Stochastic multi-objective models for network design problem

Abstract

Transportation network design problem ( NDP) is inherently multi-objective in nature, because it involves a number of stakeholders with different needs. In addition, the decision-making process sometimes has to be made under uncertainty where certain inputs are not known exactly. In this paper, we develop three stochastic multi-objective models for designing transportation network under demand uncertainty. These three stochastic multi-objective NDP models are formulated as the expected value multi-objective programming ( EVMOP) model, chance constrained multi-objective programming ( CCMOP) model, and dependent chance multi-objective programming ( DCMOP) model in a bi-level programming framework using different criteria to hedge against demand uncertainty. To solve these stochastic multi-objective NDP models, we develop a solution approach that explicitly optimizes all objectives under demand uncertainty by simultaneously generating a family of optimal solutions known as the Pareto optimal solution set. Numerical examples are also presented to illustrate the concept of the three stochastic multi-objective NDP models as well as the effectiveness of the solution approach.