The transportation problem has recently gained renewed interest due to its applications in machine learning and artificial intelligence, particularly in measuring distances between images.

To address the associated computational challenges, we propose a novel algorithm, Iterated Inside Out, for the exact resolution of the well-known transportation problem.

The core of our algorithm requires an initial basic feasible solution and consists of two iteratively repeated phases until an optimal basic feasible solution is obtained.

In the "inside" phase, the algorithm progressively improves the current solution by increasing the value of non-basic variables with negative reduced costs, typically yielding a feasible solution that is non-basic and interior to the constraint set polytope.

In the "outside" phase, the algorithm improves the current solution by iteratively setting variables to zero until a new improved basic feasible solution is reached.

Building on this core algorithm, we develop a specialized variant tailored for image processing.

Extensive computational experiments demonstrate that our approach significantly outperforms commercial solvers such as CPLEX and Gurobi, as well as other exact algorithms in the literature.

We demonstrate its superiority on both randomly generated instances and the DOTmark benchmark, a standard dataset for image processing and large-scale transportation problems.