Coherent risk measures have become a popular tool for incorporating risk aversion into stochastic optimization models. For dynamic models in which uncertainty is resolved at more than one stage, however, using coheren...
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Coherent risk measures have become a popular tool for incorporating risk aversion into stochastic optimization models. For dynamic models in which uncertainty is resolved at more than one stage, however, using coherent risk measures within a standard single-level optimization framework becomes problematic. To avoid severe time-consistency difficulties, the current state of the art is to employ risk measures of a specific nested form, which unfortunately have some undesirable and somewhat counterintuitive modeling properties. This paper summarizes the potential drawbacks of nested-form risk measure issues and then presents an alternative multilevel optimization modeling approach that enforces a form of time consistency through constraints rather than by restricting the modeler's choice of objective function. This technique leads to models that are time consistent even while using time-inconsistent risk measures and can easily be formulated to be law invariant with respect to the final wealth if so desired. We argue that this approach should be the starting point for all multistage optimization modeling. When used with time-consistent objective functions, we show its multilevel optimization constraints become redundant, and the associated models thus simplify to a more familiar single-objective form. Unfortunately, we also show that our proposed approach leads to NP-hard models, even in the simplest imaginable setting in which it would be needed: three-stage linear problems on a finite probability space, using the standard average value-at-risk and first-order mean-semideviation risk measures. Finally, we show that for a simple but reasonably realistic test application, the kind of models we propose, although drawn from an NP-hard family and certainly more time consuming to solve than those obtained from the nested-objective approach, are readily solvable to global optimality using a standard commercial mixed-integer linear programming solver. Therefore, there seems s
This paper presents the evolution and design of the Swiss reserve market and describes its two-stage stochastic market-clearing model. In Switzerland, the reserve market comprises weekly and daily auctions. The decisi...
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This paper presents the evolution and design of the Swiss reserve market and describes its two-stage stochastic market-clearing model. In Switzerland, the reserve market comprises weekly and daily auctions. The decision-making problem is to determine the amount of reserves that should be procured in each market stage. The stochasticity stems from daily offers which are not available at the beginning of the week, when the first-stage decisions are made. The new market-clearing model minimizes expected procurement costs of reserves, while taking reserve dimensioning criteria and market properties into consideration. Since the last week of January 2014, this model has been clearing the reserve market in Switzerland. To our knowledge, this is the first real-world implementation of a stochastic market-clearing model in electricity markets.
Given its complexity and relevance in healthcare, the well-known Nurse Scheduling Problem (NSP) has been the subject of several researches and different approaches have been used for its solution. The importance of th...
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Given its complexity and relevance in healthcare, the well-known Nurse Scheduling Problem (NSP) has been the subject of several researches and different approaches have been used for its solution. The importance of this problem comes from its critical role in healthcare processes as NSP assigns nurses to daily shifts while respecting both the preferences of the nurses and the objectives of hospital. Most models in NSP literature have dealt with this problem in a deterministic environment, while in the real-world applications of NSP, the vagueness of information about management objectives and nurse preferences are sources of uncertainties that need to be managed so as to provide a qualified schedule. In this study, we propose a stochastic optimization model for the Department of Heart Surgery in Razavi Hospital, which accounts for uncertainties in the demand and stay period of patients over time. Sample Average Approximation (SAA) method is used to obtain an optimal schedule for minimizing the regular and overtime assignment costs, with the numerical experiments demonstrating the convergence of statistical bounds and moderate sample size for a given numerical experiment. The results confirm the validity of the model. (C) 2016 Elsevier Ltd. All rights reserved.
We discuss the incorporation of risk measures into multistage stochastic programs. While much attention has been recently devoted in the literature to this type of model, it appears that there is no consensus on the b...
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We discuss the incorporation of risk measures into multistage stochastic programs. While much attention has been recently devoted in the literature to this type of model, it appears that there is no consensus on the best way to accomplish that goal. In this paper, we discuss pros and cons of some of the existing approaches. A key notion that must be considered in the analysis is that of consistency, which roughly speaking means that decisions made today should agree with the planning made yesterday for the scenario that actually occurred. Several definitions of consistency have been proposed in the literature, with various levels of rigor;we provide our own definition and give conditions for a multi-period risk measure to be consistent. A popular way to ensure consistency is to nest the one-step risk measures calculated in each stage, but such an approach has drawbacks from the algorithmic viewpoint. We discuss a class of risk measures which we call expected conditional risk measures that address those shortcomings. We illustrate the ideas set forth in the paper with numerical results for a pension fund problem in which a company acts as the sponsor of the fund and the participants' plan is defined-benefit. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
In this paper, we generalize the well-known Nesterov's accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems. We dem...
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In this paper, we generalize the well-known Nesterov's accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems. We demonstrate that by properly specifying the stepsize policy, the AG method exhibits the best known rate of convergence for solving general nonconvex smooth optimization problems by using first-order information, similarly to the gradient descent method. We then consider an important class of composite optimization problems and show that the AG method can solve them uniformly, i.e., by using the same aggressive stepsize policy as in the convex case, even if the problem turns out to be nonconvex. We demonstrate that the AG method exhibits an optimal rate of convergence if the composite problem is convex, and improves the best known rate of convergence if the problem is nonconvex. Based on the AG method, we also present new nonconvex stochastic approximation methods and show that they can improve a few existing rates of convergence for nonconvex stochastic optimization. To the best of our knowledge, this is the first time that the convergence of the AG method has been established for solving nonconvex nonlinear programming in the literature.
This paper presents two-stage bi-objective stochastic programming models for disaster relief operations. We consider a problem that occurs in the aftermath of a natural disaster: a transportation system for supplying ...
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This paper presents two-stage bi-objective stochastic programming models for disaster relief operations. We consider a problem that occurs in the aftermath of a natural disaster: a transportation system for supplying disaster victims with relief goods must be established. We propose bi-objective optimization models with a monetary objective and humanitarian objective. Uncertainty in the accessibility of the road network is modeled by a discrete set of scenarios. The key features of our model are the determination of locations for intermediate depots and acquisition of vehicles. Several model variants are considered. First, the operating budget can be fixed at the first stage for all possible scenarios or determined for each scenario at the second stage. Second, the assignment of vehicles to a depot can be either fixed or free. Third, we compare a heterogeneous vehicle fleet to a homogeneous fleet. We study the impact of the variants on the solutions. The set of Pareto-optimal solutions is computed by applying the adaptive Epsilon-constraint method. We solve the deterministic equivalents of the two-stage stochastic programs using the MIP-solver CPLEX.
Industrial robots undergo design and re-configuration processes to target extremely challenging precision and reliability performance with agile and efficient architectures. The need for such features currently preven...
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Industrial robots undergo design and re-configuration processes to target extremely challenging precision and reliability performance with agile and efficient architectures. The need for such features currently prevent the exploitation of reconfigurable robotics in manufacturing. The current work presents an approach to design and configure reconfigurable robots for the high precision manufacturing industry. The work proposes a configuration algorithm that enables the "identification of the robot architectures and the related reconfigurability features by selecting the type and number of robot modules to be implemented over time in order to better accomplish a number of production requirements. Particularly, assuming the robot will work by utilising a finite set of robotic modules, the algorithm determines the set of modules to form the arm and the ones to be allocated in the robot storage for possible usage over time. Results show a number of benefits such as a robotic chain with customised reaching and degrees of freedom with a reduced cost by performing an accurate module selection and configuration;this should lead the robot users to prefer reconfigurable robots to commercial rigid catalogue solutions proposed by robot manufacturers. (C) 2016 Elsevier Ltd. All rights reserved.
Evaluating performance-based contracts (PBCs) for capital equipment can be a challenge because it is difficult to map service-level improvements to operational availability. This article considers scenario-based stoch...
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Evaluating performance-based contracts (PBCs) for capital equipment can be a challenge because it is difficult to map service-level improvements to operational availability. This article considers scenario-based stochastic programming models for the evaluation of PBC alternatives for capital equipment consisting of a single-component system. In particular, PBC alternatives are evaluated for robustness under uncertainty in mean time between failures and mean downtime. The models measure expected deviation of implied contract operational availability and realized operational availability, and robustness is measured by the extent of improvement in service quality under a budget constraint. Optimal contract service levels are also computed that can be compared to service levels offered in a contract alternative. Value at risk (VaR) and conditional value at risk (CVaR) values for contracts are generated to gain insight into the readiness risk of contracts.
This article investigates the role played by both production and market risks on cash crop farmers' decision to adopt long rotations considered as innovative cropping systems. We build a multi-period recursive far...
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This article investigates the role played by both production and market risks on cash crop farmers' decision to adopt long rotations considered as innovative cropping systems. We build a multi-period recursive farm model with Discrete stochastic programming. The model arbitrates each year between conventional and innovative, longer rotations. Yearly farming operations are declined according to a decision tree, so that production risk is an intra-year risk. Market risk is considered as an inter-year risk influencing crop successions. Simulations are performed on a specialized French cash crop farm. They show that when the long rotation is subsidized by an area premium, farmers are encouraged to remain in longer rotations. They also show that a high level of risk aversion tends to slow down the conversion towards longer rotations. (C) 2015 Elsevier B.V. All rights reserved.
This paper presents a novel stochastic programming model for active and reactive power scheduling in distribution systems with renewable energy resources. In distribution systems, both active and reactive power schedu...
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This paper presents a novel stochastic programming model for active and reactive power scheduling in distribution systems with renewable energy resources. In distribution systems, both active and reactive power scheduling affects considerably the daily Volt/Var control (VVC) issue. To motivate distributed generations (DGs) to contribute in the VVC problem besides the energy markets, a generic reactive cost model is proposed for DGs. The presented approach, which will be performed in an off-line manner, is based on the decoupled day-ahead active and reactive power markets at distribution level. The uncertainties pertaining to the forecasted values for available output power of renewable energy sources are modelled by a scenario-based stochastic programming. In this paper, the CPLEX and BONMIN solvers are employed to solve the presented model in the GAMS environment. Finally, a typical 22-bus distribution network is used to verify the efficiency of the proposed method.
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