A primal–dual simplex algorithm for bi-objective network flow problems

Eusébio, Augusto and Figueira, José Rui and Ehrgott, Matthias (2009) A primal–dual simplex algorithm for bi-objective network flow problems. 4OR: A Quarterly Journal of Operations Research, 7 (3). pp. 255-273. ISSN 1619-4500

Abstract

In this paper we develop a primal–dual simplex algorithm for the bi-objective linear minimum cost network flow problem. This algorithm improves the general primal–dual simplex algorithm for multi-objective linear programs by Ehrgott et al. (J Optim Theory Appl 134:483–497, 2007). We illustrate the algorithm with an example and provide numerical results.