A Pseudo-Polynomial Primal-Dual Algorithm for Globally Solving a Production-Transportation Problem

In this paper, we propose a primal-dual algorithm for solving a class ofproduction-transportation problems. Among m(≥ 2) sources two factoriesexist, which produce given goods at some concave cost and supply them to nterminals. We show that one can globally minimize the total cost ofproduction and transportation by solving a Hitchcock transportation problemwith m sources and n terminals and a minimum linear-cost flow problem withm+n nodes. The number of arithmetic operations required by the algorithm ispseudo-polynomial in the problem input length.