Sample Average Approximation Technique for Flexible Network Design Problem

Abstract

Finding an optimal investment strategy to use scarce resources efficiently is challenging, since the transportation network parameters such as demand, capacity, and travel cost are uncertain. Sequencing investments over time can give flexibility to the planner so as to change, delay, or even abandon the future investment based on system realization. This paper presents a stochastic mathematical program with equilibrium constraints (STOCH-MPEC) formulation for a multistage network design problem, flexible network design problem (FNDP), accounting for demand stochasticity and demand elasticity. STOCH-MPEC problems can be computationally intractable, if the number of scenarios is large and/or the study network is large-scale. To reduce the associated complexity of FNDP, we develop a sample average approximate method (SAA) to efficiently solve the flexible network design problem. We implement the SAA on a test network and compare the performance of SAA with different sample sizes. We show that SAA can produce solutions that are close to the true solutions with considerably fewer scenarios and hence can be a viable computational technique for the stochastic network design problem.