The multiresponse surface problem is modelled as a multiobjective stochastic optimisation, and diverse solutions are proposed. There are several crucial differences highlighted between this approach and the other prop...
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The multiresponse surface problem is modelled as a multiobjective stochastic optimisation, and diverse solutions are proposed. There are several crucial differences highlighted between this approach and the other proposed solutions. Finally, some particular solutions are applied and described in detail in a numerical example. (C) 2013 Elsevier Inc. All rights reserved.
Traditionally, two variants of the L-shaped method based on Benders' decomposition principle are used to solve two-stage stochastic programming problems: the aggregate and the disaggregate version. In this study w...
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Traditionally, two variants of the L-shaped method based on Benders' decomposition principle are used to solve two-stage stochastic programming problems: the aggregate and the disaggregate version. In this study we report our experiments with a special convex programming method applied to the aggregate master problem. The convex programming method is of the type that uses an oracle with on-demand accuracy. We use a special form which, when applied to two-stage stochastic programming problems, is shown to integrate the advantages of the traditional variants while avoiding their disadvantages. On a set of 105 test problems, we compare and analyze parallel implementations of regularized and unregularized versions of the algorithms. The results indicate that solution times are significantly shortened by applying the concept of on-demand accuracy. (C) 2014 Elsevier B.V. All rights reserved.
In this study, an inventory-theory-based interval stochastic programming (IB-ISP) model is proposed through incorporating stochastic programming and interval parameters within an inventory model. IB-ISP can tackle unc...
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In this study, an inventory-theory-based interval stochastic programming (IB-ISP) model is proposed through incorporating stochastic programming and interval parameters within an inventory model. IB-ISP can tackle uncertainties expressed as probability density functions (PDFs) and interval parameters in constraints and objective function. The developed IB-ISP is then applied to planning electric-power generation system of Beijing. Support vector regression (SVR) is used for forecasting the electricity demand, which is useful for coping with the uncertainty of customer demand. During the coal transportation processes, various factors may affect the time consumption of coal transportation, leading to uncertainties existing in energy generation and energy inventory. Under different delay times of coal transportation, different safety stocks and inventory patterns are generated to minimize the system cost and ensure the regular operation of the coal-fired power plants. The results obtained can not only help the managers to identify desired policies for safety stock in electricity-generation processes, but also be used for minimizing system cost and generating desired inventory pattern (with optimal transferring batch and period). Compared with the traditional economic order quantity (EOQ) model, the IB-ISP model can provide an effective measure for not-timely coal supplying pattern with a reduced system-failure risk under uncertainty. (C) 2014 Elsevier Ltd. All rights reserved.
This paper presents a two-stage stochastic programming model used to design and manage biodiesel supply chains. This is a mixed-integer linear program and an extension of the classical two-stage stochastic location-tr...
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This paper presents a two-stage stochastic programming model used to design and manage biodiesel supply chains. This is a mixed-integer linear program and an extension of the classical two-stage stochastic location-transportation model. The proposed model optimizes not only costs but also emissions in the supply chain. The model captures the impact of biomass supply and technology uncertainty on supply chain-related decisions;the tradeoffs that exist between location and transportation decisions;and the tradeoffs between costs and emissions in the supply chain. The objective function and model constraints reflect the impact of different carbon regulatory policies, such as carbon cap, carbon tax, carbon cap-and-trade, and carbon offset mechanisms on supply chain decisions. We solve this problem using algorithms that combine Lagrangian relaxation and L-shaped solution methods, and we develop a case study using data from the state of Mississippi. The results from the computational analysis point to important observations about the impacts of carbon regulatory mechanisms as well as the uncertainties on the performance of biocrude supply chains. (C) 2014 Elsevier Ltd. All rights reserved.
This paper addresses the shipment planning problem with random processing times in intermodal logistics via transfer ports. Shipment activities are divided into two groups according to regional settings. Activity proc...
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This paper addresses the shipment planning problem with random processing times in intermodal logistics via transfer ports. Shipment activities are divided into two groups according to regional settings. Activity processing times in region A are assumed to be random while those in region B are deterministic. At the beginning (stage 1), the forwarder assigns agents to all job activities (planning decision). In case a shipment delay is observed, an in-process adjustment (recourse decision) is implemented (stage 2). A two-stage stochastic programming model is established and an illustrative example is discussed. Managerial insights are presented in a simulation study. (C) 2014 Published by Elsevier Ltd.
stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenario...
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stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenarios,which threatens the robustness of stochastic unit commitment and hinders its application. This paper providesa stochastic unit commitment with dynamic scenario clustering based on multi-parametric programming andBenders decomposition. The stochastic unit commitment is solved via the Benders decomposition, which decouplesthe primal problem into the master problem and two types of subproblems. In the master problem, the committedgenerator is determined, while the feasibility and optimality of generator output are checked in these twosubproblems. Scenarios are dynamically clustered during the subproblem solution process through the multiparametric programming with respect to the solution of the master problem. In other words, multiple scenariosare clustered into several representative scenarios after the subproblem is solved, and the Benders cut obtainedby the representative scenario is generated for the master problem. Different from the conventional stochasticunit commitment, the proposed approach integrates scenario clustering into the Benders decomposition solutionprocess. Such a clustering approach could accurately cluster representative scenarios that have impacts on theunit commitment. The proposed method is tested on a 6-bus system and the modified IEEE 118-bus *** results illustrate the effectiveness of the proposed method in clustering scenarios. Compared withthe conventional clustering method, the proposed method can accurately select representative scenarios whilemitigating computational burden, thus guaranteeing the robustness of unit commitment.
Consideration was given to the a priori formulation of the multistage problem of stochastic programming with a quantile criterion which is reducible to the two-stage problem. Equivalence of the two-stage problems with...
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Consideration was given to the a priori formulation of the multistage problem of stochastic programming with a quantile criterion which is reducible to the two-stage problem. Equivalence of the two-stage problems with the quantile criterion in the a priori and a posteriori formulations was proved for the general case. The a posteriori formulation of the two-stage problem was in turn reduced to the equivalent problem of mixed integer linear programming. An example was considered.
Large corporations fund their capital and operational expenses by issuing bonds with a variety of indexations, denominations, maturities and amortization schedules. We propose a multistage linear stochastic programmin...
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Large corporations fund their capital and operational expenses by issuing bonds with a variety of indexations, denominations, maturities and amortization schedules. We propose a multistage linear stochastic programming model that optimizes bond issuance by minimizing the mean funding cost while keeping leverage under control and insolvency risk at an acceptable level. The funding requirements are determined by a fixed investment schedule with uncertain cash flows. Candidate bonds are described in a detailed and realistic manner. A specific scenario tree structure guarantees computational tractability even for long horizon problems. Based on a simplified example, we present a sensitivity analysis of the first stage solution and the stochastic efficient frontier of the mean-risk trade-off. A realistic exercise stresses the importance of controlling leverage. Based on the proposed model, a financial planning tool has been implemented and deployed for Brazilian oil company Petrobras. (C) 2014 Elsevier B.V. All rights reserved.
The stochastic transportation problem involves in many areas such as production scheduling, facility location, resource allocation, logistics management. Constructing an operable solving method has important theoretic...
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The stochastic transportation problem involves in many areas such as production scheduling, facility location, resource allocation, logistics management. Constructing an operable solving method has important theoretical and practical value. In this paper, we first analyze the characteristic and deficiencies of the existing stochastic programming methods, such as higher computation complexity. We then give the concept of reliability coefficient and a quasi-linear processing pattern based on expectation and variance. We further analyze the relationship between reliability coefficient and reliability degree, also give the selecting strategy of reliability coefficient. Based on that, we establish a quasi-linear programming model for stochastic transportation problem, and we analyze its performance by a case-based example. The results indicate that this model has good interpretability and operability. It can effectively solve the transportation problem under complex stochastic environment or with incomplete information. (C) 2013 Elsevier Inc. All rights reserved.
In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for forward-backward control system under consistent convex expectation dominated by G-expectation. Under...
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