Serimlerde dayanıklı kapasite arttırımı ve rotalama kararları

In this thesis, we consider a robust capacity expansion-routing problem withuncertain demand. Given a network with source and demand nodes and a ca-pacity budget, the capacity expansion problem is related to the determination ofthe arcs on which additional capacity will be installed in order to minimize theoverall routing cost while satisfying the demand of the nodes. We make use ofthe Robust Counterpart (RC) approach in the literature in order to make capac-ity installation and routing decisions. RC approach is important since it doesnot allow any constraint violation for any realization of the uncertainty and suchapproaches are often necessary in engineering applications in real life.We apply the classical RC formulation to our problem that results in a sim-ple one-stage model. The two-stage version of the RC formulation, namely theAdjustable Robust Counterpart (ARC), is also applicable to our problem. Theformulation of the ARC is given but since it is not computationally tractable, anapproximation to ARC developed recently, namely Affinely Adjustable RobustCounterpart (AARC) formulation, is applied to our problem and solved.The efficiencies of the RC formulation and AARC formulation are tested viatwo different sets of numerical studies in the experimental part. The main modelthat allows capacity installation in continuous amounts as well as two extensionsthat make use of the modular capacity approach are used in the experimentalstudy. The computational experiments illustrate that AARC approach providesrobust solutions at a much cheaper cost in terms of objective function value whencompared to RC approach. In addition the loss of optimality due to applicationof AARC formulation is minor.Keywords: Robust Optimization, Capacity Expansion Problem Robust Counter-part, Adjustable Robust Counterpart, Affinely Adjustable Robust Counterpart.i