Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

with us for a long time and has become a satisfying analytic abstraction.
Smith's contribution was to formulate once again the transportation prob-
lem and to explicitly derive Cournot's equilibrium relations and the con-
ditions under which they would hold.
The latest step in the development of the many-market, variable
export and import, fixed transport charge model was the development of
a solution algorithm in 1964 by Takayama and Judge. 9 They were able to
formulate the Samuelson problem in a quadratic programming context and
develop a specialization of the simplex linear programming algorithm for
its solution.
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We have traced the development of what we shall refer to as the
many-market single-mode transportation model. It is an analysis of the
production, flow and consumption of a single commodity in and between
many regions or markets. Each region may both produce and consume the
commodity and transportation between all pairs of regions is feasible.
All transport charges are given and are independent of volume. Capacity
constraints are never binding for the transporters. This model must be
considered as a system served by a single mode of transport although the
actual means of transportation are usually not specified, as all regions
are cOnnected by some means of transport whose only distinguishing at- .
tribute is its per unit charge.
While it is somewhat paradoxical that the analytical models of
transportation flows have almost completely disregarded the supply of
9. T. Takayama, and G. Judge, "Equilibrium Among Spatially Separated
Markets: A Reformulation," Econometrica, Vol. 32, No. 6 (Oct. 1964), .
510-524.
11