An alternative method to solve the biobjective minimum cost flow problem

Single commodity flow problems simultaneously optimizing two objectives are addressed. We propose a method that finds all the efficient extreme points in the objective space. To accomplish this task, we introduce an auxiliary problem, with a single objective, that makes use of the weighted maximum distance. This problem allows making a guided search for efficient solutions taking into account the preferences of the decision-maker. The proposed method is characterized by the use of the classic resolution tools of network flow problems, such as the Network Simplex method. Multi-objective linear programming methodology is not used, and furthermore, the solution to the problem is determined directly in the objective space. Results of extensive tests are presented and discussed.