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Process scheduling under uncertainty: Review and challenges
, 2008
"... Uncertainty is a very important concern in production scheduling since it can cause infeasibilities and production disturbances. Thus scheduling under uncertainty has received a lot of attention in the open literature in recent years from chemical engineering and operations research communities. The ..."
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Cited by 20 (5 self)
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Uncertainty is a very important concern in production scheduling since it can cause infeasibilities and production disturbances. Thus scheduling under uncertainty has received a lot of attention in the open literature in recent years from chemical engineering and operations research communities. The purpose of this paper is to review the main methodologies that have been developed to address the problem of uncertainty in production scheduling as well as to identify the main challenges in this area. The uncertainties in process scheduling are first analyzed, and the different mathematical approaches that exist to describe process uncertainties are classified. Based on the different descriptions for the uncertainties, alternative scheduling approaches and relevant optimization models are reviewed and discussed. Further research challenges in the field of process scheduling under uncertainty are identified and some new ideas are discussed.
Stochastic Programming Models in Financial Optimization: A Survey
"... In this paper, we survey the stochastic programming models developed to deal with financial optimization problems. A few methods are introduced in details to generate reasonable scenarios which are of much importance for a successful model. Besides, computation aspect as well as some open problems ..."
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Cited by 9 (0 self)
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In this paper, we survey the stochastic programming models developed to deal with financial optimization problems. A few methods are introduced in details to generate reasonable scenarios which are of much importance for a successful model. Besides, computation aspect as well as some open problems in this area are addressed.
A stochastic integer programming approach to solving a synchronous optical network ring design problem
 Networks
"... We develop stochastic integer programming techniques tailored toward solving a Synchronous Optical Network (SONET) ring design problem with uncertain demands. Our approach is based on an Lshaped algorithm, whose (integer) master program prescribes a candidate network design, and whose (continuous) ..."
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Cited by 7 (3 self)
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We develop stochastic integer programming techniques tailored toward solving a Synchronous Optical Network (SONET) ring design problem with uncertain demands. Our approach is based on an Lshaped algorithm, whose (integer) master program prescribes a candidate network design, and whose (continuous) subproblems relay information regarding potential shortage penalty costs to the ring design decisions. This naive implementation performs very poorly due to two major problems: (1) the weakness of the master problem relaxations, and (2) the limited information passed to the master problem by the optimality cuts. Accordingly, we enforce certain necessary conditions regarding shortage penalty contributions to the objective function within the master problem, along with a corresponding set of valid inequalities that improve the solvability of the master problem. We also detail how a nonlinear reformulation of the model can be used to capture an exponential number of optimality cuts generated by the linear model. We augment these techniques with a powerful upperbounding heuristic to further accelerate the convergence of the algorithm, and demonstrate the effectiveness of our methodologies on a test bed of randomly generated stochastic SONET instances. 1
Robust Dynamic Continuous Network Design Problem
"... A robust optimization model is presented for the dynamic traffic assignment–based continuous network design problem, which accounts for a bilevel objective and longterm origin–destination demand uncertainty. The model also embeds Daganzo’s cell transmission model. The objective minimizes the trade ..."
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Cited by 6 (2 self)
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A robust optimization model is presented for the dynamic traffic assignment–based continuous network design problem, which accounts for a bilevel objective and longterm origin–destination demand uncertainty. The model also embeds Daganzo’s cell transmission model. The objective minimizes the tradeoff between expected total system travel time (TSTT) and expected risk. As such, the robust model provides the optimal solution that is least sensitive to the variation of travel demand, given the degree of robustness by transportation planners. The new robust model is compared with the existing network design models on a simple cell transmission test network. The robust model with greater degree of robustness yields less expected risk with the sacrifice of higher expected TSTT. The robust model yields the most robust solution, and no other model provides a satisfactory solution across the budget range. In addition, how a visualized graph may be used to elicit the preference information from transportation planners on the desired degree of robustness is illustrated.
Explicit reformulations of robust optimization problens with general uncertainty sets
 SIAM J. Optim
"... Abstract. We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explici ..."
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Cited by 5 (3 self)
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Abstract. We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explicit optimization problems. Moreover, we develop simplified reformulations for problems with uncertainty sets defined by convex homogeneous functions. Our results provide a unified treatment of many situations that have been investigated in the literature, and are applicable to a wider range of problems and more complicated uncertainty sets than those considered before. The analysis in this paper makes it possible to use existing continuous optimization algorithms to solve more complicated robust optimization problems. The analysis also shows how the structure of the resulting reformulation of the robust counterpart depends both on the structure of the original nominal optimization problem and on the structure of the uncertainty set. Key words. Robust optimization, data uncertainty, mathematical programming, homogeneous functions, convex analysis AMS subject classifications. 90C30, 90C15, 90C34, 90C25, 90C05.
On Robustness/Performance Tradeoffs in Linear Programming and Markov Decision Processes
"... Computation of a satisfactory policy for a decision problem when the parameters of the model are uncertain is a problem encountered in many applications. The traditional robust approach is based on a worstcase analysis and may lead to overly conservative solutions. In this paper we directly quantif ..."
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Cited by 1 (0 self)
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Computation of a satisfactory policy for a decision problem when the parameters of the model are uncertain is a problem encountered in many applications. The traditional robust approach is based on a worstcase analysis and may lead to overly conservative solutions. In this paper we directly quantify the robustness to uncertainty and consider the tradeoff between the nominal performance and robustness measures. Optimization in both linear programming and Markov decision processes is discussed. For linear programming we consider the tradeoff between the nominal cost of a solution and a robustness measure that quantifies the magnitude of constraint violation under the most adversarial parameters. We propose an algorithm that computes the whole set of Pareto efficient solutions based on parametric linear programming. For Markov decision processes, we consider the tradeoff between the performance under nominal parameters and the performance under adversarial parameters. For the special case where only the rewards are uncertain, we propose an algorithm that computes the whole set of Pareto efficient policies in a single pass. Subject classifications: dynamical programming: Markov, finite state; programming: linear, multiple criteria; uncertainty; robustness.
A Robust Approach to LocationAllocation Problem under Uncertainty
, 2008
"... This paper presents a new mathematical model for locationallocation problem considering uncertain parameter. In realworld cases, demand, distance, traveling time or any parameters in classical models may change over the period of time. So, considering uncertainty yields more flexibility for the re ..."
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This paper presents a new mathematical model for locationallocation problem considering uncertain parameter. In realworld cases, demand, distance, traveling time or any parameters in classical models may change over the period of time. So, considering uncertainty yields more flexibility for the results and its applications. In our study, environmental uncertainty is described by discrete scenarios where probability of occurrence each of them is not known. So, we use robust optimization technique to analyze the model. Therefore, we introduce a formulation of the robust locationallocation problem in which we have budget constraint. Also, we present mean value model where each uncertain parameter is replaced by its mean to compare with robust model. Finally, some numerical examples are illustrated to show effectiveness of the robust solutions.
Robustness Approach to the Integrated Network Design Problem, Signal Optimization and Dynamic Traffic Assignment Problem
, 2006
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Theory and Methodology A heuristic to minimax absolute regret for linear programs with interval objective function coecients
"... Abstract Decision makers faced with uncertain information often experience regret upon learning that an alternative action would have been preferable to the one actually selected. Models that minimize the maximum regret can be useful in such situations, especially when decisions are subject to ex p ..."
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Abstract Decision makers faced with uncertain information often experience regret upon learning that an alternative action would have been preferable to the one actually selected. Models that minimize the maximum regret can be useful in such situations, especially when decisions are subject to ex post review. Of particular interest are those decision problems that can be modeled as linear programs with interval objective function coecients. The minimax regret solution for these formulations can be found using an algorithm that, at each iteration, solves ®rst a linear program to obtain a candidate solution and then a mixed integer program (MIP) to maximize the corresponding regret. The exact solution of the MIP is computationally expensive and becomes impractical as the problem size increases. In this paper, we develop a heuristic for the MIP and investigate its performance both alone and in combination with exact procedures. The heuristic is shown to be eective for problems that are signi®cantly larger than those previously reported in the literature. Ó
Stress Testing via Contamination
"... Abstract. When working with stochastic financial models, one exploits various simplifying assumptions concerning the model, its stochastic specification, parameter values, etc. In addition, approximations are used to get a solution in an efficient way. The obtained results, recommendations for the r ..."
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Abstract. When working with stochastic financial models, one exploits various simplifying assumptions concerning the model, its stochastic specification, parameter values, etc. In addition, approximations are used to get a solution in an efficient way. The obtained results, recommendations for the risk and portfolio manager, should be then carefully analyzed. This is done partly under the heading “stress testing”, which is a term used in financial practice without any generally accepted definition. In this paper we suggest to exploit the contamination technique to give the “stress test ” a more precise meaning. Using examples from portfolio and risk management we shall point out the directly applicable cases and will discuss also limitations of the proposed method. Key words: Scenariobased stochastic programs, stress testing, contamination bounds, portfolio management, CVaR AMS subject classification: 90C15, 90C31, 91B28 1