Capacity and maximal value of the network flow with multiplicative constraints

A class of network flows, called multiplicative or M-flows is investigated in this paper. M-flows are subject to multiplicative capacity constraints. These constraints are sums of products with positive coefficients of flow function values on the arcs of subsets of the network arcs. A definition is given to the flow capacity of a cutting set. Maximality conditions for multiplicative flow optimality are obtained. A theorem, analogous to the mincut-maxflow theorem for the classical network flow is proved.