The Nonlinear Generalized Transportation Problem with convex costs

We investigate the Nonlinear Generalized Transportation Problem (NGTP), where the transportation costs and the costs that depend on the amount of good delivered to the destination points are strictly convex functions. The amounts of goods change during the transportation process. This model may correspond, for example, with a congested network where the time costs are involved. First, we present the NGTIP model, then provide a method of solving the problems of this type and then we prove convergence of the method. The numerical experiments prove the effectiveness of the presented algorithm

Solving the nonlinear transportation problem by global optimization

The aim of this paper is to present the suitability of three different global optimization methods for specifically the exact optimum solution of the nonlinear transportation problem (NTP). The evaluated global optimization methods include the branch and reduce method, the branch and cut method and the combination of global and local search strategies. The considered global optimization methods were applied to solve NTPs with reference to literature. NTPs were formulated as nonlinear programming (NLP) optimization problems. The obtained optimal results were compared with those got from literature. A comparative evaluation of global optimization methods is presented at the end of the paper to show their suitability for solving NTPs. First published online: 10 Feb 201