Simple algorithms for minimizing the sum of linear shipment costs and convex port costs

Several methods are discussed for minimizing the sum of linear collection/distribution costs from/to a number of zones, and non-linear costs at processing ports. The non-optimality and computational implications of approximating non-linear cost functions for use with the linear programming technique are discussed. A simple graphical technique is presented and two computational algorithms are developed which make use of the special structure of the problem. The algorithms are illustrated using a simple example. Both algorithms converge to global optima. One is more suitable for hand calculation and the other is easier to program, but both are easily programmed and are computationally efficient.