Browsing by Subject "Robust Optimization"

Now showing 1 - 5 of 5

Open Access
An application of stochastic programming on robust airline scheduling
(2014) Karacaoğlu, Nil
The aim of this study is to create flight schedules which are less susceptible to unexpected flight delays. To this end, we examine the block time of the flight in two parts, cruise time and non-cruise time. The cruise time is accepted as controllable within some limit and it is taken as a decision variable in our model. The non-cruise time is open to variations. In order to consider the variability of non-cruise times in the planning stage, we propose a nonlinear mixed integer two stage stochastic programming model which takes the non-cruise time scenarios as input. The published departure times of flights are determined in the first stage and the actual schedule is decided on the second stage depending on the non-cruise times. The objective is to minimize the airline’s operating and passenger dissatisfaction cost. Fuel and CO2 emission costs are nonlinear and this nonlinearity is handled by second order conic inequalities. Two heuristics are proposed to solve the problem when the size of networks and number of scenarios increase. A computational study is conducted using the data of a major U.S. carrier. We compare the solutions of our stochastic model with the ones found by using expected values of non-cruise times and the company’s published schedule.
Open Access
Equilibrium in an ambiguity-averse mean-variance investors market
(Elsevier, 2014-09-16) Pınar, M. Ç.
In a financial market composed of n risky assets and a riskless asset, where short sales are allowed and mean–variance investors can be ambiguity averse, i.e., diffident about mean return estimates where confidence is represented using ellipsoidal uncertainty sets, we derive a closed form portfolio rule based on a worst case max–min criterion. Then, in a market where all investors are ambiguity-averse mean–variance investors with access to given mean return and variance–covariance estimates, we investigate conditions regarding the existence of an equilibrium price system and give an explicit formula for the equilibrium prices. In addition to the usual equilibrium properties that continue to hold in our case, we show that the diffidence of investors in a homogeneously diffident (with bounded diffidence) mean–variance investors’ market has a deflationary effect on equilibrium prices with respect to a pure mean–variance investors’ market in equilibrium. Deflationary pressure on prices may also occur if one of the investors (in an ambiguity-neutral market) with no initial short position decides to adopt an ambiguity-averse attitude. We also establish a CAPM-like property that reduces to the classical CAPM in case all investors are ambiguity-neutral.
Open Access
Models and algorithms for deterministic and robust discrete time/cost trade-off problems
(2008) Hazır, Öncü
Projects are subject to various sources of uncertainties that often negatively impact activity durations and costs. Therefore, it is of crucial importance to develop effective approaches to generate robust project schedules that are less vulnerable to disruptions caused by uncontrollable factors. This dissertation concentrates on robust scheduling in project environments; specifically, we address the discrete time/cost trade-off problem (DTCTP). Firstly, Benders Decomposition based exact algorithms to solve the deadline and the budget versions of the deterministic DTCTP of realistic sizes are proposed. We have included several features to accelerate the convergence and solve large instances to optimality. Secondly, we incorporate uncertainty in activity costs. We formulate robust DTCTP using three alternative models. We develop exact and heuristic algorithms to solve the robust models in which uncertainty is modeled via interval costs. The main contribution is the incorporation of uncertainty into a practically relevant project scheduling problem and developing problem specific solution approaches. To the best of our knowledge, this research is the first application of robust optimization to DTCTP. Finally, we introduce some surrogate measures that aim at providing an accurate estimate of the schedule robustness. The pertinence of proposed measures is assessed through computational experiments. Using the insight revealed by the computational study, we propose a two-stage robust scheduling algorithm. Furthermore, we provide evidence that the proposed approach can be extended to solve a scheduling problem with tardiness penalties and earliness rewards.
Open Access
Robust capacity expansion and routing in networks
(2006) Kahramanoğlu, İbrahim Evren
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.
Open Access
The robust shortest path problem with interval data uncertainties
(2001) Karaman, Abdullah Sıddık
In this study, we investigate the well-known shortest path problem on directed acyclic graphs under arc length uncertainties. We structure data uncertainty by taking the arc lengths as interval ranges. In order to handle uncertainty in the decision making process, we believe that a robustness approach is appropriate to use. The robustness criteria we used are the minimax (absolute robustness) criterion and the minimax regret (relative robustness) criterion. Under these criteria, we de ne and identify paths which perform satisfactorily under any likely input data and give mixed integer programming formulation to nd them. In order to simplify decision making, we classify arcs based on the realization of the input data. We show that knowing which arcs are always on shortest paths and which arcs are never on shortest paths we can preprocess a graph for robust path problems. Computational results support our claim that the preprocessing of graphs helps us signi cantly in solving the robust path problems.