Browsing by Subject "Robust optimization"

Now showing 1 - 20 of 22

Open Access
Delegated portfolio management under ambiguity aversion
(2014) Fabretti, A.; Herzel, S.; Pınar, M. Ç.
We examine the problem of setting optimal incentives for a portfolio manager hired by an investor who wants to induce ambiguity-robust portfolio choices with respect to estimation errors in expected returns. Adopting a worst-case max-min approach we obtain the optimal compensation in various cases where the investor and the manager, adopt or relinquish an ambiguity averse attitude. We also provide examples of applications to real market data.
Open Access
An improved probability bound for the Approximate S-Lemma
(Elsevier, 2007) Derinkuyu, K.; Pınar, M. Ç.; Camcı, A.
The purpose of this note is to give a probability bound on symmetric matrices to improve an error bound in the Approximate S-Lemma used in establishing levels of conservatism results for approximate robust counterparts.
Open Access
A note on robust 0-1 optimization with uncertain cost coefficients
(Springer, 2004) Pınar, M. Ç.
Based on the recent approach of Bertsimas and Sim (2004, 2003) to robust optimization in the presence of data uncertainty, we prove an easily computable and simple bound on the probability that the robust solution gives an objective function value worse than the robust objective function value, under the assumption that only cost coefficients are subject to uncertainty. We exploit the binary nature of the optimization problem in proving our results. A discussion on the cost of ignoring uncertainty is also included.
Open Access
On robust mean-variance portfolios
(Taylor and Francis, 2016) Pınar, M. Ç.
We derive closed-form portfolio rules for robust mean–variance portfolio optimization where the return vector is uncertain or the mean return vector is subject to estimation errors, both uncertainties being confined to an ellipsoidal uncertainty set. We consider different mean–variance formulations allowing short sales, and derive closed-form optimal portfolio rules in static and dynamic settings.
Open Access
On the S-procedure and some variants
(Springer, 2006) Derinkuyu, K.; Pınar, M. Ç.
We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.
Open Access
Provisioning virtual private networks under traffic uncertainty
(Wiley, 2007) Altın, Ayşegül; Amaldi, E.; Belotti, P.; Pınar, Mustafa Çelebi
We investigate a network design problem under traffic uncertainty that arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network to support all possible traffic matrices while minimizing the total reservation cost. The problem admits several versions depending on the desired topology of the reserved links, and the nature of the traffic data uncertainty. We present compact linear mixed-integer programming formulations for the problem with the classical hose traffic model and for a less conservative robust variant relying on the traffic statistics that are often available. These flow-based formulations allow us to solve optimally medium-to-large instances with commercial MIP solvers. We also propose a combined branch-and-price and cutting-plane algorithm to tackle larger instances. Computational results obtained for several classes of instances are reported and discussed.
Open Access
Restricted robust uniform matroid maximization under interval uncertainty
(Springer, 2007) Yaman, H.; Karaşan, O. E.; Pınar, M. Ç.
For the problem of selecting p items with interval objective function coefficients so as to maximize total profit, we introduce the r-restricted robust deviation criterion and seek solutions that minimize the r-restricted robust deviation. This new criterion increases the modeling power of the robust deviation (minmax regret) criterion by reducing the level of conservatism of the robust solution. It is shown that r-restricted robust deviation solutions can be computed efficiently. Results of experiments and comparisons with absolute robustness, robust deviation and restricted absolute robustness criteria are reported.
Open Access
Robust decentralized investment games
(2016-09) Çelik, Burak
In the first part of the thesis, assuming a one-period economy with an investor and two portfolio managers who are experts in investing each in a risky asset (or an index) with first and second moment information available to all parties, we consider the problem of the principal in distributing her wealth optimally among the two managers as well as setting optimally the fees to the portfolio managers under the condition that the principal wants to safeguard against uncertainty in the expert forecasts of the managers regarding the mean return of assets. In the second part, simple games are devised to ensure a fair allocation of contracts between the two managers under the conditions assumed in the first part. Furthermore, the game concept is extended in which three or more managers are involved.
Unknown
The robust Merton problem of an ambiguity averse investor
(Springer, 2017) Biagini, S.; Pınar, M. Ç.
We derive a closed form portfolio optimization rule for an investor who is diffident about mean return and volatility estimates, and has a CRRA utility. Confidence is here represented using ellipsoidal uncertainty sets for the drift, given a (compact valued) volatility realization. This specification affords a simple and concise analysis, as the agent becomes observationally equivalent to one with constant, worst case parameters. The result is based on a max–min Hamilton–Jacobi–Bellman–Isaacs PDE, which extends the classical Merton problem and reverts to it for an ambiguity-neutral investor.
Unknown
The robust network loading problem under hose demand uncertainty: formulation, polyhedral analysis, and computations
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2011) Altın, A.; Yaman, H.; Pınar, M. Ç.
We consider the network loading problem (NLP) under a polyhedral uncertainty description of traffic demands. After giving a compact multicommodity flow formulation of the problem, we state a decomposition property obtained from projecting out the flow variables. This property considerably simplifies the resulting polyhedral analysis and computations by doing away with metric inequalities. Then we focus on a specific choice of the uncertainty description, called the "hose model," which specifies aggregate traffic upper bounds for selected endpoints of the network. We study the polyhedral aspects of the NLP under hose demand uncertainty and use the results as the basis of an efficient branch-and-cut algorithm. The results of extensive computational experiments on well-known network design instances are reported.
Open Access
Robust optimization for the discrete time-cost tradeoff problem with cost uncertainty
(Springer International Publishing, 2015) Hazır, Öncü; Haouari, Mohamed; Erel, Erdal
Projects are subject to various sources of uncertainty that hamper reaching project targets; hence, it is crucial importance to use effective approaches to generate robust project schedules, which are less vulnerable to disruptions caused by uncontrollable factors. In this vein, this chapter examines analytical models and algorithms of robust multi-mode project scheduling, specifically, the robust discrete time-cost tradeoff problem (DTCTP). The models and algorithms presented in this chapter can support project managers from a wide range of industries in scheduling activities to minimize deviations from project goals. Furthermore, some surrogate measures that aim at providing an accurate estimate of the schedule robustness are developed and related experimental results are presented. Finally, some potential research areas are proposed and discussed. © Springer International Publishing Switzerland 2015.
Open Access
Robust optimization for the discrete time-cost tradeoff problem with cost uncertainty
(Springer, 2015) Hazır, Ö.; Haouari, M.; Erel, Erdal; Schwindt, C.; Zimmermann, J.
Projects are subject to various sources of uncertainty that hamper reaching project targets; hence, it is crucial importance to use effective approaches to generate robust project schedules, which are less vulnerable to disruptions caused by uncontrollable factors. In this vein, this chapter examines analytical models and algorithms of robust multi-mode project scheduling, specifically, the robust discrete time-cost tradeoff problem (DTCTP). The models and algorithms presented in this chapter can support project managers from a wide range of industries in scheduling activities to minimize deviations from project goals. Furthermore, some surrogate measures that aim at providing an accurate estimate of the schedule robustness are developed and related experimental results are presented. Finally, some potential research areas are proposed and discussed.
Open Access
Robust optimization models for network revenue management
(2024-07) Bahtiyar, İrem
Effective capacity allocation methods play a crucial role in Network Revenue Management. Yet, current methods for determining optimal capacity controls under uncertainty, such as stochastic optimization, often assume a known probability distribution for unknown parameters. This assumption may degrade a model’s performance when faced with unexpected data patterns. This thesis explores a novel approach through robust optimization to address stochastic resource allocation problems. We introduce a heuristic based on these robust formulations to derive actionable results. Through extensive simulations focused on seat allocation problems within the revenue management domain, our proposed formulations demonstrate improved worst-case performances. Notably, even under favorable scenarios, our solutions remain comparable to existing methods in the revenue management literature.
Open Access
Robust optimization models for the dicrete time/cost trade-off problem
(Elsevier, 2011-03) Hazır, O.; Erel, E.; Günalay, Y.
Developing models and algorithms to generate robust project schedules that are less sensitive to disturbances are essential in today’s highly competitive uncertain project environments. This paper addresses robust scheduling in project environments; specifically, we address the discrete time/cost trade-off problem (DTCTP). We formulate the robust DTCTP with three alternative optimization models in which interval uncertainty is assumed for the unknown cost parameters. We develop exact and heuristic algorithms to solve these robust optimization models. Furthermore, we compare the schedules that have been generated with these models on the basis of schedule robustness. & 2010 Elsevier B.V. All rights reserved.
Open Access
Robust optimization of multi-objective multi-armed bandits with contaminated bandit feedback
(2022-06) Bozgan, Kerem
Multi-objective multi-armed bandits (MO-MAB) is an important extension of the standard MAB problem that has found a wide variety of applications ranging from clinical trials to online recommender systems. We consider Pareto set identification problem in the adversarial MO-MAB setting, where at each arm pull, with probability ϵ ∈ (0,1/2), an adversary corrupts the reward samples by replacing the true samples with the samples from an arbitrary distribution of its choosing. Existing MO-MAB methods in the literature are incapable of handling such attacks unless there are strict restrictions on the contamination distributions. As a result, these methods perform poorly in practice where such restrictions on the adversary are not valid in general. To fill this gap in the literature, we propose two different robust, median-based optimization methods that can approximate the Pareto optimal set from contaminated samples. We prove a sample complexity bound of the form O(1/α^2 log(1/δ)) for the proposed methods, where α>0 and δ ∈ (0,1) are accuracy and confidence parameters, respectively, that can be set by the user according to his/her preference. This bound matches, in the worst case, the bounds from [1, Theorem 4] and [2, Theorem 3] that consider the adversary free setting. We compare the proposed methods with a mean-based method from the MO-MAB literature on real-world and synthetic experiments. Numerical results verify our theoretical expectations and show the importance of robust algorithm design in the adversarial setting.
Open Access
Robust profit opportunities in risky financial portfolios
(Elsevier, 2005) Pınar, M. Ç.; Tütüncü, R. H.
For risky financial securities with given expected return vector and covariance matrix, we propose the concept of a robust profit opportunity in single- and multiple-period settings. We show that the problem of finding the "most robust" profit opportunity can be solved as a convex quadratic programming problem, and investigate its relation to the Sharpe ratio.
Embargo
Robust resource allocation under uncertainty
(2024-07) Demir, Ali Eren
Current methods for determining optimal capacity controls under uncertainty, such as stochastic optimization, often assume a known distribution for unknown parameters. This paper presents a novel approach using robust optimization to address the stochastic resource allocation problem in airline seat-inventory control. Our static formulations account for demand dependencies, offering a streamlined alternative to existing customer-choice models in revenue management literature. We analyze the structure of our proposed formulations, and provide insights on several robust counterparts of the seat-inventory control problem, considering various measures of robustness. We introduce algorithms based on these robust formulations to derive actionable results. Through extensive simulations focused on seat allocation problems within the revenue management domain, our proposed formulations demonstrate significantly improved worst-case performances. Notably, even under favorable scenarios, the performance of our solutions are comparable to those of the existing methods in the revenue management literature. By providing protection against forecasting errors in demand distribution parameters and offering improved booking limit controls when demand falls below expected value, our formulations demonstrate superior revenue retention compared to existing methods in our comparative analyses.
Open Access
Robust screening under ambiguity
(Springer, 2017) Pınar, M. Ç.; Kızılkale, C.
We consider the problem of screening where a seller puts up for sale an indivisible good, and a buyer with a valuation unknown to the seller wishes to acquire the good. We assume that the buyer valuations are represented as discrete types drawn from some distribution, which is also unknown to the seller. The seller is averse to possible mis-specification of types distribution, and considers the unknown type density as member of an ambiguity set and seeks an optimal pricing mechanism in a worst case sense. We specify four choices for the ambiguity set and derive the optimal mechanism in each case.
Open Access
The robust spanning tree problem with interval data
(Elsevier, 2001) Yaman, H.; Karaşan, O. E.; Pınar, M. Ç.
Motivated by telecommunications applications we investigate the minimum spanning tree problem where edge costs are interval numbers. Since minimum spanning trees depend on the realization of the edge costs, we de5ne the robust spanning tree problem to hedge against the worst case contingency, and present a mixed integer programming formulation of the problem. We also de5ne some useful optimality concepts, and present characterizations for these entities leading to polynomial time recognition algorithms. These entities are then used to preprocess a given graph with interval data prior to the solution of the robust spanning tree problem. Computational results show that these preprocessing procedures are quite e9ective in reducing the time to compute a robust spanning tree.
Open Access
Robust stock assortment and cutting under defects in automotive glass production
(Wiley-Blackwell Publishing, Inc., 2022-07-23) Arbib, Claudio; Marinelli, Fabrizio; Pınar, Mustafa Ç.; Pizzuti, Andrea
We address an assortment-and-cutting problem arising in the glass industry. The objective is to provide minimum waste solutions that are robust against such raw material imperfections as those possibly occurring with float glass production technology. The stochastic realization of defects is modeled as a spatial Poisson point process. A mixed integer program in the classical vein of robust optimization is presented and tested on data taken from a real plant application. Defective final products must in any case be discarded as waste but, if a recourse strategy is adopted, faults in glass sheets can sometimes be recovered. Closed forms for the computation of faulty item probabilities are provided in simple cases, and obtained via Monte Carlo simulation in more complex ones. The computational results demonstrate the benefits of the robust approach in terms of the reduction of back-orders and overproduction, thereby showing that recourse strategies can enable nonnegligible improvements. Encouraged by this result, the management is presently evaluating the possibility of adopting the proposed model in plant operation.