Fairness In a Multi-Commodity FixedCharge Network Flow Problem

Specialeforsvar: Karoline Amalie Trond Reich

Titel: Fairness In a Multi-Commodity Fixed Charge Network Flow Problem

Abstract: Solutions to multi-commodity fixed-charge network flow (MCFCNF) problems are studied to investigate their fairness as a supplement to traditional transport planning where the issue at stake is transport availability. Fairness is defined as the ratio between the distance travelled from origin to destination and the actual Euclidian distance. This definition is proposed as
more appropriate than other suggestions found in the literature. A model for the MCFCNF problem is established and three classes of networks are generated using the Python programming language and the Gurobi Optimizer solver. In the computational study the resulting effects for each class of instances are studied based on an analysis of effect frequency graphs indicating the fairness of routes. The same instances are then analyzed by applying as measures of fairness the mean absolute deviation (MAD), the Gini coefficient, and the conditional β-mean. These measures support the initial analysis and this gives reason to considering adding some or all of these measures as further constraints to the model. Because of time limitations only the linear MAD is implemented as an additional constraint and it is found that the cost increases when this constraint is added but also that run time of the model increases and that adding the constraint to instances which are already fair does not increase their fairness further. Application of this work range from container shipping to public transportation networks. Further research and modelling in the area of adding the conditional β-mean as a constraint is suggested.

Vejleder: Giovanni Pantuso
Censor: Line B. Reinhardt, RUC