Collaboration based supply is a common problem of supply chain systems. In recent time , there was an article proposing a multi-depot cooperate supply mathematical model . Furthermore , that article gave the solution of the model , and the corresponding algorithm was regarded as a heuristic method. This paper , however , gives a proof that the algorithm is actually optimal , not heuristic. Our conclusion consummates prophase researches , and this pa2 per also gives a theoretical base on the application of the algorithm.