38,866 research outputs found
DEA Problems under Geometrical or Probability Uncertainties of Sample Data
This paper discusses the theoretical and practical aspects of new methods for solving DEA problems under real-life geometrical uncertainty and probability uncertainty of sample data. The proposed minimax approach to solve problems with geometrical uncertainty of sample data involves an implementation of linear programming or minimax optimization, whereas the problems with probability uncertainty of sample data are solved through implementing of econometric and new stochastic optimization methods, using the stochastic frontier functions estimation.DEA, Sample data uncertainty, Linear programming, Minimax optimization, Stochastic optimization, Stochastic frontier functions
The Orienteering Problem under Uncertainty Stochastic Programming and Robust Optimization compared
The Orienteering Problem (OP) is a generalization of the well-known traveling salesman problem and has many interesting applications in logistics, tourism and defense. To reflect real-life situations, we focus on an uncertain variant of the OP. Two main approaches that deal with optimization under uncertainty are stochastic programming and robust optimization. We will explore the potentialities and bottlenecks of these two approaches applied to the uncertain OP. We will compare the known robust approach for the uncertain OP (the robust orienteering problem) to the new stochastic programming counterpart (the two-stage orienteering problem). The application of both approaches will be explored in terms of their suitability in practice
Data-driven Optimization Approaches to the Power System Planning under Uncertainty
In order to protect the environment and address fossil fuel scarcity,
renewable energy is increasingly used for power generation. However, due to the
uncertainties it brings to electricity production, deterministic optimization
is no longer sufficient for operational needs. Therefore, a large number of
optimization techniques under uncertainty have been proposed, which provide
good ways to address uncertainties. This paper selects three of the more
important optimization techniques under uncertainty to introduce: stochastic
programming (SP), robust optimization (RO), and a novel approach named
distributionally robust optimization (DRO) based on the first two. We explain
the basic framework and general process of each approach using specific
examples. The focus is on how each method addresses the uncertainties. In
addition, we also compare their strengths and weaknesses and discuss future
research directions
Comparing the performances of two techniques for the optimization under parametric uncertainty of the simultaneous design and planning of a multiproduct batch plant
This paper addresses the comparison between two techniques for the optimization under parametric uncertainty of multiproduct batch plants integrating design and production planning decisions. This problem has been conceived as a two-stage stochastic mixed integer linear programming (MILP) in which the first-stage decisions consist of design variables that allow determining the batch plant structure, and the second-stage decisions consist of production planning continuous variables in a multiperiod context. The objective function maximizes the expected net present value. In the first solving approach, the problem has been tackled through mathematical programming considering a discrete set of scenarios. In the second solving approach, the multi-scenario MILP problem has been reformulated by adopting a simulation-based optimization scheme to accommodate the variables belonging to different management levels. Advantages and disadvantages of both approaches are demonstrated through a case study. Results allow concluding that a simulation-based optimization strategy may be a suitable technique to afford two-stage stochastic programming problems.Sociedad Argentina de Informática e Investigación Operativ
Distributionally robust optimization with applications to risk management
Many decision problems can be formulated as mathematical optimization models. While deterministic
optimization problems include only known parameters, real-life decision problems
almost invariably involve parameters that are subject to uncertainty. Failure to take this
uncertainty under consideration may yield decisions which can lead to unexpected or even
catastrophic results if certain scenarios are realized.
While stochastic programming is a sound approach to decision making under uncertainty, it
assumes that the decision maker has complete knowledge about the probability distribution
that governs the uncertain parameters. This assumption is usually unjustified as, for most
realistic problems, the probability distribution must be estimated from historical data and
is therefore itself uncertain. Failure to take this distributional modeling risk into account
can result in unduly optimistic risk assessment and suboptimal decisions. Furthermore, for
most distributions, stochastic programs involving chance constraints cannot be solved using
polynomial-time algorithms.
In contrast to stochastic programming, distributionally robust optimization explicitly accounts
for distributional uncertainty. In this framework, it is assumed that the decision maker has
access to only partial distributional information, such as the first- and second-order moments
as well as the support. Subsequently, the problem is solved under the worst-case distribution
that complies with this partial information. This worst-case approach effectively immunizes
the problem against distributional modeling risk.
The objective of this thesis is to investigate how robust optimization techniques can be used
for quantitative risk management. In particular, we study how the risk of large-scale derivative
portfolios can be computed as well as minimized, while making minimal assumptions about
the probability distribution of the underlying asset returns. Our interest in derivative portfolios
stems from the fact that careless investment in derivatives can yield large losses or even
bankruptcy. We show that by employing robust optimization techniques we are able to capture
the substantial risks involved in derivative investments. Furthermore, we investigate how
distributionally robust chance constrained programs can be reformulated or approximated as
tractable optimization problems. Throughout the thesis, we aim to derive tractable models
that are scalable to industrial-size problems
A primal-dual decomposition based interior point approach to two-stage stochastic linear programming
Decision making under uncertainty is a challenge faced by many decision makers. Stochastic programming is a major tool developed to deal with optimization with uncertainties that has found applications in, e.g. finance, such as asset-liability and bond-portfolio management. Computationally however, many models in stochastic programming remain unsolvable because of overwhelming dimensionality. For a model to be well solvable, its special structure must be explored. Most of the solution methods are based on decomposing the data. In this paper we propose a new decomposition approach for two-stage stochastic programming, based on a direct application of the path-following method combined with the homogeneous self-dual technique. Numerical experiments show that our decomposition algorithm is very efficient for solving stochastic programs. In particular, we apply our deompostition method to a two-period portfolio selection problem using options on a stock index. In this model the investor can invest in a money-market account, a stock index, and European
options on this index with different maturities. We experiment our model with market prices of options on the S&P500
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