North West Corner Method (NWCM) , Least Cost Method (LCM) and Vogel’s Approximation Method (VAM) are the classical methods for solving transportation problems and are well discussed in all the operation research books.
NWCM was introduced by Charnes in 1953, VAM was introduced by Reinfeld and Vogel in1958,
Just to be clear -- your references seem to be to useful starting or approximation methods to get decent feasible starting solutions. The Hitchcock/Koopmans transportation problem is correctly solved to optimality by methods such as linear programming solvers. It is widely known that this method was used by Dantzig to solve practical logistics problems at the end of World War II. Are you asking for references to the originators of this idea? There have been many many creative approaches to this problem.
I did a little more checking and Hitchcock has a 1941 reference.
The Distribution of a Product from Several Sources to Numerous Localities
Frank L. Hitchcock
Journal of Mathematics and Physics
Volume 20, Issue 1-4, pages 224–230, April 1941
This algorithm provides good result using comparatively less calculation and is available almost all literature. But I didn't get any evidence on any literature about the author who introduce LCM.
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