Direct Solutions to Some Multidimensional Transportation Problems

A certain analogy that exists between the mathematical formulation of the standard (two dimensional) quadratic cost transportation problem as a minimum value problem and the mathematical formulation (as a minimum value problem) of the maximum likelihood estimation of the regression coefficient matrix of a multivariate normal linear regression model, subjected to double linear restrictions, is utilized to demonstrate that the transportation problem can be solved within the framework of available statistical linear regression theory methodology. Two known multidimensional transportation problems are solved within the framework of statistical linear regression theory methodology by converting them essentially as extensions of two dimensional transportation problems. The methodology is illustrated by numerical examples.