Solution of constrained generalized transportation problems using the pivot and probe algorithm

In this paper we use a specialized version of our pivot and probe algorithm to solve generalized transportation problems with side constraints. The dual of an m x n generalized transportation problem with t side constraints is a linear program with m + n + t variables and up to m x n constraints. We solve the dual problem using the probe operation to select only the most important constraints to consider. We present computational experience on problems of sizes up to 180 x 180, having various degrees of density and having as many as 10 side constraints. It was found that for a given size and density, problems become harder to solve as the number of side constraints increases. Also, for a fixed number of side constraints, the solution difficulty increases with size and density. We found that our method was able to solve problems of the quoted sizes relatively quickly, with relatively few pivots, and without using basis reinversion.