Technical Note—Exact Solution of the Fixed-Charge Transportation Problem

In the fixed-charge transportation problem, a fixed charge is associated with each route that can be opened, in addition to the variable transportation cost proportional to the amount of goods shipped- This note presents an exact solution of this mixed integer programming problem by decomposing it into a master integer program and a series of transportation subprograms. To reduce the number of vertices that need to be examined, bounds are established on the maximum and minimum values of the total fixed cost, and feasibility conditions for the transportation problem are used extensively. Computational results show the method to be particularly suitable when fixed costs are large compared to variable costs. A composite algorithm based on Murty's and the author's results is proposed.