An algorithm to find optimal routeing for distribution‐related problems is presented. Usually these problems are formulated as transportation problems (TP) and solved using the stepping‐stone (SS) technique. In practice, however, the SS algorithm encounters major obstacles including difficulties in identifying an initial basic feasible solution, resolving SS degeneracy, and enumerating SS paths. The proposed algorithm solves the linear programming (LP) formulation of TP in a novel way and, unlike simplex or dual simplex methods, does not require artificial or slack/surplus variables. A general‐purpose algorithm is proposed which not only solves the classical TP, but also can effectively handle an unbalanced condition and additional side‐constraints on the routes. The proposed algorithm uses only the Gauss Jordan row operation, as used in the simplex method. As such, it is much easier to understand and apply, and can serve as an effective tool for teaching TP. Numerical examples are presented to illustrate applications of the proposed method. It is assumed that the reader is familiar with simplex terminology.