Fixed-Charge Transportation Problem: Facets of the Projection Polyhedron

In this paper we consider the well-known fixed-charge transportation problem. To send any flow from source si to destination tj, we incur a unit variable shipping cost of cij and a fixed cost fij. Here we study the structure of the projection polyhedron of this problem, in the space of 0-1 variables associated with fixed charges, and we develop several classes of valid inequalities and derive conditions under which they are facet defining. In some cases, if the conditions are not satisfied, we show how they can be lifted to define facets. Several heuristics for generating and adding these facets are presented. Using these results, we develop a computationally effective algorithm for solving the problem. The computational results clearly indicate the usefulness of this approach.