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Transportation Problem
Solves the (Hitchcock) Transportation Problem via the CPLEX API.
2024.May.16 14:29:24
Cost, supply, demand Cost matrix, supply, demand (integer or real)*

Insert a final 0.*

*(See below) •
Show interm. ? Shows CPLEX intermediate results.;
Show values ? Shows the coordinates of the graph. •

Solves a typical Transportation Problem (TP) or Hitchcock's problem, using the IBM ILOG CPLEX software. The data structure must be the classical cost matrix, surrounded (to the right) by the sources' supplies and (below) by the destinations' demands. (Here, total supply must equal total demand.)

The data must be separated by standard characters: space, tab (such as from Excel by copy-paste) or csv, in coherent American or European style.

The last value must be 0 (dummy) or another value. In the latter case, it is compared to the problem capacity (sum of supplies or sum of demands).

With the default data, the problem (which has multiple, 2, solutions) gives z* = 1400.

A graph is done showing the costs related to each place (set of source places, then of destination places). Obviously, in each set, the cost equals the minimum cost computed.

Acknowledgements: See CPLEX problem.

References: Plate: Hitchcock

• Wikipedia: IBM ILOG CPLEX

• Wikipedia: Hitchcock, Frank L. (1875–1957)

Bai, Z., et al., eds., 2000, Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide, SIAM, Philadelphia (Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, editors).
J. Dongarra, Sparse Matrix Storage Formats.

• 1820-07-03: De Jonquières, Ernest Jean Philippe Fauque (1901-08-12).

 
 
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Created: 2018-07-03 — Last modified: 2018-07-09