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Abstract: This paper deals with multi-commodity flow problem with fractional objective function. The optimality conditions and the duality concepts of this problem are given. For this aim, the fractional linear programming formulation of this problem is considered and the weak duality, the strong direct duality and the weak complementary slackness theorems are proved applying the traditional duality theory of linear programming problems which is different from same results in Chadha and Chadha (2007) [1]. In addition, a strong (strict) complementary slackness theorem is derived which is firstly presented based on the best of our knowledge. These theorems are transformed in order to find the new reduced costs for fractional multi-commodity flow problem. These parameters can be used to construct some algorithms for considered multi-commodity flow problem in a direct manner. Throughout the paper, the boundedness of the primal feasible set is reduced to a weaker assumption about solvability of primal problem which is another contribution of this paper. Finally, a real world application of the fractional multi-commodity flow problem is presented. [Copyright &y& Elsevier]

The Gate Allocation Problem (GAP) is one of the numerous operational problems that all busy airports have to handle and to optimize every day. In this article, we focus on two important objectives for the GAP: the robustness and the taxiing times. We first analyze a basic model which optimizes the robustness of the solution to the GAP and propose a more realistic and compact Multi-commodity Flow Problem model (MFP) to optimize both the robustness and the taxiing times. Based on tests with real data at Paris-Charles-de-Gaulle airport, this new efficient MFP model outperforms the basic one by orders of magnitude. • New Multi-commodity Flow model optimally solves large-scale Gate Allocation Problem. • Schedule robustness and taxiing optimized to improve airport operations. • Outperforms former model by orders of magnitude on real data at major airport. • Fast enough to enable real-time applications. [ABSTRACT FROM AUTHOR]