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International Conference on Probabilistic Methods Applied to Power Systems (PMAPS)

作者： Gross, Arne Lenders, Antonia Zech, Tobias Wittwer, Christof Dieh, Moritz Fraunhofer Inst Solar Energy Syst ISE Freiburg Germany Univ Freiburg IMTEK Freiburg Germany

ISBN: (纸本)9781728128221

In the coming years, the energy system will be transformed from central carbon-based power plants to decentralized renewable generation. Due to the dependency of these systems on external influences such as the weather, forecast uncertainties pose a problem. In this paper, we will compare different methods that mitigate the impact of these forecast uncertainties. Our results suggest that estimating these uncertainties and modeling them for optimization can increase the benefit for the individual system.

关键词： stochastic dynamic programming Model Predictive Control Probabilistic PV Forecasting Probabilistic Load Forecasting PV Battery Systems

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The impact of water conservation regulations on mining firms: A stochastic control approach

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WATER RESOURCES AND ECONOMICS 2021年 36卷

作者： Huang, Yichun Insley, Margaret Univ Waterloo Dept Econ Waterloo ON Canada Univ Waterloo Water Inst Waterloo ON Canada

Large water demands by the mining industry are of increasing concern around the world. The cost of a specific water management regulation is studied for an oil sands mining operation in Canada, where restrictions on water withdrawals vary with fluctuations in the river. A stochastic optimal control problem is formulated for a firm choosing production, water use, and the timing to build a water storage facility, under conditions of uncertain oil prices and uncertain water withdrawal limits. As no closed form solution is available, a stochastic dynamic programming approach is implemented to determine the difference in value and optimal controls for the oil-producing asset, with and without water restrictions. The cost of the restrictions is estimated to be quite small given historical river flow conditions, while cost is shown to increase under drier conditions. A long run marginal cost curve is developed showing the cost of increasing restrictions given expectations about future river conditions and oil prices.

关键词： Oil sands Water conservation Storage Optimal control HJB equation Semi-Lagrangian stochastic dynamic programming

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An Analytical Method for Fast Optimization of Multireservoir Hydropower Systems Operations Considering Risk-Return Tradeoffs

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Water Resources Research 2025年第6期61卷

作者： S. Jamshid Mousavi Kumaraswamy Ponnambalam Department of Civil and Environmental Engineering Amirkabir University of Technology Tehran Iran Department of Systems Design Engineering University of Waterloo Waterloo ON Canada

Long-term multireservoir operations optimization is challenging for existing optimization methods such as stochastic dynamic programming (SDP) and implicit stochastic programming (ISP) suffering from excessive computing time requirements. More difficult is to tackle a risk-based optimization problem and provide an efficient frontier of the objective function for multireservoir systems. The Fletcher–Ponnambalam (FP) method is an explicit stochastic optimization method suitable for multireservoir operations optimization which faces no curse of dimensionality of SDP and has no need for scenario generations of ISP, thus is extremely fast. Earlier implementations have developed expressions for mean and variance of storages and releases, including deficits and surpluses, to estimate fairly accurate values of the linear and quadratic objective functions when compared with other well-known methods. This paper introduces analytical derivations of hydropower equations to be used in the recent extension of the FP method and applies it to a long-term operations optimization problem of a three-reservoir system in Iran. The objective function is to maximize the expected value of the annual energy, which is a multiplicative nonlinear function of both releases and storage levels. The computational results from simulations for the 60 years of available inflow data for the chosen multireservoir system using the policies derived by the FP, ISP, and SDP methods were compared. The solution qualities were nearly the same, but the FP method has tremendous speedups over the other methods. Secondly, expressions for the variances of monthly energy productions were derived to compute efficient frontier for risk-return tradeoffs of annual energy to guide decision makers. Analytic expressions are derived for the moments of energy function to be used in hydropower multireservoir operations optimization, not considered before The derived expressions for the second moment of the generated energy i

关键词： multireservoir hydropower operations stochastic dynamic programming implicit stochastic programming risk and efficient frontier

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The impacts of uncertainties on the carbon mitigation design: Perspective from abatement cost and emission rate

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JOURNAL OF CLEANER PRODUCTION 2019年 232卷 213-223页

作者： Guo, Jian-Xin Tan, Xianchun Gu, Baihe Qu, Xinglong Chinese Acad Sci Inst Sci & Dev Beijing 100190 Peoples R China Univ Chinese Acad Sci Beijing 100190 Peoples R China Hangzhou Dianzi Univ Res Ctr Informat Technol & Social & Econ Dev Hangzhou 310018 Zhejiang Peoples R China Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China

In this paper, we use a stochastic dynamic programming model to evaluate the impacts of uncertainties on the abatement planning process. By involving the endogenous emission path, we differentiate two types of uncertainties during the planning process, which come from the volatility of the abatement cost and the ambiguity of emission rate. Results suggest that the considered uncertainties influence the decision-making process in several aspects by shaping the abatement path as well as emission path. (1) The impacts vary with the expected value and the level of variance of the uncertainty effects. Uncertainties caused by abatement costs from 0.02 to 0.06 and emission factors from 0.01 to 0.03 increase the total abatement costs around 7% and 5% respectively. (2) Both of these uncertainties can generate precautionary abatement in short-term. Especially during the early stages, the abatement task will be increased by 1% around in each period due to the uncertainties. However such an action will be diminishing as the duration elapses. (3) Both of these uncertainties influence the long-term abatement performances, however, with different forms and mechanisms. With small volatility, the emission rate changes the priority sequence of abatement actions more substantially in the short-term than the emission rate does. (4) The combined uncertainties can behave in a compound way to improve the uncertainty performance in the model. The difference between the emission peaks of conservative and extreme cases is significant with the gap being about 5 million metric ton. These results have potentially important policy implications and can provide a rationale for abatement actions. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Climate change mitigation Abatement strategy Abatement uncertainty stochastic dynamic programming

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From imperfection to advantage: Quantifying the benefits of imperfect advance load information for multi-truck carriers

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Transportation Research Part E: Logistics and Transportation Review 2025年 201卷

作者： Mohammadjalal Mirbeygishahabad Mehdi Najafi Hossein Zolfagharinia University of Mannheim Business School Graduate School of Economic and Social Sciences (GESS) Mannheim Germany Ted Rogers School of Management Toronto Metropolitan University Toronto Canada

Considering the dynamic and volatile conditions of spot markets, small trucking companies often struggle with load selection due to imperfect advance load information (iALI). This study develops a mathematical approach to better leverage iALI in the spot market. Using mathematical and statistical techniques, it examines two key aspects: (i) quantifying the benefit of iALI for multi-truck companies, and (ii) analyzing how market attributes affect its value. The proposed framework integrates iALI into truck activity planning via two decision-making policies: (i) Look-ahead (LOAH) and (ii) Value Function Approximation (VFA). LOAH assumes all loads materialize deterministically, while VFA uses a stochastic framework to dynamically incorporate imperfect information. To benchmark these policies, a Greedy policy is also considered as a baseline, where all advance load information is treated as completely unreliable, and decisions rely solely on currently available loads. To ensure practical relevance, the model includes real-world factors like domicile visits, truck coordination, and shipper classifications. Results show that VFA, by dynamically using iALI, improves profits by over 70% compared to LOAH, especially in classified markets, while also achieving faster solution times. A real-world case study confirms the model’s effectiveness for small trucking firms.

关键词： Imperfect information Advance load information Mathematical formulation stochastic dynamic programming Multi-truck company

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Simultaneous Optimization of Speed and Buffer Times with an Application to Liner Shipping

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TRANSPORTATION SCIENCE 2019年第2期53卷 365-382页

作者： Mulder, Judith van Jaarsveld, Willem Dekker, Rommert Erasmus Univ Econometr Inst NL-3062 PA Rotterdam Netherlands Eindhoven Univ Technol Sch Ind Engn NL-5600 MB Eindhoven Netherlands

Transport companies often have a published timetable. To maintain timetable reliability despite delays, companies include buffer times during timetable development and adjust the traveling speed during timetable execution. We develop an approach that integrates timetable development and execution. We model execution of the timetable as a stochastic dynamic program (SDP). An SDP is a natural framework to model random events causing (additional) delay, propagation of delays, and real-time optimal speed adjustments. However, SDPs alone cannot incorporate the buffer allocation during timetable development, as buffer allocation requires choosing the same action in different states of the SDP. Motivated by the practical need for timetables that operate well during timetable execution, our model seeks the buffer allocation that yields the SDP that has minimal long-run average costs. We derive several analytical insights into the model. We prove that costs are joint convex in the buffer times, and we develop theory to compute subgradients. Our fast and exact algorithm for buffer time allocation is based on these results. Our case study considers container vessels sailing a round tour consisting of 14 ports based on Maersk data. The algorithm finds the optimal timetable in roughly 70 seconds for realistic problem instances. The optimal timetable yields cost reductions of about four to 10 million U.S. dollars per route per year in comparison with the current timetable. Finally, we show the robustness of our solution approach for different parameter settings using a sensitivity analysis.

关键词： robust timetabling (online) speed optimization stochastic dynamic programming

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Sponsored search advertising and dynamic pricing for perishable products under inventory-linked customer willingness to pay

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期276卷 119-132页

作者： Tunuguntla, Vaishnavi Basu, Preetam Rakshit, Krishanu Ghosh, Debabrata Indian Inst Management Calcutta Operat Management Grp Diamond Harbor Rd Kolkata 700104 India Malaysia Inst Supply Chain Innovat MIT Global Scale Network Operat Management Grp 2A Persiaran Tebar LayarSeksyen U8 Selangor 40150 Malaysia

Several online retailers provide inventory availability information on their websites in addition to leveraging sponsored search advertising to drive customer traffic to their retail websites. The increased ability of users to interact over the internet encourages retailers to shift to sponsored search advertising. In this paper, we design a decision support model to provide strategic bid and pricing decisions to a retailer selling a perishable product over a short horizon using sponsored search advertising to attract customers to his website. The retailer complements sponsored search bidding with dynamic pricing in a multi-period stochastic dynamic programming framework. Our analyses show that it is optimal for the retailer to invest heavily in bidding at low inventory levels, whereas at high levels of inventory he should use price promotions to enhance profits. We also find that the optimal bid and price increase with the increase in mean and variability of the customer's reservation price. (C) 2019 Elsevier B.V. All rights reserved.

关键词： E-Commerce Sponsored search advertising dynamic pricing Customer willingness to pay stochastic dynamic programming

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Optimal timing of airline promotions under dilution

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第3期277卷 981-995页

作者： Otero, Daniel F. Escallon, Mariana Lopez, Cristina Akhavan-Tabatabaei, Raha Univ Los Andes Dept Ind Engn Bogota Colombia Sabanci Sch Management Istanbul Turkey Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

Offering promotions has become common practice in the airline industry as a strategy to boost the total revenue. An effective promotion campaign should be adequately priced and timed to attract sufficient extra demand and compensate for the markdown price. Diversion of demand from the regular fare to the markdown price is also a side-effect of offering promotions, which needs to be considered in designing successful campaigns. Demand dilution occurs when customers are attracted to the promotional fare from higher fare families, or from future purchases to the promotional time window. We propose a stochastic dynamic model for the optimal timing of promotions, considering both types of dilution and given fixed prices for the regular and promotional fares. We prove the existence of an optimal policy, and derive structural properties to find the minimum number of unsold seats that justifies the promotion under dilution. We examine the performance of this model on two cases from a Latin American airline and demonstrate considerable savings by applying our proposed optimal policy versus the airline's current policy. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Revenue management stochastic dynamic programming Dilution Airline promotion

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Optimal delivery of two similar products to N ordered customers with product preferences

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2019年 209卷 194-204页

作者： Kyriakidis, Epaminondas G. Dimitrakos, Theodosis D. Karamatsoukis, Constantinos C. Athens Univ Econ & Business Dept Stat Patiss 76 Athens 10434 Greece Univ Aegean Dept Math Karlovassi 83200 Samos Greece Hellen Mil Acad Dept Mil Sci Vari 16673 Attica Greece

We study a mathematical model for a specific vehicle routing problem in which a vehicle starts its route from a depot loaded with items of two similar but not identical products. The vehicle must deliver the products to N customers according to a predefined sequence. It is assumed that each customer prefers either product 1 or product 2 with known probabilities and the quantity that each customer demands is a random variable with known distribution. The actual preference and demand of each customer are revealed upon the vehicle's arrival at customer's site. The demand of each customer cannot exceed the vehicle capacity and the vehicle is allowed during its route to return to the depot to restock with quantities of both products. The travel costs between consecutive customers and the travel costs between the customers and the depot are known. If there is shortage for the desired product it is permitted to deliver the other product at a reduced price. The optimal routing strategy is found by implementing a suitable stochastic dynamic programming algorithm. It is possible to prove that the optimal routing strategy has a specific threshold-type structure. Furthermore, if we consider the same problem without the assumption that the customers are ordered, numerical experiments indicate that the optimal routing strategy can be computed for N <= 8.

关键词： Vehicle routing stochastic dynamic programming Similar products

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Analysis and Improvement of Blood Collection Operations

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M&SOM-MANUFACTURING & SERVICE OPERATIONS MANAGEMENT 2019年第1期21卷 29-46页

作者： Ayer, Turgay Zhang, Can Zeng, Chenxi White, Chelsea C., III Joseph, V. Roshan Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Duke Univ Fuqua Sch Business Durham NC 27708 USA

Because of the importance, limited supply, and perishable nature of blood products, effective management of blood collection is critical for high-quality healthcare delivery. In this paper, working closely with the American Red Cross (ARC), we study a blood collection problem focusing on whole blood that is to be processed into cryoprecipitate (cryo), a critical blood product for controlling massive hemorrhaging. In particular, we aim to determine when and from which mobile collection sites to collect blood for cryo production, such that the weekly collection target is met while the collection costs are minimized. The cryo collection problem imposes a unique challenge: if blood collected is to be processed into cryo units, it has to be processed within eight hours after collection, while this time limit is 24 hours for most other blood products. To analyze the cryo collection problem, we first develop a mathematical program to represent and compare two different blood collection business models, namely, the status quo nonsplit model and an alternative model we propose, which splits each collection window into two intervals and allows different types of collections in the two intervals. Then, we establish several structural properties of the proposed mathematical program and develop a near-optimal solution algorithm to determine the cryo collection schedules under each collection model. Our extensive computational analyses based on real data indicated that, compared with the status quo, our proposed collection model can significantly reduce total collection costs. Based on this significant potential impact, our proposed collection model has been implemented by the ARC Douglasville manufacturing facility, the largest ARC blood manufacturing facility supplying blood to about 120 hospitals in the southern United States. Field data from postimplementation indicated that our proposed solution has resulted in (i) reducing inconsistencies in supply of cryo collections, and

关键词： blood collection cryoprecipitate humanitarian operations stochastic dynamic programming

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