The management of electrical power systems requires the resolution of large-scale problems whose agents are linked by coupling constraints. Nevertheless, decomposition methods cannot provide an exact solution while de...
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The management of electrical power systems requires the resolution of large-scale problems whose agents are linked by coupling constraints. Nevertheless, decomposition methods cannot provide an exact solution while dealing with temporal dynamics in a stochastic environment. Indeed, each agent would have to solve a local minimisation in which future quantities intervene. However, these quantities depend on other agents' future decisions which are still unknown. In order to enhance the existing approximate approaches to this challenge, the proposed method involves Alternating Direction Method of Multipliers to overcome the large dimension by an iterative resolution of local coordinated minimisations. Uncertain temporal dynamics are handled by a stochastic dynamic programming approach. In order to make local problems solvable, the online learning of a Markov process is added. The agents can then anticipate future global variations in a local probabilistic way. The optimal charging of an electric vehicle fleet paired with a wind power plant is considered as a case study. The expected benefits are highlighted, both at the outset and after training the anticipative models. The discussion addresses the learning parameters allowing the fastest convergence.
stochastic dynamic programming (SDP) is an optimization technique used in the operation of reservoirs for many years. However, being an iterative method requiring considerable computational time, it is important to es...
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stochastic dynamic programming (SDP) is an optimization technique used in the operation of reservoirs for many years. However, being an iterative method requiring considerable computational time, it is important to establish adequate convergence criterion for its most effective use. Based on two previous studies for the optimization of operations in one of the most important multi-reservoir systems in Mexico, this work uses SDP, centred on the interest in the convergence criterion used in the optimization process. In the first trial, following the recommendations in the literature consulted, the difference in the absolute value of two consecutive iterations was taken and compared against a set tolerance value and a discount factor. In the second trial, it was decided to take the squared difference of the two consecutive iterations. In each of the trials, the computational time taken to obtain the optimal operating policy was quantified, along with whether the optimal operating policy was obtained by meeting the convergence criterion or by reaching the maximum number of iterations. With each optimization policy, the operation of the system under study was simulated and four variables were taken as evaluators of the system behaviour. The results showed few differences in the two operation policies but notable differences in the computation time used in the optimization process, as well as in the fulfilment of the convergence criterion.
We consider the real-life problem of a coach bus manufacturer located in Turkey, facing the problem of setting ordering quantities for a part procured from an unreliable supplier, where the number of items delivered i...
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We consider the real-life problem of a coach bus manufacturer located in Turkey, facing the problem of setting ordering quantities for a part procured from an unreliable supplier, where the number of items delivered is binomially distributed with an unknown yield parameter, p. We use the well-defined finite-horizon planning context with deterministic demand per period, purchasing, holding, and shortage costs to investigate the effectiveness of a fill-rate based approximate learning scheme in comparison to an exact Bayesian learning scheme, where observations on the supplier's delivery performance are used to update the assumed distribution ofp. We formulate the exact optimal learning problem as a Bayes-adaptive Markov decision process and solve the corresponding finite horizon stochasticdynamic program to provide insights on the value of online learning in comparison to the unrealistic perfect information (PI) and no information (NT) benchmarks. We contrast the performance of the so-called Bayesian Updating (BU) policy to other practical approaches such as using an assumed/guessed value ofp and implementing a constant safety stock. Noting the significant value of learning, we finally study the effectiveness of an approximate learning formulation that does not enjoy the asymptotic consistency and convergence properties but involves much lower computational burden, and demonstrate its confounding performance, at times beating the BU policy with exact Bayesian updates.
An important strategy used by two-location firms is lateral transshipment which allows sharing the inventory between the locations to reduce the impact of shortages. Transshipment can particularly be appealing as a po...
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An important strategy used by two-location firms is lateral transshipment which allows sharing the inventory between the locations to reduce the impact of shortages. Transshipment can particularly be appealing as a policy used between unreliable production facilities as it can reduce the effects of these uncertainties. We study a manufacturing system that allows transshipment between two failure-prone production facilities with different capacities. An integrated production-transshipment control policy is proposed with the aim of minimizing the total cost that comprises holding, backlog and transshipment costs. The structure of the proposed policy is obtained using the stochastic dynamic programming. It consists of a combination of a hedging point policy for production control and a state dependant economic transshipment order quantity. The parameters of the obtained control policy are optimized by adopting a simulation-based optimization approach. The robustness of the results is verified by performing sensitivity analysis. A comparative study that considers our proposed policy with the most relevant policies from the literature that we adapt to our system is conducted and shows that our proposed policy outperforms the others in terms of cost.
The Fletcher-Ponnambalam (FP) method is an explicit stochastic optimization method for design and operations management of real-world storage systems including surface water reservoir and groundwater management proble...
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The Fletcher-Ponnambalam (FP) method is an explicit stochastic optimization method for design and operations management of real-world storage systems including surface water reservoir and groundwater management problems. The FP method faces no curse of dimensionality and no need for scenario generation. The paper introduces a novel implementation for the FP method, named FP-2022 here for clarity, by removing the need for nonlinear constraints and by decreasing the number of decision variables to just one third of its original value, significantly reducing solving time (similar to 27 times faster than the original formulation). Additionally, new expressions derived for the first and second moments of both reservoir release deficit and surplus variables and the already-derived expression for the second moments of reservoir storages are incorporated into the FP-2022 formulation enabling the method to reach an improved optimality for a nonlinear objective function. The enhanced procedure is applied to solving a reservoir operation optimization problem for a major dam in Brazil. The result comparisons made with other methods along with a thorough analysis of release operation policies prove the optimality of this highly numerically efficient and convenient-to-use FP-2022 method. Finally, a multi-reservoir application of the model is also tested with corrective simulations for improved estimates of some additional variables of interest. A specific constraint-handling approach regarding reservoir release lower and upper bounds is also presented. Satisfactory results are obtained for solving the Parambikulam-Aliyar reservoir system, a real world five-reservoir operation optimization problem from India.
In this work, we investigate how flexible assets within a residential building influence the long-term impact of operation. We use a measured-peak grid tariff (MPGT) that puts a cost on the highest single-hour peak im...
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In this work, we investigate how flexible assets within a residential building influence the long-term impact of operation. We use a measured-peak grid tariff (MPGT) that puts a cost on the highest single-hour peak import over the month. We apply a mathematical model of a Home Energy Management System (HEMS) together with stochastic dynamic programming (SDP), which calculates the long-term impact of operating as a non-linear expected future cost curve (EFCC) from the end of the scheduling period to the start. The proposed model is applied to a case study for a Norwegian building with smart control of a battery energy storage system (BESS), Electric vehicle (EV) charging and space heating (SH). Each of the flexible assets are investigated individually with MPGT and for an energy-based grid tariff. The results showed that EV charging has the highest peak-power impact in the system, decreasing the total electricity cost by 14.6% with MPGT when controllable compared to a reference case with passive charging. It is further shown how the EFCC helps achieve optimal timing and level of the peak demand, where it co-optimizes both real-time pricing and the MPGT.
We used a stochastic dynamic programming (SDP) model to quantify the consequences of disturbance on pregnant western gray whales during one foraging season. The SDP model has a firm basis in bioenergetics, but detaile...
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We used a stochastic dynamic programming (SDP) model to quantify the consequences of disturbance on pregnant western gray whales during one foraging season. The SDP model has a firm basis in bioenergetics, but detailed knowledge of minimum reproductive length of females (L-min) and the relationship between length and reproductive success (R-fit) was lacking. We varied model assumptions to determine their effects on predictions of habitat use, proportion of animals disturbed, reproductive success, and the effects of disturbance. Smaller L-min values led to higher predicted nearshore habitat use. Changes in L-min and R-fit had little effect on predictions of the effect of disturbance. Reproductive success increased with increased L-min and with higher probability of reproductive success by length. Multiple seismic surveys were conducted in 2015 off the northeast coast of Sakhalin Island, with concomitant benthic prey surveys, photo-identification studies, and whale distribution sampling, thus providing a unique opportunity to compare output from SDP models with empirical observations. SDP model predictions of reproductive success and habitat use were similar with and without acoustic disturbance, and SDP predictions of reproductive success and large-scale habitat use were generally similar to values and trends in the data. However, empirical estimates of the proportion of pregnant females nearshore were much higher than SDP model predictions (a large effect, measured by Cohen's d) during the first week, and the SDP model overestimated whale density in the south and underestimated density around the mouth of Piltun Bay. Such differences in nearshore habitat use would not affect SDP predictions of reproductive success or survival under the current seismic air gun disturbance scenario.
Photovoltaic (PV) battery systems allow citizens to take part in a more sustainable energy system. Using the electric energy produced on-site usually entails a financial benefit for the consumer. Furthermore, feed-in ...
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Photovoltaic (PV) battery systems allow citizens to take part in a more sustainable energy system. Using the electric energy produced on-site usually entails a financial benefit for the consumer. Furthermore, feed-in peaks during high photovoltaic generation sometimes cause local voltage violations. Therefore, a feed-in limit applies to PV battery systems. In our study, we present a method to generate an optimal control that takes into account the forecast uncertainties. To that end, a stochastic forecast model is developed and used in a dynamicprogramming framework. We carry out a simulation study assuming the regulatory constraints in Germany. In this setup, our method is shown to mitigate the effects of the forecast uncertainties better than comparable methods. (c) 2020 European Control Association. Published by Elsevier Ltd. All rights reserved.
We evaluate the practical usefulness of incorporating maximum ramping rates and minimum environmental flows into a linear programming based water value calculator for hydropower plants that participate in the day-ahea...
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We evaluate the practical usefulness of incorporating maximum ramping rates and minimum environmental flows into a linear programming based water value calculator for hydropower plants that participate in the day-ahead electricity market. The methodology consists of three steps: first computing the water value once with and once without environmental constraints, then simulating the plant operations using each water value, and finally comparing the simulation profits. A set of nine representative hydropower plants formed by combinations of three real locations (in Colombia, Norway and Spain) and three turbine configurations (from one to three Francis units) are individually analyzed. Each plant is simulated in two synthetic 10-year long series subject to fifteen combinations of maximum ramping rates and minimum flows with the two above-mentioned water values, totaling 540 simulations. The results indicate that incorporating the analyzed environmental constraints into a linear programming based water value calculator can be significantly profitable only when the hydropower plants have only one or at most two turbines.
This paper investigates the stochastic Container Relocation Problem in which a flexible service policy is adopted in the import container retrieval process. The flexible policy al-lows the terminal operators to determ...
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This paper investigates the stochastic Container Relocation Problem in which a flexible service policy is adopted in the import container retrieval process. The flexible policy al-lows the terminal operators to determine the container retrieval sequence to some extent, which provides more opportunity for reducing the number of relocations and the truck waiting times. A more general probabilistic model that captures customers' arrival preference is presented to describe the randomness for external truck arrivals within their appointed time windows. Being a multi-stage stochastic sequential decision-making problem, it is first formulated into a stochastic dynamic programming (SDP) model to minimize the expected number of relocations. Then, the SDP model is extended considering a secondary objective representing the truck waiting times. Tree search-based algorithms are adapted to solve the two models to their optimality. Heuristic algorithms are designed to seek high-quality solutions efficiently for larger problems. A discrete-event simulation model is developed to evaluate the optimal solutions and the heuristic solutions respectively on two performance metrics. Extensive computational experiments are performed based on instances from literature to verify the effectiveness of the proposed models and algorithms. (C) 2020 Elsevier Ltd. All rights reserved.
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