Abstract
A break in a {0, 1}-matrix is defined as a 0 with at least one 1 to its left and at least one 1 to its right in the same row. This paper is concerned with {0, 1}-matrices with given column sums and an upper limit for the row sums. In addition, there are limits on the distance from the first to the last 1 in a row. The problem that is considered is to find a {0, 1}-matrix satisfying the conditions such that the total number of breaks is minimum. An algorithm for solving this problem is presented. Computational results illustrate the effectiveness of the algorithm.
The investigation originated in a problem of crew rostering.
Similar content being viewed by others
References
M.L. Balinski, “On recent developments in integer programming”, in: H.W. Kuhn, ed.,Proceedings of the Princeton symposium on mathematical programming (Princeton University Press, Princeton, N.J., 1970) pp. 267–302.
J.F. Benders, “Partitioning procedures for solving mixed-variables programming problems”,Numerische Mathematik 4 (1962) 238–252.
G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, N.J., 1963).
L.R. Ford and D.R. Fulkerson,Flows in networks (Princeton University Press, Princeton, N.J., 1962).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Salzborn, F.J.M. Break minimization. Mathematical Programming 8, 43–53 (1975). https://doi.org/10.1007/BF01580427
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01580427