Algorithms.

This article presents procedures for solving of equations related to algorithm. Procedure determines the least-cost flow over an upper and lower bound capacitated flow network. Each directed network arc a is defined by nodes I[a] and J[a], has upper and lower flow bounds hi{a] and lo[a], and cost per unit of flow cost[a]. Costs and flow bounds may be any positive or negative integers. An upper flow bound must be greater than or equal to its corresponding lower flow bound for a feasible solution to exist. There may be any number of parallel arcs connecting any two nodes.