Risk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non convex due to integ...
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Risk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non convex due to integrality restrictions, and the objective function is nonlinear in general. We propose a scenario tree decomposition approach, namely group subproblem approach, to obtain bounds for such problems with an objective of dynamic mean conditional value-at-risk (mean-CVaR). Our approach does not require any special problem structure such as convexity and linearity, therefore it can be applied to a wide range of problems. We obtain lower bounds by using different convolution of mean-CVaR risk measures and different scenario partition strategies. The upper bounds are obtained through the use of optimal solutions of group subproblems. Using these lower and upper bounds, we propose a solution algorithm for risk-averse mixed-integer multi-stage stochastic problems with mean-CVaR risk measures. We test the performance of the proposed algorithm on a multi-stage stochastic lot sizing problem and compare different choices of lower bounds and partition strategies. Comparison of the proposed algorithm to a commercial solver revealed that, on the average, the proposed algorithm yields 1.13% stronger bounds. The commercial solver requires additional running time more than a factor of five, on the average, to reach the same optimality gap obtained by the proposed algorithm. (C) 2017 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.
We derive formulas for constants of strong convexity (CSCs) of expectation functions encountered in two-stage stochastic programs with linear recourse. One of them yields a CSC as the optimal value of a certain quadra...
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We derive formulas for constants of strong convexity (CSCs) of expectation functions encountered in two-stage stochastic programs with linear recourse. One of them yields a CSC as the optimal value of a certain quadratically constrained quadratic program, another one in terms of the thickness of the feasibility polytope of the dual problem associated to the recourse problem. CSCs appear in Hoelder-type estimates relating the distance of optimal solution sets of stochastic programs to a suitable distance of underlying probability distributions. (c) 2021 Elsevier B.V. All rights reserved.
We consider a supply chain design problem to provide new ways to buffer the effect of demand uncertainty when designing supply chains. The problem is formulated as a two-stage stochastic programming with fixed recours...
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We consider a supply chain design problem to provide new ways to buffer the effect of demand uncertainty when designing supply chains. The problem is formulated as a two-stage stochastic programming with fixed recourse. A special sampling procedure based on uniform experiment designs provides superior quality approximate solutions for a simple supply chain structure when demands are correlated.
Operating theatre scheduling is a critical task that directly impacts the efficient delivery of surgical care. In this context, we propose a comprehensive stochastic programming modelling framework which handles the i...
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Operating theatre scheduling is a critical task that directly impacts the efficient delivery of surgical care. In this context, we propose a comprehensive stochastic programming modelling framework which handles the inherent uncertainty characterizing the arrival of emergency patients and the duration of surgery. In particular, three recourse strategies are presented with the aim of modelling different reactive scheduling policies actually adopted by hospital managers. In order to solve realistic-sized instances in a reasonable amount of time, we develop tailored heuristic solution strategies that exploit the problem structure. Computational results obtained on a set of randomly generated problems show the effective impact of the stochastic programming approach and the efficiency of the proposed heuristics.
In this work we consider the optimal investment and operational planning of gas field developments under uncertainty in gas reserves. The resolution of uncertainty in gas reserves, and hence the shape of the scenario ...
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In this work we consider the optimal investment and operational planning of gas field developments under uncertainty in gas reserves. The resolution of uncertainty in gas reserves, and hence the shape of the scenario tree associated with the problem depends on the investment decisions. A novel stochastic programming model that incorporates the decision-dependence of the scenario tree is presented. A decomposition based approximation algorithm for the solution of this model is also proposed. We show that the proposed approach yields solutions with significantly higher expected net present value (ENPV) than that of solutions obtained using a deterministic approach. For a small sized example, the proposed approximation algorithm is shown to yield the optimal solution with more than one order of magnitude reduction in solution time, as compared to the full space method. "Good" solutions to larger problems, that require up to 165,000 binary variables in full space, are obtained in a few hours using the proposed approach. (C) 2003 Elsevier Ltd. All rights reserved.
This paper addresses the problem of designing robust emergency medical services. Under this respect, the main issue to consider is the inherent uncertainty which characterizes real life situations. Several approaches ...
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This paper addresses the problem of designing robust emergency medical services. Under this respect, the main issue to consider is the inherent uncertainty which characterizes real life situations. Several approaches can be used to design robust mathematical models which are able to hedge uncertain conditions. We are using here the stochastic programming framework and, in particular, the probabilistic paradigm. More specifically, we develop a stochastic programming model with probabilistic constraints aimed to solve both the location and the dimensioning problems, i.e. where service sites must be located and how many emergency vehicles must be assigned to each site, in order to achieve a reliable level of service and minimize the overall costs. In doing so, we consider the randomness of the system as far as the demand of emergency service is concerned. The numerical results, which have been collected on a large set of test problems, demonstrate the validity of the proposed model, particularly in dealing with the trade-off between quality of service and costs management. (C) 2003 Elsevier B.V. All rights reserved.
Multi-period guarantees are often embedded in life insurance contracts. In this paper we consider the problem of hedging these multi-period guarantees in the presence of transaction costs. We derive the hedging strate...
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Multi-period guarantees are often embedded in life insurance contracts. In this paper we consider the problem of hedging these multi-period guarantees in the presence of transaction costs. We derive the hedging strategies for the cheapest hedge portfolio for a multi-period guarantee that with certainty makes the insurance company able to meet the obligations from the insurance policies it has issued. We find that by imposing transaction costs, the insurance company reduces the rebalancing of the hedge portfolio. The cost of establishing the hedge portfolio also increases as the transaction cost increases. For the multi-period guarantee there is a rather large rebalancing of the hedge portfolio as we go from one period to the next. By introducing transaction costs we find the size of this rebalancing to be reduced. Transaction costs may therefore be one possible explanation for why we do not see the insurance companies performing a large rebalancing of their investment portfolio at the end of each year. (C) 2006 Elsevier B.V. All rights reserved.
Reliability based techniques has been an area of active research in structural design during the last decade, and different methods have been developed. The same has occurred with stochastic programming, which is a fr...
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Reliability based techniques has been an area of active research in structural design during the last decade, and different methods have been developed. The same has occurred with stochastic programming, which is a framework for modeling optimization problems involving uncertainty. The discipline of stochastic programming has grown and broadened to cover a wide range of applications, such as agriculture, capacity planning, energy, finance, fisheries management, production control, scheduling, transportation, water management, etc., and because of this, techniques for solving stochastic programming models are of great interest for the scientific community. This paper presents a new approach for solving a certain type of stochastic programming problems presenting the following characteristics: (i) the joint probability distributions of random variables are given, (ii) these do not depend on the decisions made, and (iii) random variables only affect the objective function. The method is based on mathematical programming decomposition procedures and first-order reliability methods, and constitutes an efficient method for optimizing quantiles in high-dimensional settings. The solution provided by the method allows us to make informed decisions accounting for uncertainty. (C) 2010 Elsevier Ltd. All rights reserved.
A critical process in brass casting is the blending of pure and scrap materials to satisfy specified metal ratios. The primary focus in such blending problems has always been cost minimization. The optimal blends prod...
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A critical process in brass casting is the blending of pure and scrap materials to satisfy specified metal ratios. The primary focus in such blending problems has always been cost minimization. The optimal blends produced by mathematical models use large amounts of scrap materials, which are cheaper but have high variations in ingredient ratios. This gives rise to quality problems. This study aims at joint optimization of cost and quality. A chance-constrained nonlinear mathematical model is developed for maximizing the minimum process capability level for a fixed cost. Then parametric programming is used to run the model for different costs to produce a Pareto-optimal frontier. An application to data from a brass factory showed that the frontier is highly nonlinear, enabling the decision maker to select a competitive process capability and cost value combination. The proposed approach is applicable to any blending problem in which ingredient amounts have statistical variation.
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