In different branches of economics-especially in the construction industry - supply systems are found, in which producers and consumers are connected by production and transport. By the occurrence of random or foreseeable perturbations an optimal control of the supply processes is appropriate. First directed graphs are assigned to special supply systems. On there graphs multistage decision processes are defined to yield an optimal control of the supply processes. The explicit representation of the perturbing quantities by parameters is decisive for optimal control. Next, an optimization problem is formulated, which includes as a special case the problem of optimal control of supply processes. This mathematical modelling and the solution of the optimization problems require some extensions of the known theory of multistage decision processes.