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A sequential dynamic pricing model and its applications

NAVAL RESEARCH LOGISTICS 2004年第4期51卷 501-521页

作者： Lin, KY Virginia Polytech Inst & State Univ Grado Dept Ind & Syst Engn Blacksburg VA 24061 USA

Consider a sequential dynamic pricing model where a seller sells a given stock to a random number of customers. Arriving one at a time, each customer will purchase one item if the product price is lower than her personal reservation price. The seller's objective is to post a potentially different price for each customer in order to maximize the expected total revenue. We formulate the seller's problem as a stochastic dynamic programming model, and develop an algorithm to compute the optimal policy. We then apply the results from this sequential dynamic pricing model to the case where customers arrive according to a continuous-time point process. In particular, we derive tight bounds for the optimal expected revenue, and develop an asymptotically optimal heuristic policy. (C) 2004 Wiley Periodicals, Inc.

关键词： dynamic pricing inventory control stochastic dynamic programming asymptotically optimal policy

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Index heuristics for multiclass M/G/1 systems with nonpreemptive service and convex holding costs

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QUEUEING SYSTEMS 2003年第2期45卷 81-111页

作者： Glazebrook, KD Lumley, RR Ansell, PS Univ Edinburgh Sch Management Edinburgh EH8 9JY Midlothian Scotland Univ Newcastle Upon Tyne Dept Stat Newcastle Upon Tyne NE1 7RU Tyne & Wear England

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.

关键词： indexability index policy service control stochastic dynamic programming restless bandit

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A scenario simulation approach for market power analysis in hydrothermal systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2003年第3期18卷 1046-1053页

作者： Vargas, LS Rodrigo, PB Oscar, MA Rigoberto, TA Univ Chile Dept Ingn Elect Santiago 2007 Chile

This paper focuses on markets based on physical bilateral contracts combined with a power exchange (PX). The main feature to be analyzed is the behavior of the hydrothermal system where one or more companies have a big reservoir with capacity for inter annual regulation. In this work, inter annual regulation means the ability of a reservoir to allocate water from consecutive years. The use of the reservoirs in a context of a power exchange market with competition is the main objective of this study. Results on the Chilean Central Interconnected System using stochastic dynamic programming are presented and discussed.

关键词： bilateral contracts hydrothermal systems market power power exchange stochastic dynamic programming

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stochastic wafer fabrication scheduling

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IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING 2003年第1期16卷 2-14页

作者： Shen, YX Leachman, RC Agilent Technol Inc Semicond Prod Grp Ft Collins CO 80525 USA Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA

To meet the challenge of integrating uncertainty analysis into wafer fabrication scheduling, this paper proposes a stochastic dynamic programming model for scheduling new releases and bottleneck processing by stage. Based on the paradigm of stochastic linear quadratic control (SLQ), the lab scheduling model incorporates considerable analysis of uncertainties in yields and demands. The SLQ scheduling model explicitly captures the reentrant flow structure characteristic of wafer fabrication. Moreover, the SLQ scheduling model removes a major weakness in applying dynamic programming to production control by accommodating noninteger values for lead times Embedded in the SLQ scheduling model is what the authors term a degree-2 yield distribution that subsumes most popular yield distributions in the literature. As long as the underlying system dynamics behave in a degree-2 fashion, the corresponding optimal scheduling policy turns out to he a linear control rule that is easy to compute and implement. Industrial data are used to test the effectiveness and robustness of the SLQ machinery versus the LP rolling horizon and pull heuristic methodologies. Encouraging results and valuable insights are obtained from extensive numerical experiments that show promise for successfully managing uncertainties surrounding fab scheduling.

关键词： fab scheduling linear quadratic control stochastic dynamic programming uncertainty analysis

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Evaluating the magnitudes of financial transactions costs on risk behavior

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AGRICULTURAL SYSTEMS 2003年第2-3期75卷 235-249页

作者： Atwood, JA Buschena, DE Montana State Univ Dept Agr Econ & Econ Bozeman MT 59717 USA

The model presented in this paper relies on financial constraints and transactions costs to operationalize model of behavior akin to safety rules. The decision maker is taken to maximize long term (40 period) expected wealth in the presence of financial transactions costs. The model allows exploration of the implications of these constraints and transactions costs for measurable choice patterns over risk. The optimization analysis demonstrates very rich behavior despite the restrictive assumption of risk neutral preferences. The optimal decisions show instances of "risk aversion" with willingness to pay less than a risky option's expected value, and of "risk preference" or plunging with willingness to pay greater than a risky option's expected value. These varied behavioral patterns in the presence of risk depend on the individual's financial standing, the magnitude of the random outcomes, the underlying distribution, and the farm policy environment. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： risk transaction costs plunging stochastic dynamic programming safety rules

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Uncertainty based operation of large scale reservoir systems: Dez and Karoon experience

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JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 2003年第4期39卷 961-975页

作者： Karamouz, M Mousavi, SJ Amirkabir Univ Technol Sch Civil & Environm Engn Tehran Iran Iran Univ Sci & Technol Struct & Hydrostruct Res Ctr Dept Civil Engn Tehran Iran

Reservoir operation involves a complex set of human decisions depending upon hydrologic conditions in the supply network including watersheds, lakes, transfer tunnels, and rivers. Water releases from reservoirs are adjusted in an attempt to provide a balanced response to different demands. When a system involves more than one reservoir, computational burdens have been a major obstacle in incorporating uncertainties and variations in supply and demand. A new generation of stochastic dynamic programming was developed in the 1980s and 1990s to incorporate the forecast and demand uncertainties. The Bayesian stochastic dynamic programming (BSDP) model and its extension, Demand Driven stochastic dynamic programming (DDSP) model, are among those models. Recently, a Fuzzy stochastic dynamic programming model (FSDP) also was developed for a single reservoir to model the errors associated with discretizing the variables using fuzzy set theory. In this study the DDSP and the FSDP models were extended and simplified for a complex system of Dez and Karoon reservoirs in the southwestern part of Iran. The simplified models are called Condensed Demand Driven stochastic programming (CDDSP) and Condensed Fuzzy stochastic dynamic programming (CFSDP). The optimal operating policies developed by the CDDSP and the CFSDP models were simulated in a classical model and a fuzzy simulation model, respectively. The case study was used to demonstrate the advantages of implementing the proposed algorithm, and the results show the significant value of the proposed fuzzy based algorithm.

关键词： stochastic dynamic programming reservoir operation fuzzy set theory uncertainty imprecision reservoir system fuzzy rule-based modeling

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A gridding method for Bayesian sequential decision problems

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2003年第3期12卷 566-584页

作者： Brockwell, AE Kadane, JB Carnegie Mellon Univ Dept Stat Pittsburgh PA 15213 USA

This article introduces a numerical method for finding optimal or approximately optimal decision rules and corresponding expected losses in Bayesian sequential decision problems. The method, based on the classical backward induction method, constructs a grid approximation to the expected loss at each decision time, viewed as a function of certain statistics of the posterior distribution of the parameter of interest. In contrast with most existing techniques, this method has a computation time which is linear in the number of stages in the sequential problem. It can also be applied to problems with insufficient statistics for the parameters of interest. Furthermore, it is well-suited to be implemented using parallel processors.

关键词： backward induction batch sequential Bayesian sequential analysis fully sequential Monte Carlo integration parallel computing stochastic dynamic programming

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stochastic optimization of a hydroelectric reservoir using piecewise polynomial approximations

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INFOR 2003年第1期41卷 51-69页

作者： Lamond, BF Univ Laval Fac Sci Adm Dept Operat & Syst Decis Quebec City PQ G1K 7P4 Canada

We propose a method for optimizing a single hydro-electric reservoir using a piecewise polynomial approximation of the future value functions. Unlike previous methods based on splines, we avoid discretizing the inflow distribution. Instead, we carry out the expectation step of dynamic programming using an exact, easy-to-evaluate formula for the integral of a piecewise polynomial function. We then apply our method to solving a model which assumes a piecewise linear reward function of the energy produced, and takes into account the turbine head effects.

关键词： Markov decision processes stochastic dynamic programming piecewise polynomial approximation optimal reservoir management energy planning

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The value of information in a long-term hydro-thermal electrical planning model

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International Transactions in Operational Research 2003年第1期10卷 89-100页

作者： Contesse, Luis Donoso, Patricio Prina, José Pontificia Universidad Católica de Chile Chile

This article presents the analysis, comparison, and application of two alternative models to the optimal long-term operation planning of an hydro-thermal power system under conditions of uncertainty. The electrical system considered comprises one large reservoir, with interannual regulation capacity, and several smaller ones. The analyzed models employ stochastic dynamic programming as the solution methodology. The fundamental problem is to decide, on every temporal stage, how much water to use for generating purposes and how much to store, in order to minimize the total thermal and shortage costs. The original version of the studied model, created originally to forecast fuel consumption, assumes that the decision regarding the water release from the main reservoir is taken knowing the future hydrologic conditions. This criterion is known as wait-and-see. On the contrary, the new versions of the model, proposed in this article, consider a here-and-now criterion. Specifically, it is assumed that the future hydrologic conditions are not known at the time of making the operational decisions. The difference between the optimal cost of the proposed models and the original model defines the value of having the information regarding future hydrologic conditions before taking any decision. This value is generally known as the expected value of perfect information. © 2003 International Federation of Operational Research Societies.

关键词： Hydro-thermal power system planning Long-term planning under uncertainty stochastic dynamic programming

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Optimal market timing strategies under transaction costs

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2002年第2期30卷 97-108页

作者： Li, W Lam, K Hong Kong Polytech Univ Fac Business & Informat Syst Dept Business Studies Kowloon Hong Kong Peoples R China Hong Kong Baptist Univ Sch Business Dept Finance & Decis Sci Kowloon Tong Peoples R China

In this paper, we consider optimal market timing, strategies under transaction costs. We assume that the asset's return follows an auto-regressive model and use long-term investment growth as the objective of a market timing strategy which entails the shifting of funds between a risky asset and a riskless asset. We give the optimal trading strategy for a finite investment horizon, and analyze its limiting behavior. For a finite horizon, the optimal decision in each step depends on two threshold values. If the return today is between the two values, nothing needs to be done, otherwise funds will be shifted from one asset to another, depending on which threshold value is being exceeded. When investment horizon tends to infinity, the optimal strategy converges to a stationary policy, which is shown to be closely related to a well-known technical trading rule, called Momentum Index trading rule. An integral equation of them two threshold values is given. Numerical results for the limiting stationary strategy are presented. The results confirm the obvious guess that the no-transaction region increases as the transaction cost increase. Finally, the limiting stationary strategy is applied to data in the Hang Seng Index Futures market in Hong Kong. The out-of-sample performance of the limiting stationary strategy is found to be better than the simple strategy sed in literature, which is based on an 1-step ahead forecast of return. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： market timing autoregressive models growth-optimal investment strategy stochastic dynamic programming

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