Design and Implementation of Large-Scale Primal Transshipment Algorithms

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Author
Bradley, Gordon H.
Brown, Gerald G.
Graves, Glen W.
Date
1977-09Metadata
Show full item recordAbstract
A complete description is given of the design, implementation and use of a
family of very fast and efficient large scale minimum cost (primal simplex)
network programs. The class of capacitated transshipment problems solved
is the most general of the minimum cost network flow models which include
the capacitated and uncapacitated transportation problems and the classical
assignment problem; these formulations are used for a large number of
diverse applications to determine how (or at what rate) a good should flow
through the arcs of a network to minimize total shipment costs. The
presentation tailors the unified mathematical framework of linear
programming to networks with special emphasis on data structures which are
not only useful for basis representation, basis manipulation, and pricing
mechanisms, but which also seem to be fundamental in general
mathematical programming. A review of pertinent optimization literature
accompanies computational testing of the most promising ideas. Tuning
experiments for the network system, GNET, are reported along with important
extensions such as exploitation of special problem structure, element
generation techniques, postoptimality analysis, operation with problem
generators and external problem files, and a simple noncycling pivot selection
procedure which guarantees finiteness for the algorithm.
Description
“Exceptional Paper” in Management Science, 24, 1, pp. 1-34, (1977 Lanchester Prize Finalist).
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defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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