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作者： Lendel, Gabriel Charles University of Prague

Title: stochastic dynamic programming Problems: Theory and Applications Author: Gabriel Lendel Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Karel Sladký CSc. Supervisors e-mail address: sladky@*** Abstract: In the present work we study Markov decision processes which provide a mathematical framework for modeling decision-making in situations where outcomes are partly random and partly under the control of a decision maker. We study iterative procedures for finding policy that is optimal or nearly optimal with respect to the selec- ted criteria. Specifically, we mainly examine the task of finding a policy that is optimal with respect to the total expected discounted reward or the average expected reward for discrete or continuous systems. In the work we study policy iteration algorithms and aproximative value iteration algorithms. We give numerical analysis of specific problems. Keywords: stochastic dynamic programming, Markov decision process, policy ite- ration, value iteration

关键词： stochastic dynamic programming Markov decision processes policy iteration value iteration

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Optimal Electric Energy Storage Operation

Optimal Electric Energy Storage Operation

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IEEE Power and Energy Society General Meeting

作者： Junjie Qin Raffi Sevlian David Varodayan Ram Rajagopal the Institute of Computational and Mathematical Engineering and the Stanford Sustainable Systems Lab Stanford University Stanford CA 94305 the Department of Electrical Engineering and the Stanford Sustainable Systems Lab Stanford University Stanford CA 94305 the Department of Civil and Environmental Engineering and the Stanford Sustainable Systems Lab Stanford University Stanford CA 94305

ISBN: (纸本)9781467327299

Estimating the arbitrage value of storage is an important problem in power systems planning. Various studies have reported different values based numerical solutions of variations of a basic model. In this paper, we instead rely on a closed form solution for storage control. The closed form highlights the right type of forecasting that is required and allows large horizon problems to be solved. We study various scenarios and provide a simple methodology for evaluating the arbitrage value of storage.

关键词： Index Terms-Energy storage operation stochastic dynamic programming warehousing problem

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Exploring the effects of reductions in krill biomass in the Southern Ocean on blue whales using a state-dependent foraging model

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ECOLOGICAL MODELLING 2011年第18期222卷 3366-3379页

作者： Wiedenmann, John Cresswell, Katherine A. Goldbogen, Jeremy Potvin, Jean Mangel, Marc Univ Calif Santa Cruz Dept Ocean Sci Santa Cruz CA 95064 USA Univ Calif Santa Cruz Dept Appl Math & Stat Ctr Stock Assessment Res CSTAR Santa Cruz CA 95064 USA Cascadia Res Collect Olympia WA 98501 USA St Louis Univ Dept Phys St Louis MO 63103 USA Univ Bergen Dept Biol Bergen Norway

Many species of baleen whales were hunted to near extinction in the Southern Hemisphere. The recovery of these populations will be affected by the availability of krill, a major dietary component, in the Southern Ocean. We combine a novel energetics model for baleen whales with a state dependent foraging model to explore the impacts of an expanding krill fishery on baleen whales. We parameterize the model for blue whales, but with simple modifications it could be applied to most baleen whales. We predict that an expanding fishery will have a small but significant impact on the blue whale population through decreased birth rates. However, spreading the catch limit throughout the range of krill can reduce these effects. In addition, whales may be able to reduce these impacts through adaptive changes in foraging behavior. The relationship between krill abundance and blue whale foraging and reproductive success is nonlinear, such that larger reductions in krill biomass, potentially following a loss of sea ice due to climate change, could have a much larger negative impact on the recovery of blue whales. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Blue whales Antarctic krill Energetics Climate change stochastic dynamic programming Fishing impact

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Optimizing competitive uses of water for irrigation and fisheries

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AGRICULTURAL WATER MANAGEMENT 2011年第1期101卷 42-51页

作者： Lap Doc Tran Schilizzi, Steven Chalak, Morteza Kingwell, Ross Univ Western Australia Sch Agr & Resource Econ Ctr Environm Econ & Policy Crawley WA 6009 Australia Nong Lam Univ Dept Econ Ho Chi Minh City Vietnam Dept Agr & Food S Perth WA 6151 Australia

Choosing the appropriate reservoir water management strategy can be difficult when the water has multiple uses. This study examines this problem for reservoir managers where water use involves irrigation and fisheries. A stochastic dynamic programming (SDP) model is developed to facilitate reservoir management, using a case study illustration for southern Vietnam. The model includes the response of rice and fish yields to key factors including reservoir water levels, the timing and quantity of water release, and climatic conditions. The model also accounts for variation in rainfall patterns, irrigation requirements, and the demand for low water levels during the fish harvest season. Three production scenarios are examined where the reservoir's water is used for: only producing rice (scenario 1), only producing fish (scenario 2), and producing rice and fish (scenario 3). Key findings are: (1) for scenario 1, adequate water should be released to meet rice growing water requirements and residual water should be stored as a source of water in case of low rainfall, (2) for scenario 2, sufficient water needs to be released prior to the fish harvest to maximize this harvest;and (3) for scenario 3, water should be released prior to fish harvest, but sufficient water should remain to satisfy the water requirements of rice. When the reservoir is managed for joint production of rice and fish, net benefits are 6% greater than when the reservoir is managed solely for rice production. The SDP model developed in this paper could be adapted and applied to other multiple-use resources such as forests, river basins, and land. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Reservoir water management Irrigation Fisheries Optimization Multiple-use resources stochastic dynamic programming

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Development of Operational Policy for a Multi-reservoir System in India using Genetic Algorithm

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WATER RESOURCES MANAGEMENT 2011年第10期25卷 2405-2423页

作者： Jothiprakash, V. Shanthi, Ganesan Arunkumar, R. Indian Inst Technol Dept Civil Engn Bombay 400076 Maharashtra India Shivani Engn Coll Tiruchirappalli 620009 Tamil Nadu India

A genetic algorithm (GA) and a backward moving stochastic dynamic programming (SDP) model has been developed for derivation of operational policies for a multi-reservoir system in Kodaiyar River Basin, Tamil Nadu, India. The model was developed with the objective of minimizing the annual sum of squared deviation of desired target releases. The total number of population, crossover probability and number of generations of the GA model was optimized using sensitivity analysis, and penalty function method was used to handle the constraints. The policies developed using the SDP model was evaluated using a simulation model with longer length of inflow data generated using monthly time stepped Thomas-Fiering model. The performance of the developed policies were evaluated using the performance criteria namely, the monthly frequency of irrigation deficit (MFID), Monthly average irrigation deficit (MAID), Percentage monthly irrigation deficit (PMID), Annual frequency of irrigation deficit (AFID), Annual average irrigation deficit (AAID), and Percentage annual irrigation deficit (PAID). Based on the performance, it was concluded that the robostic, probabilistic, random search GA resulted in better optimal operating policies for a multi-reservoir system than the SDP models.

关键词： Genetic algorithm stochastic dynamic programming Kodaiyar river basin Multi-reservoir Operational policies

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Myopic optimal policy for a multi-period, two-delivery-lead-times, stochastic inventory problem with minimum cumulative commitment and capacity

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2011年第2期133卷 719-727页

作者： Xu, Ningxiong Cornell Univ Sch Civil & Environm Engn Ithaca NY 14853 USA

This paper studies a single-product, multi-period, stochastic inventory problem that imposes the lower and upper bounds on the cumulative order quantity during a planning horizon and allows two delivery lead times. This model includes three features. The first one is that a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer's total cumulative order quantity during the planning horizon is constrained with the capacity. The second one is that the buyer agrees to purchase the product at least a certain percentage of the purchased capacity during the planning horizon. The third one is that the supplier allows the buyer to order the product with two-delivery-lead-times. We identify conditions under which a myopic ordering policy is optimal. We also develop an algorithm to calculate the optimal capacity when the minimum cumulative order quantity commitment is a certain percentage of the capacity. We then use the algorithm to evaluate the effect of the various parameters on the buyer's minimum expected total cost during the planning horizon. Our computation shows that the buyer would benefit from the commitments and two-delivery-lead-times. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Additive function Capacity Minimum cumulative order quantity commitment Myopic policy stochastic dynamic programming Two-delivery-lead-times

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Scheduling unit length jobs on parallel machines with lookahead information

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JOURNAL OF SCHEDULING 2011年第4期14卷 335-350页

作者： Mandelbaum, Marvin Shabtay, Dvir Ben Gurion Univ Negev Dept Ind Engn & Management IL-84105 Beer Sheva Israel

This paper studies two closely related online-list scheduling problems of a set of n jobs with unit processing times on a set of m multipurpose machines. It is assumed that there are k different job types, where each job type can be processed on a unique subset of machines. In the classical definition of online-list scheduling, the scheduler has all the information about the next job to be scheduled in the list while there is uncertainty about all the other jobs in the list not yet scheduled. We extend this classical definition to include lookahead abilities, i.e., at each decision point, in addition to the information about the next job in the list, the scheduler has all the information about the next h jobs beyond the current one in the list. We show that for the problem of minimizing the makespan there exists an optimal (1-competitive) algorithm for the online problem when there are two job types. That is, the online algorithm gives the same minimal makespan as the optimal offline algorithm for any instance of the problem. Furthermore, we show that for more than two job types no such online algorithm exists. We also develop several dynamic programming algorithms to solve a stochastic version of the problem, where the probability distribution of the job types is known and the objective is to minimize the expected makespan.

关键词： Multipurpose machine scheduling Lookahead information Online algorithms Eligibility constraint stochastic dynamic programming

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Unreliable newsboy problem with a forecast update

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OPERATIONS RESEARCH LETTERS 2011年第4期39卷 278-282页

作者： Tiwari, Divya Patil, Rahul Shah, Janat IIM Bangalore Bangalore 560076 Karnataka India Indian Inst Technol SJMSOM Bombay 400076 Maharashtra India

In this paper, we derive an optimal ordering policy for an unreliable newsboy who can place two sequential orders before the start of a single selling season by using a demand forecast update. Supply yield is modeled using a uniform distribution considering both the minimum order guarantee and the maximum yield. Our results indicate that a firm should focus on increasing the minimum order guarantee from a first stage supplier to reduce its total supply chain cost. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Newsboy problem Forecast update Random yield Inventory management stochastic dynamic programming

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stochastic optimisation of Hydro-Quebec hydropower installations: a statistical comparison between SDP and SSDP methods

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CANADIAN JOURNAL OF CIVIL ENGINEERING 2011年第12期38卷 1427-1434页

作者： Cote, Pascal Haguma, Didier Leconte, Robert Krau, Stephane Univ Sherbrooke Dept Civil Engn Fac Engn Sherbrooke PQ J1K 2R1 Canada Ecole Polytech Super Dept Construct Engn Montreal PQ H3C 1K3 Canada Hydroquebec Montreal PQ H3A 3C2 Canada

This paper examines the problem of finding an optimal operating policy for Hydro-Quebec's Manicouagan River and Outardes River hydroelectric installations. The solution method is based on the sampling dynamic programming (SSDP) algorithm. We use a new hydrologic state variable to capture the inflows regime, and this variable is given by a linear combination of the snow water equivalent and soil moisture. In real-time operation, this variable is calculated by a hydrologic model and incorporated in the operating policy to calculate the water released at each power plant. The algorithm is compared to the lag-1 stochastic dynamic programming (SDP) already implemented at Hydro-Quebec, through a statistical analysis with a set of 40 synthetic historical inflow scenarios obtained by hydrologic modeling, using synthetic temperature and precipitation produced by a stochastic weather generator. The results of the analysis show that the SSDP operating policy is statistically superior to the operating policy of the lag-1 SDP model. The SSDP operating policy does not underestimate the volume of runoff occurring during the spring season contrary to SDP. Consequently, there is a reduction in the hm(3) of water spilled, while the average annual generation is increased.

关键词： hydropower system stochastic dynamic programming sampling stochastic dynamic programming snow water equivalent soil moisture operating policy weather generator

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Distribution of High-Definition Video in 802.11 Wireless Home Networks

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IEEE TRANSACTIONS ON CONSUMER ELECTRONICS 2011年第1期57卷 53-61页

作者： Miguel, Victor Cabrera, Julian Jaureguizar, Fernando Garcia, Narciso Univ Politecn Madrid GTI E-28040 Madrid Spain

Wireless distribution of multimedia contents through 802.11 networks in the home environment presents a number of advantages which have fueled the interest of industry in recent years, such as simple connectivity and data delivery to a variety of devices. Together with High-Definition (HD) contents, multimedia wireless distribution has been proposed for several applications, such as IPTV and Digital TV distribution for multiple devices in the home environment. However, the quality of wireless multimedia services is deteriorated by random packet losses caused by the changing channel behavior. For these scenarios, we propose in this paper a multicast distribution system for High-Definition video over 802.11 wireless networks based on rate-limited packet retransmission. Unlike previous works, which require on-line calculation of the optimal retransmission strategies, the presented system employs optimal retransmission strategies obtained through an off-line optimization process. This approach, based on stochastic dynamic programming, allows a lower on-line complexity and, when compared to another limited rate ARQ system, offers a higher packet recovery and improvements in video quality for low end-to-end delays requirements(1).

关键词： HD multimedia distribution wireless home network stochastic dynamic programming ARQ

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