This paper proposes a framework that includes a penalty function incorporated stochastic dynamic programming (SDP) model in order to derive the operation policy of the reservoir of a hydropower plant, with an aim to r...
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This paper proposes a framework that includes a penalty function incorporated stochastic dynamic programming (SDP) model in order to derive the operation policy of the reservoir of a hydropower plant, with an aim to reduce the amount of spill during operation of the reservoir. SDP models with various inflow process assumptions (independent and Markov-I) are developed and executed in order to derive the reservoir operation policies for the case study of a storage type hydropower plant located in Japan. The policy thus determined consists of target storage levels (end-of-period storage levels) for each combination of the beginning-of-period storage levels and the inflow states of the current period. A penalty function is incorporated ill the classical SDP model with objective function that maximizes annual energy generation through operation of the reservoir. Due to the inclusion of the penalty function, operation policy of the reservoir changes in a way that ensures reduced spill. Simulations are carried out to identify reservoir storage guide curves based on the derived operation policies. Reservoir storage guide curves for different values of the coefficient of penalty function a are plotted for a study horizon of 64 years, and the corresponding average annual spill values are compared. It is observed that, with increasing values of a, the average annual spill decreases;however, the simulated average annual energy value is marginally reduced. The average annual energy generation can be checked vis-a-vis the average annual spill reduction, and the optimal value of a can be identified based on the cost functions associated with energy and spill. (C) 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.
Big data and the curse of dimensionality are common vocabularies that researchers in different communities have recently been dealing with, e.g. dynamicprogramming (DP) in automatic control system society. A novel un...
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Big data and the curse of dimensionality are common vocabularies that researchers in different communities have recently been dealing with, e.g. dynamicprogramming (DP) in automatic control system society. A novel unweighted sampled based least square projection approach is proposed in this study to address the issue of the large state space in the DP optimisation problem. The method, in particular, takes into account both contraction mapping and monotonicity properties of the DP algorithm for value function approximation. Specifically, the batch of samples are gathered by uniform probability distribution at first, and an unweighted LS sub-problem in the subspace is solved. As the case study, a new Markov decision process model associated with a resource allocation problem is considered to illustrate the technique and evaluate its effectiveness. It is noted that the approach can be employed for different applications as well. Moreover, a MATLAB based software is developed to implement and examine different parts of the proposed method. Simulation examples are considered to support the results of the approach via developed software. The idea makes a connection between the recent advances in big data analysis and approximate DP as well.
This article considers a quasi-batch process where items are continuously processed while they move on a conveyor belt. In addition, the products arriving into the processor require variable amounts of processing, whi...
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This article considers a quasi-batch process where items are continuously processed while they move on a conveyor belt. In addition, the products arriving into the processor require variable amounts of processing, which translate into different processor levels. Keeping the processing level constant in such a system results in severe inefficiency in terms of consumption of energy and resources with high production costs and a poor level of environmental performance. A stochastic dynamic programming model is formulated that strikes a balance between consumption of energy and material, processor performance, and product quality. The model minimizes total system-wide cost, which is essentially a unified measure across all the objectives. The structural properties of the optimal policy and value functions are analyzed taking into account high-dimensionality of the state space. Based on some of these results, efficient heuristic methodologies are developed to solve large instances of the problem. It is shown using several numerical experiments that a significant amount of energy or material resources can be saved and total costs can be reduced considerably compared to the current practices in the process industry. Insights on the sensitivity of results with respect to the cost parameters are provided.
This paper describes two methods that are introduced to improve the computational effort of stochastic dynamic programming (SDP) as applicable to the operation of multiple urban water supply reservoir systems. The sto...
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This paper describes two methods that are introduced to improve the computational effort of stochastic dynamic programming (SDP) as applicable to the operation of multiple urban water supply reservoir systems. The stochastic nature of streamflow is incorporated explicitly by considering it in the form of a multivariate probability distribution. The computationally efficient Gaussian Legendre quadrature method is employed to compute the conditional probabilities of streamflow, which accounts for the serial correlation of streamflow into each storage and the cross correlation between the streamflow into various storages. A realistic assumption of cross correlation of streamflow is introduced to eliminate the need to consider the streamflow combinations which are unlikely to occur in the SDP formulation. A "corridor" approach is devised to eliminate the need to consider the infeasible and/or inferior storage volume combinations in the preceding stage in computing the objective function in the recursive relation. These methods are verified in terms of computational efficiency and accuracy by using a hypothetical example of three interconnected urban water supply reservoirs. Therefore, it can be concluded that these methods allow SDP to be more attractive for deriving optimal operating rules for multiple urban water supply reservoir systems.
This article presents and discusses research with the aim of developing a stand-level management scheduling model for short-rotation coppice systems that may take into account the risk of wildfire. The use of the copp...
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This article presents and discusses research with the aim of developing a stand-level management scheduling model for short-rotation coppice systems that may take into account the risk of wildfire. The use of the coppice regeneration method requires the definition of both the optimal harvest age in each cycle and the optimal number of coppice cycles within a full rotation. The scheduling of other forest operations such as stool thinning and fuel treatments (e.g., shrub removals) must be further addressed. In this article, a stochastic dynamic programming approach is developed to determine the policy (e.g., fuel treatment, stool thinning, coppice cycles, and rotation length) that maximizes expected net revenues. stochastic dynamic programming stages are defined by the number of harvests, and state variables correspond to the number of years since the stand was planted. Wildfire occurrence and damage probabilities are introduced in the model to analyze the impact of the wildfire risk on the optimal stand management schedule policy. For that purpose, alternative wildfire occurrence and postfire mortality scenarios were considered at each stage. A typical Eucalyptus globulus Labill. stand in Central Portugal was used as a test case. Results suggest that the proposed approach may help integrate wildfire risk in short-rotation coppice systems management scheduling. They confirm that the maximum expected discounted revenue decreases with and is very sensitive to the discount rate and further suggest that the number of cycles within a full rotation is not sensitive to wildfire risk. Nevertheless, the expected rotation length decreases when wildfire risk is considered. FOR. SCI. 58(4):353-365.
This paper proposes an iterative process to select the cuts that model the cost-to-go functions of stochastic dynamic programming (SDP) and stochastic dual dynamicprogramming (SDDP) algorithms. This approach is appli...
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This paper proposes an iterative process to select the cuts that model the cost-to-go functions of stochastic dynamic programming (SDP) and stochastic dual dynamicprogramming (SDDP) algorithms. This approach is applied to the medium/long-term operation planning of hydrothermal systems. The main idea of the proposed algorithm is to improve the performance of the SDP and SDDP methods applied to the problem by iteratively adding cuts to the linear programming instances. Also, some case studies considering the Brazilian power system are presented. The results show a significant reduction in computational time with few modifications to the original algorithm. (C) 2015 Elsevier B.V. All rights reserved.
The study focuses on the dynamic multi-site capacity planning problem in the thin film transistor liquid crystal display (TFT-LCD) industry under stochastic demand. Capacity planning refers to the process of simultane...
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The study focuses on the dynamic multi-site capacity planning problem in the thin film transistor liquid crystal display (TFT-LCD) industry under stochastic demand. Capacity planning refers to the process of simultaneously implementing a robust capacity allocation plan and capacity expansion policy across multiple sites against stochastic demand. In addition, the demand situation in TFT-LCD manufacturing follows Markov properties, in which the correlations of the demand variations in the consecutive periods are high, and the demand status in the next period is stochastically determined by the present one. Therefore, this study constructs a stochastic dynamic programming (SDP) model with an embedded linear programming (LP) to generate a capacity planning policy as the demand in each period is revealed and updated. Using the backward induction algorithm, the SDP model considers several capacity expansion and budget constraints to determine a robust and dynamic capacity expansion policy in response to newly available demand information. The LP model then considers numerous TFT-LCD practical characteristics and constraints to decide a capacity allocation plan, and generate a one-period immediate reward used by the optimality recursion equation of the SDP model. Numerical results are also illustrated to prove the feasibility and robustness of the proposed SDP model compared to the traditional deterministic capacity planning model currently applied by the industry. (C) 2013 Elsevier B.V. All rights reserved.
This study makes use of stochastic dynamic programming to set up a multi-period asset allocation model and derives an analytic formula for the optimal proportions invested in short and long bonds. Then maximum likelih...
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This study makes use of stochastic dynamic programming to set up a multi-period asset allocation model and derives an analytic formula for the optimal proportions invested in short and long bonds. Then maximum likelihood method is employed to estimate the relevant parameters. Finally, we implement the model through backward recursion algorithm to find numerically the optimal allocation of funds between short and long bonds for an investor with power utility and an investment horizon of ten years. Our results show that an investor will hold a larger proportion of short bond if his/her investment horizon gets shorter and/or if he/she is more risk averse. (C) 2007 Elsevier Inc. All rights reserved.
This paper describes a serial and parallel implementation of a hybrid stochastic dynamic programming and progressive hedging algorithm. Numerical experiments show good speedups in the parallel implementation. In spite...
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This paper describes a serial and parallel implementation of a hybrid stochastic dynamic programming and progressive hedging algorithm. Numerical experiments show good speedups in the parallel implementation. In spite of this, our hybrid algorithm has difficulties competing with a pure stochastic dynamic programming approach on a given test case from macroeconomic control theory.
A two-phase stochastic dynamic programming model is developed for optimal operation of irrigation reservoirs under a multicrop environment. Under a multicrop environment, the crops compete for the available water when...
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A two-phase stochastic dynamic programming model is developed for optimal operation of irrigation reservoirs under a multicrop environment. Under a multicrop environment, the crops compete for the available water whenever the water available is less than the irrigation demands. The performance of the reservoir depends on how the deficit is allocated among the competing crops. The proposed model integrates reservoir release decisions with water allocation decisions. The water requirements of crops vary from period to period and are determined from the soil moisture balance equation taking into consideration the contribution of soil moisture and rainfall for the water requirements of the crops. The model is demonstrated over an existing reservoir and the performance of the reservoir under the operating policy derived using the model is evaluated through simulation.
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