A note of the knapsack problem with special ordered sets

Authors:
Ellis L. Johnson;Manfred W. Padberg
Affiliations:
IBM Thomas J. Watson Research Center,Yorktown Heights, NY 10598, U.S.A.;New York University, New York, NY 10006, U.S.A.
Venue:
Operations Research Letters
Year:
1981

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Abstract

The knapsack problem with special ordered sets and arbitrarily signed coefficients is shown to be equivalent to a standard problem of the same type but having all coefficients positive. Two propositions are proven which define an algorithm for the linear programming relaxation of the standard problem that is a natural generalization of the Dantzig solution to the problem without special ordered sets/ Several properties of the corvex hull of the associated zero-one polytope are derived.