Improved modelling of physical distribution

This paper describes a procedure for modelling the costs of production and distribution between several production facilities with economies of scale and many customers who are widely dispersed. The problem takes the form of a large transportation problem on which is superimposed a cost minimization problem involving variable production quantities. These costs involve fixed costs for initiating production and variable costs with diminishing returns to scale. It models the problem as a non-linear integer programming problem and then solves it using a recently developed non-linear integer algorithm. It describes two applications in Australia and New Zealand and illustrates how comparison with a mixed-integer linear programming formulation shows a significant improvement.