A New Algorithm for Locating Sources Among Destinations

The problem considered is the location of m sources among n locations (m < n) and the assignment of the location requirements to the sources in order that the total transportation cost is minimized. A branch and bound algorithm is developed to achieve an optimal solution. Two lower bounds are developed for the algorithm; one is efficient for small problems while the other is more efficient for larger problems. An illustrative example is given, and a detailed application of the algorithm to the thirty largest metropolitan centers in the United States is presented for various numbers of destination (10, 20 and 30) and sources (2, 4 and 6). The branch and bound algorithm was coded in Fortran IV and tested on a number of problems. Some of the example problems that were tested are included in this paper.