Abstract
We consider large-scale mixed-integer programming problems containing fixed charge variables. In practice such problems are frequently approached by using commercial mathematical programming systems. Depending on the formulation, size and structure of the problem this approach may or may not be successful. We describe algorithms for preprocessing and optimization of such problems and discuss the design of an experimental software system based on MPSX/370. Numerical results for solving some large real life problems are also presented.
Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.References
M. Benichou, J.M. Gauthier, G. Hentges and G. Ribiere, “The efficient solution of large-scale linear programming problems”,Mathematical Programming 1 (1971) 76–94.
M. Benichou, J.M. Gauthier and G. Ribiere, “Some considerations on timing and throughput when running MPSX/370 under MVS”, Paper presented at SHARE 49, Washington DC, August 1977.
A. Brearley, G. Mitra, and H.P. Williams, “Analysis of mathematical programming problems prior to applying the simplex method”,Mathematical Programming 8 (1975) 54–83.
H.P. Crowder, E.L. Johnson, and M.W. Padberg, “Solving large-scale zero–one linear programming problems”,Operations Research 31(5) (1983) 803–834.
J.J.H. Forrest, J.P.H. Hirst, and J.A. Tomlin, “Practical solution of large scale mixed integer programming problems with UMPIRE”,Management Science 20(5) (1974) 736–733.
J.M. Gauthier and G. Ribiere, “Experiments in mixed-integer linear programming using pseudocosts”,Mathematical Programming 12 (1977) 26–47.
K. Spielberg and U.H. Suhl, “An experimental software system for large scale 0–1 problems with efficient data structures and access to MPSX/370”, Research Report RC 8219, IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, 1980.
E.L. Johnson, M.M. Kostreva, and U.H. Suhl, “Solving 0–1 integer programming problems arising from large-scale planning models”, General Motors Research Report GMR-4990, Warren, Michigan, 1982 (to appear inOperations Research).
P.G. McKeown, “A branch-and-bound algorithm for solving fixed charge problems”,Naval Research Logistics Quarterly, 28 (1981) 607–617.
L.A. Oley and R.S. Sjoquist, “Automatic reformulation of mixed and pure integer models to reduce solution time in APEX IV”, Paper presented at the ORSA/TIMS Meeting in San Diego, California, October 1982.
L. Slate and K. Spielberg, “The extended control language of MPSX/370 and possible applications”, IBM Systems Journal 17 (1978) 64–81.
J.A. Tomlin and J.S. Welch, “Formal optimization of some reduced linear problems”,Mathematical Programming 27 (1983) 232–240.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Suhl, U.H. Solving large-scale mixed-integer programs with fixed charge variables. Mathematical Programming 32, 165–182 (1985). https://doi.org/10.1007/BF01586089
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01586089