The Group-Theoretic Structure in the Fixed-Charge Transportation Problem

J. L. Kennington and V. E. Unger
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J. L. Kennington: Southern Methodist University, Dallas, Texas
V. E. Unger: Georgia Institute of Technology, Atlanta, Georgia

Operations Research, 1973, vol. 21, issue 5, 1142-1153

Abstract: The multiparametric integer programming problem for the right-hand side is to minimize c ′ t subject to At = b ( y ), t ≧ 0, t = 0 (mod 1), where b ( y ) can be expressed in the form b ( y ) = b̄ + F ( y ), where F is a matrix of constant coefficients, and y is an integer vector parameter. The group problem associated with any integer programming problem may be viewed as a multiparametric integer programming problem. The purpose of this paper is to show that the group problem associated with the fixed-charge transportation problem can be viewed as a multiparametric integer programming problem having a totally unimodular constraint matrix.

Date: 1973
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