On the number of acceptable solutions to the transport problem

The paper gives estimates of the number of acceptable solutions to transport problems of a wide class. These estimates are made based on the structural properties of transport tasks, regardless of the type of target function and specific values of stocks, needs and tariffs. Basic solutions satisfying only classical technological constraints and the condition of the absence of cycles in a closed problem are considered. Bipartite graphs and appropriate trees are also considered. The methods of combinatorics and graph theory are used in the work. The obtained quantitative and qualitative characteristics of the set of acceptable transport task solutions can be useful as a upper estimation of amount of solutions in particular transport problem as well as in solving various modifications of transport problems.