The Transportation-Production Problem

A transportation-production problem with increasing marginal production costs and linear shipping costs is considered. This problem is shown to be a convex programming problem, and an efficient iterative solution technique is presented. Numerical results are presented for various problems having 2,500 variables, 100 linear constraints, and 2,500 nonnegativity constraints. As expected, the number of iterations for an accurate solution depends on the degree of non-linearity of the objective function. Computing times on the CDC Cyber 70, Model 72, varied from 10 to 70 seconds among the different problems.