodular}. Several hard combinatorial optimization problems can be posed in this framework. For example, the problem of(More)
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We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch and bound tree We present classes of models for which this approach decomposes the problem provides tighter LP(More)
We study several ways of obtaining valid inequalities for mixed integer programs. We show how inequalities obtained from a disjunctive argument can be represented by superadditive functions and we show how the superadditive inequalities relate to Gomory's mixed integer cuts. We also show how all valid inequalities for mixed 0 1 programs can be generated(More)
The nine universities in the Atlantic Coast Conference (ACC) have a basketball competition in which each school plays home and away games against each other over a nine-week period. The creation of a suitable schedule is a very di cult problem with a myriad of con icting requirements and preferences. We develop an approach to scheduling problems that uses a(More)