Robust capacity expansion and routing in networks

Abstract

In this thesis, we consider a robust capacity expansion-routing problem with uncertain demand. Given a network with source and demand nodes and a capacity budget, the capacity expansion problem is related to the determination of the arcs on which additional capacity will be installed in order to minimize the overall routing cost while satisfying the demand of the nodes. We make use of the Robust Counterpart (RC) approach in the literature in order to make capacity installation and routing decisions. RC approach is important since it does not allow any constraint violation for any realization of the uncertainty and such approaches are often necessary in engineering applications in real life. We apply the classical RC formulation to our problem that results in a simple one-stage model. The two-stage version of the RC formulation, namely the Adjustable Robust Counterpart (ARC), is also applicable to our problem. The formulation of the ARC is given but since it is not computationally tractable, an approximation to ARC developed recently, namely Affinely Adjustable Robust Counterpart (AARC) formulation, is applied to our problem and solved. The efficiencies of the RC formulation and AARC formulation are tested via two different sets of numerical studies in the experimental part. The main model that allows capacity installation in continuous amounts as well as two extensions that make use of the modular capacity approach are used in the experimental study. The computational experiments illustrate that AARC approach provides robust solutions at a much cheaper cost in terms of objective function value when compared to RC approach. In addition the loss of optimality due to application of AARC formulation is minor.