The randomness and fluctuation of wind power output will cause certain waste in capacity allocation of integrated energy system. Therefore, a robust chance constrained optimization model is proposed to solve the short...
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The randomness and fluctuation of wind power output will cause certain waste in capacity allocation of integrated energy system. Therefore, a robust chance constrained optimization model is proposed to solve the shortcomings of the traditional model in wind power output analysis, such as weak reliability and conservative results. First, the uncertainty of wind power output is analyzed. Second, a robust chance constrained optimization model combining stochastic programming and robust optimization is established to deal with the uncertainty of the output power of the integrated energy system objectively. Finally, the results are compared with the existing integrated energy system capacity configuration, and the validity of the model is verified. The results show that the robust chance constrained optimization model proposed in this paper can effectively reduce the capacity cost by 38.2% while ensuring the robustness of the system in wind power uncertainty analysis.
In this paper we propose a crash-start technique for interior point methods applicable to multi-stage stochastic programming problems. The main idea is to generate an initial point for the interior point solver by dec...
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In this paper we propose a crash-start technique for interior point methods applicable to multi-stage stochastic programming problems. The main idea is to generate an initial point for the interior point solver by decomposing the barrier problem associated with the deterministic equivalent at the second stage and using a concatenation of the solutions of the subproblems as a warm-starting point for the complete instance. We analyse this scheme and produce theoretical conditions under which the warm-start iterate is successful. We describe the implementation within the OOPS solver and the results of the numerical tests we performed.
In this paper, we introduce a new stochastic approximation type algorithm, namely, the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programmi...
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In this paper, we introduce a new stochastic approximation type algorithm, namely, the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method possesses a nearly optimal rate of convergence if the problem is convex. We discuss a variant of the algorithm which consists of applying a postoptimization phase to evaluate a short list of solutions generated by several independent runs of the RSG method, and we show that such modification allows us to improve significantly the large-deviation properties of the algorithm. These methods are then specialized for solving a class of simulation-based optimization problems in which only stochastic zeroth-order information is available.
In this study, we present a stochastic programming asset-liability management model which deals with decision-dependent randomness. The model focuses on a pricing problem and the subsequent asset-liability management ...
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In this study, we present a stochastic programming asset-liability management model which deals with decision-dependent randomness. The model focuses on a pricing problem and the subsequent asset-liability management problem describing the typical life of a consumer loan. Such problems are frequently tackled by many companies, including multinationals. When doing so, they must consider numerous factors. These factors include the possibility of their customer rejecting the loan, the possibility of the customer defaulting on the loan and the possibility of prepayment. The randomness associated with these factors have a clear relationship with the offered interest rate of the loan which is the company's decision and thus, induces decision-dependent randomness. Another important factor, which plays a major role for liabilities, is the price of money in the market. This is determined by the market interest rates. We captured their evolution in the form of a scenario tree. In summary, we formulated a non-linear, multi-stage stochastic program with decision-dependent randomness, which spanned the lifetime of a typical consumer loan. Its solution showed us the optimal decisions that the company should make. In addition, we performed a sensitivity analysis demonstrating the results of the model for various parameter settings that described different types of customers. Finally, we discuss the losses caused if companies do not act in the optimal way.
This paper focuses on addressing uncertainties in disasters when considering lateral transshipment opportunities for pre-positioning relief supplies. To deal with uncertain demands the problem is formulated as a two-s...
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This paper focuses on addressing uncertainties in disasters when considering lateral transshipment opportunities for pre-positioning relief supplies. To deal with uncertain demands the problem is formulated as a two-stage stochastic programming model, which decides simultaneously on the locations of relief facilities and the allocations of relief supplies to demand nodes. Meanwhile, different damage levels caused by disasters are considered and reflected by a survival rate of usable stocked relief items. Multiple types of supplies with various priorities, values and spaces are explored. A real-world case study based on the Gulf Coast region of the United States is conducted to illustrate the application of the developed model. By comparison with the direct shipment solution, the lateral transshipment solution is demonstrated to be more cost-effective and flexible. The sensitivity analysis of out-of-stock penalty cost and maximum travel distance provides managerial insights for relief agencies.
Market power, defined as the ability to raise prices above competitive levels profitably, continues to be a prime concern in the restructured electricity markets. Market power must be mitigated to improve market perfo...
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Market power, defined as the ability to raise prices above competitive levels profitably, continues to be a prime concern in the restructured electricity markets. Market power must be mitigated to improve market performance and avoid inefficient generation investment, price volatility, and overpayment in power systems. For this reason, involving market power in the transmission expansion planning (TEP) problem is essential for ensuring the efficient operation of the electricity markets. In this regard, a methodological bilevel stochastic framework for the TEP problem that explicitly includes the market power indices in the upper level is proposed, aiming to restrict the potential market power execution. A mixed-integer linear/quadratic programming (MILP/MIQP) reformulation of the stochastic bilevel model is constructed utilizing Karush-Kuhn-Tucker (KKT) conditions. Wind power and electricity demand uncertainty are incorporated using scenario-based two-stage stochastic programming. The model enables the planner to make a trade-off between the market power indices and the investment cost. Using comparable results of the IEEE 118-bus system, we show that the proposed TEP outperforms the existing models in terms of market power indices and facilitates open access to the transmission network for all market participants.
The increasing penetration of renewable energy sources in distribution networks has brought new challenges in ensuring reliable and resilient operation during natural disasters. The proposed approach considers the unc...
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The increasing penetration of renewable energy sources in distribution networks has brought new challenges in ensuring reliable and resilient operation during natural disasters. The proposed approach considers the uncertainties associated with renewable energy sources, natural disasters, and demand using scenario-based stochastic programming to minimize the expected operational cost of the distribution network. Due to the huge uncertainties related to renewable resources, an efficient risk analysis is applied to obtain a sense of the worst realizations of uncertainties using the downside risk constraints method. Besides, two types of demand response schemes (DRSs) are considered to prevent widespread blackouts in the distribution network. This study provides insights into the integration of renewable energy sources in distribution networks and highlights the importance of considering resiliency optimization of this networks. The effectiveness of the proposed approach is demonstrated through simulations on a 33-bus test distribution system, and the results show successful ride-through of the islanding hours with 100% risk reduction by only 2.91% increase in operation cost over the considered scenarios, while risks may still be present in other set of scenarios. Overall, this research contributes to the investigate the uncertainty-driven operational risks of renewable energy integration of resilient distribution network.
The forest planning problem with road construction consists of managing the timber production of a forest divided into harvest cells for a given planning horizon. Subject to uncertainty, it becomes a complex large-sca...
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The forest planning problem with road construction consists of managing the timber production of a forest divided into harvest cells for a given planning horizon. Subject to uncertainty, it becomes a complex large-scale multi-stage stochastic problem expressed through scenarios. A suitable algorithm for these problems is progressive hedging (PH), which decomposes the problem by scenarios. A two-phase solving approach, in which PH is used as a heuristic method to obtain a directly optimized restricted model with fixed variables, is implemented. Multiple adjustments to improve the performance of the method are adopted and tested in a tactical case study. The performance of the proposed method is compared with those of traditional approaches. Thanks to these enhancements, we solved a real original problem including all the complexities of a practical problem not addressed in previous studies. Comprehensive computational results indicate the advantages of the method, including its ability to efficiently solve instances of up to 1000 scenarios by exploiting its parallel implementation.
Combined heat and power (CHP) plants are main generation units in district heating systems that produce both heat and electric power simultaneously. Moreover, CHP plants can participate in electricity markets, selling...
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Combined heat and power (CHP) plants are main generation units in district heating systems that produce both heat and electric power simultaneously. Moreover, CHP plants can participate in electricity markets, selling and buying the extra power when profitable. However, operational decisions have to be made with unknown electricity prices. The distribution of unknown electricity prices is also not known exactly and uncertain in practice. Therefore, the need of tools to schedule CHP units' production under distributional uncertainty is necessary for CHP producers. On top of that, a heating network could serve as a heat storage and an additional source of flexibility for CHP plants. In this paper, a distributionally robust short-term operational model of CHP plants in the day-ahead electricity market is developed. The model accounts for the heating network and considers temperature dynamics in the pipes. The problem is formulated in a data-driven manner, where the production decisions explicitly depend on the historical data for the uncertain day-ahead electricity prices. A case study is performed, and the resulting profit of the CHP producer is analyzed. The proposed operational strategy shows high reliability in the out-of-sample performance and a profit gain of the CHP producer, who is aware of the temperature dynamics in the heating network.
In planning evacuation services against the threat of disasters, it is important to optimize pickup point location and rescue vehicle routing decisions while recognizing the risks of service disruptions. In this paper...
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In planning evacuation services against the threat of disasters, it is important to optimize pickup point location and rescue vehicle routing decisions while recognizing the risks of service disruptions. In this paper, a reliable location and routing model with backup service plans is proposed to plan targeted strategic evacuation, which minimizes the total expected cost for deployment of pickup stations, rescue vehicle routing, and evacuee assignments and exposure while the service is subject to probabilistic disruptions. We formulate the problem as a mixed-integer non-linear program, and develop two customized solution algorithms, one based on Lagrangian relaxation (LR) and the other based on meta-heuristic, to decompose and solve the problem. Numerical experiments with various parameters are conducted to not only demonstrate the applicability of the proposed model and effectiveness of the solution algorithms, but also to draw managerial insights. The impacts of demand distribution, facility cost, disruption probability, and evacuee exposure risk are assessed in a series of sensitivity analyses, so as to inform agencies how to carefully consider these factors while developing a reliable targeted evacuation service plan.
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