This paper presents a specialized method for solving transportation problems with several additional linear constraints. The method is basically the primal simplex method, specialized to exploit fully the topological structure embedded in the problem. It couples the poly-ω technique of Charnes and Cooper with the row-column sum method to yield an “inverse compactification” that minimizes the basis information to be stored between successive iterations, and in addition minimizes the arithmetic calculations required in pivoting. In particular, the solution procedure only requires the storage of a spanning tree and a (q + 1) × q matrix (where q is the number of additional constraints) for each basis. The steps of updating costs and finding representations reduce to a sequence of simpler operations that utilize fully the triangularity of the spanning tree. Procedures for obtaining basic primal “feasible” starts are also presented.