We propose a class of partially observable multistage stochastic programs and describe an algorithm for solving this class of problems. We provide a Bayesian update of a belief-state vector, extend the stochastic prog...
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We propose a class of partially observable multistage stochastic programs and describe an algorithm for solving this class of problems. We provide a Bayesian update of a belief-state vector, extend the stochastic programming formulation to incorporate the belief state, and characterize saddle-function properties of the corresponding cost-to-go function. Our algorithm is a derivative of the stochastic dual dynamic programming method. (C) 2020 Elsevier B.V. All rights reserved.
Forest supply chain planning must deal with many natural disturbance uncertainties such as fires, insects, and windthrow. One important consideration is wood infestation by invasive insects, as it causes environmental...
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Forest supply chain planning must deal with many natural disturbance uncertainties such as fires, insects, and windthrow. One important consideration is wood infestation by invasive insects, as it causes environmental and economic harm. An example of invasive insects in Eastern Canada is the spruce budworm (Choristoneura fumiferana (Clemens)), which is the most destructive insect in North America's conifer stands. In 2017, more than 5 million ha of forest were defoliated by spruce budworm in Quebec. Repeated defoliation causes tree mortality, reduction of growth rates, and reduced lumber quality. Consequently, different wood qualities with greatly varied values are found in the forest. Changes in the outbreak intensity impact wood values throughout the forest. One of the common actions to mitigate the economic and environmental damages is salvage harvesting. However, because of the large uncertainties and lack of detailed information, it is a difficult problem to model. We propose a multistage stochastic mixed-integer programming model for harvest scheduling under various outbreak intensities. The objective is to maximize revenues of wood value minus logistic costs while satisfying demand for wood in the industry. The results show that when there is an outbreak throughout the forest, the priority for salvage harvesting is to focus on forest areas with the lowest level of infestation.
This paper proposes an integrated model for a multi-period reverse logistics (RL) network design problem under return and demand uncertainty. The reverse logistics network is modeled as a two-stage stochastic programm...
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This paper proposes an integrated model for a multi-period reverse logistics (RL) network design problem under return and demand uncertainty. The reverse logistics network is modeled as a two-stage stochastic programming model to make strategic and tactical decisions. The strategic decisions are the first stage decisions in establishing network's facilities and tactical decisions are the second stage decisions on material flow, inventory, backorder, shortage, and outsourcing. The uncertainties considered in this study are the primary market return and secondary market demand. The model aims to determine optimal numbers of sorting centers and warehouses, optimal lot sizes, and transportation plan that minimize the expected total system cost over the planning horizon. A case study was conducted to validate the proposed model. Numerical results indicate that the stochastic model solution outperforms result of expected value solution.
The objective of the proposed article is to minimize the transportation costs of foods and medicines from different source points to different hospitals by applying stochastic mathematical programming model to a trans...
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The objective of the proposed article is to minimize the transportation costs of foods and medicines from different source points to different hospitals by applying stochastic mathematical programming model to a transportation problem in a multi-choice environment containing the parameters in all constraints which follow the Logistic distribution and cost coefficients of objective function are also multiplicative terms of binary variables. Using the stochastic programming approach, the stochastic constraints are converted into an equivalent deterministic one. A transformation technique is introduced to manipulate cost coefficients of objective function involving multi-choice or goals for binary variables with auxiliary constraints. The auxiliary constraints depends upon the consecutive terms of multi-choice type cost coefficient of aspiration levels. A numerical example is presented to illustrate the whole idea.
A preventive maintenance scheduling problem is studied on behalf of generation companies (GENCOs) with natural gas power plants, while taking into account their signed natural gas contracts and the opportunities of pu...
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A preventive maintenance scheduling problem is studied on behalf of generation companies (GENCOs) with natural gas power plants, while taking into account their signed natural gas contracts and the opportunities of purchasing and selling natural gas in the spot market. This paper considers the uncertain prices of both natural gas and electricity in the spot market, and proposes a multistage stochastic mixed integer programming (MSMIP) model seeking the optimal operations regarding maintenance outage scheduling and natural gas trading. Large-scale MSMIP problems suffer not only the curse of dimensionality, but also computational difficulties with both discrete and continuous variables at each stage. To this respect, this paper leverages the progressive hedging algorithm based on scenario-based decomposition to solve large MSMIP problems. The solutions obtained from the algorithm exhibit promising quality under our numerical studies. Due to the independence among all the subproblems after the decomposition, the algorithm is amenable to parallel computing, which leads to faster convergence as demonstrated in the numerical results. Computational experiments also show that it is beneficial to use MSMIP while considering both maintenance planning and natural gas contracting. In addition, the results also indicate the GENCOs with a larger number of small generators perform better than those with a smaller number of big generators. (C) 2020 Elsevier B.V. All rights reserved.
An alternative way of looking at tolerance optimization is presented through a stochastic perspective by accounting for both manufacturing process uncertainty as well as uncertain market conditions. This can be accomp...
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An alternative way of looking at tolerance optimization is presented through a stochastic perspective by accounting for both manufacturing process uncertainty as well as uncertain market conditions. This can be accomplished by looking at a two-stage stochastic programming model where the decision maker takes a course of action in the first stage, such as setting the product selling prices based on product quality, after which a random event occurs, leading to a recourse decision in the second stage. Production processes face uncertainties which impact product characteristics. The recourse decisions are the specification limits and upper and lower guard bands are necessary to monitor the process. This leads to the binning of a product based on its quality, uncertain market demand, and uncertain production process. The selling prices, the specification limits and the guard bands are then determined based on these uncertain conditions. The model presented is based on chance-constrained programming, utilizing sample average approximation methods to solve the problem.
To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The unce...
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To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The uncertainties over the multiple stages are characterized by a scenario tree and the optimal dispatch scheme is cast as a decision tree which guarantees the flexibility to decide the reasonable outputs of generation and the adequate reserves accounting for different realizations of renewable energy. Most importantly, to deal with the "Curse of Dimensionality" of stochastic programming, stochastic dual dynamic programming (SDDP) is employed, which decomposes the original problem into several sub-problems according to the stages. Specifically, the SDDP algorithm performs forward pass and backward pass repeatedly until the convergence criterion is satisfied. At each iteration, the original problem is approximated by creating a linear piecewise function. Besides, an improved convergence criterion is adopted to narrow the optimization gaps. The results on the IEEE 118-bus system and real-life provincial power grid show the effectiveness of the proposed model and method.
The aim of this paper is to show that in some cases risk averse multistage stochastic programming problems can be reformulated in a form of risk neutral setting. This is achieved by a change of the reference probabili...
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The aim of this paper is to show that in some cases risk averse multistage stochastic programming problems can be reformulated in a form of risk neutral setting. This is achieved by a change of the reference probability measure making "bad" (extreme) scenarios more frequent. As a numerical example we demonstrate advantages of such change-of-measure approach applied to the Brazilian Interconnected Power System operation planning problem. (C) 2020 Elsevier B.V. All rights reserved.
Due to the interaction between the planning and operation of micro energy network, considering the operation optimization can better play the role of micro energy network. But due to the influence of various uncertain...
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Due to the interaction between the planning and operation of micro energy network, considering the operation optimization can better play the role of micro energy network. But due to the influence of various uncertainties, the deterministic programming solution may be sub-optimal. In this context, the two-stage stochastic programming of micro energy network is of great significance. In this paper, from the perspective of electric energy, the closely related P2G, storage system and fuel cell are modeled as a whole, so that the model is simplified to a certain extent. stochastic scenarios that considers multiple uncertain factors are constructed considering the correlation between electricity demand, wind speed and solar radiation intensity. And a two-stage stochastic programming model of micro energy network is established. Through the case study, the influence of P2GSS on micro energy network planning under uncertainty environment as well as the difference between stochastic programming and deterministic programming of micro energy network is analyzed. The simulation results show that P2GSS can reduce the economic cost and CO2 emission of micro energy network planning solution. Through the comparison of different planning schemes, it can provides a reference for the planning and construction of the micro-energy network.
A regional healthcare coalition enables its member hospitals to conduct an integrated emergency supply management, which is seldom addressed in the existing literature. In this work, we propose a two-stage stochastic ...
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A regional healthcare coalition enables its member hospitals to conduct an integrated emergency supply management, which is seldom addressed in the existing literature. In this work, we propose a two-stage stochastic emergency supply planning model to facilitate cooperation and coordination in a regional healthcare coalition. Our model integrates pre-disaster emergency supplies pre-positioning and post-disaster emergency supplies transshipment and procurement and considers two planning goals, i.e., minimizing the expected total cost and the maximum supply shortage rate. With some comparison models and a case study on the West China Hospital coalition of Sichuan Province, China, under the background of the COVID-19 epidemic, we demonstrate the effectiveness and benefits of our model and obtain various managerial insights and policy suggestions for practice. We highlight the importance of conducting integrated management of emergency supplies prepositioning, transshipment and procurement in the regional healthcare coalition for better preparation and responding to future potential disasters.
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