A multi-criteria multi-commodity flow model for analysing transportation networks

This article proposes a novel multi-criteria multi-commodity network flow (MCMCNF) model to help transport planners and other analysts holistically assess different types of transportation systems (TS). This model provides a tool to autonomously analyse the effect of expansions, tolls, different levels of congestion and accidents leading to potential insights into a networks resilience and vulnerability, emissions distribution and risk. Unlike the mono criterion network flow models used for some time, we propose the application of multiple objectives. In this article we investigate the application of two objectives. The first maximises the flow of commodities and the second minimises travel related costs. The travel cost is modelled generically and may include the distance travelled, travel time and access charges. The considered cost function is non-linear, so different linearization strategies are suggested. These permit the model to be solved efficiently using Separable Programming techniques and the e-constraint method (ECM). We have applied the proposed model to a variety of case studies and demonstrate how different forms of sensitivity analysis can be performed. The numerical investigations have highlighted the specific features of the Pareto frontiers and the resilience and flexibility of the networks considered.