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How to Schedule Measurements of a Noisy Markov Chain in Decision Making?

IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第7期59卷 4440-4461页

作者： Krishnamurthy, Vikram Univ British Columbia Dept Elect & Comp Engn Vancouver BC V6T 1Z4 Canada

A decision maker records measurements of a finite-state Markov chain corrupted by noise. The goal is to decide when the Markov chain hits a specific target state. The decision maker can choose from a finite set of sampling intervals to pick the next time to look at the Markov chain. The aim is to optimize an objective comprising of false alarm, delay cost, and cumulative measurement sampling cost. Taking more frequent measurements yields accurate estimates but incurs a higher measurement cost. Making an erroneous decision too soon incurs a false alarm penalty. Waiting too long to declare the target state incurs a delay penalty. What is the optimal sequential strategy for the decision maker? This paper shows that under reasonable conditions, the optimal strategy has the following intuitive structure: when the Bayesian estimate (posterior distribution) of the Markov chain is away from the target state, look less frequently;while if the posterior is close to the target state, look more frequently. Bounds are derived for the optimal strategy. Also the achievable optimal cost of the sequential detector as a function of transition dynamics and observation distribution is analyzed. The sensitivity of the optimal achievable cost to parameter and strategy variations is bounded in terms of the Kullback divergence. Also structural results are obtained for joint optimal sampling and measurement control (active sensing).

关键词： Change detection optimal sequential sampling quickest state estimation decision making active sensing Bayesian filtering stochastic dominance submodularity stochastic dynamic programming partially observed Markov decision process

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A computationally efficient state-space partitioning approach to pricing high-dimensional American options via dimension reduction

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第2期231卷 362-370页

作者： Jin, Xing Li, Xun Tan, Hwee Huat Wu, Zhenyu Univ Warwick Coventry CV4 7AL W Midlands England Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China Natl Univ Singapore Dept Math Singapore 119076 Singapore Univ Manitoba Asper Sch Business Winnipeg MB R3T 2N2 Canada

This paper studies the problem of pricing high-dimensional American options. We propose a method based on the state-space partitioning algorithm developed by Jin et al. (2007) and a dimension-reduction approach introduced by Li and Wu (2006). By applying the approach in the present paper, the computational efficiency of pricing high-dimensional American options is significantly improved, compared to the extant approaches in the literature, without sacrificing the estimation precision. Various numerical examples are provided to illustrate the accuracy and efficiency of the proposed method. Pseudcode for an implementation of the proposed approach is also included. (C) 2013 Elsevier B.V. All rights reserved.

关键词： High dimensional American-style option Dimension reduction stochastic dynamic programming

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Energy-Efficient, Heterogeneous Sensor Selection for Physical Activity Detection in Wireless Body Area Networks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2013年第7期61卷 1581-1594页

作者： Zois, Daphney-Stavroula Levorato, Marco Mitra, Urbashi Univ So Calif Ming Hsieh Dept Elect Engn Los Angeles CA 90007 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA

In this paper, the problem of efficient operation of an energy-constrained, heterogeneous Wireless Body Area Network (WBAN) to optimize an activity detection application is addressed. WBANs constitute a new class of wireless sensor networks that enable diverse applications in healthcare, entertainment, sports, military and emergency situations. A typical WBAN consists of a few, heterogeneous sensors wirelessly coupled to an energy-constrained fusion center which, according to observations of a real-world prototype WBAN, imposes critical restrictions on system lifetime. To address this issue, a novel stochastic control framework is introduced, which considers both sensor heterogeneity and application requirements, for achieving the two-fold goal: energy savings with satisfactory detection performance. An optimal dynamic programming algorithm for the sensor selection problem is also derived. Important properties of the cost functionals are derived and used to design three approximation algorithms, which offer near optimal performance with significant complexity reduction. Simulations on real-world data show energy gains as high as 68% in comparison to an equal allocation scheme with probability of detection error on the order of 10(-4).

关键词： Approximation algorithms body sensor networks controlled sensing dynamic sensor selection energy-efficient tracking heterogeneous resource management partially observable Markov decision processes (POMDP) physical activity detection stochastic dynamic programming

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Optimal admission control for tandem loss systems with two stations

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OPERATIONS RESEARCH LETTERS 2013年第4期41卷 351-356页

作者： Silva, Daniel F. Zhang, Bo Ayhan, Hayriye Georgia Inst Technol H Milton Stewart Sch Syst & Ind Engn Atlanta GA 30332 USA IBM TJ Watson Res Ctr Yorktown Hts NY 10598 USA

We study a system of two queues in tandem with finite buffers, Poisson arrivals to the first station, and exponentially distributed service times at both stations. Losses are incurred either when a customer is rejected at the time of arrival to the first station or when the second station is full at the time of service completion at the first station. The objective is to determine the optimal admission control policy that minimizes the long-run average cost. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Admission control Loss systems Tandem queues Markov decision processes stochastic dynamic programming

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Optimality of myopic inventory policy for a single-product, multi-period, stochastic inventory problem with batch ordering and capacity commitment

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IIE TRANSACTIONS 2013年第8期45卷 925-938页

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

The single-product, multi-period, stochastic inventory problem with batch ordering has been studied for decades. However, most existing research focuses only on the case in which there is no capacity constraint on the ordered quantity. This article generalizes that research to the case in which the capacity is purchased at the beginning of a planning horizon and the total ordered quantity over the planning horizon is constrained by the capacity. The objective is to minimize the expected total cost (the cost of purchasing capacity plus the minimum expected sum of the ordering, storage, and shortage costs incurred over the planning horizon for the given capacity). The conditions that ensure that a myopic ordering policy is optimal for any given capacity commitment are obtained. The structure of the expected total cost is characterized under these conditions and an algorithm is presented that can be used to calculate the optimal capacity commitment. A simulation study is performed to better understand the impact of various parameters on the performance of the model.

关键词： Batch ordering capacity inventory myopic policy stochastic dynamic programming

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A Factorial-based dynamic Analysis Method for Reservoir Operation Under Fuzzy-stochastic Uncertainties

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WATER RESOURCES MANAGEMENT 2013年第13期27卷 4591-4610页

作者： Fu, D. Z. Li, Y. P. Huang, G. H. North China Elect Power Univ SC Resources & Environm Res Acad MOE Key Lab Reg Energy Syst Optimizat Beijing 102206 Peoples R China

In this study, a factorial-based fuzzy-stochastic dynamic programming (FFS-DP) method is developed for tackling multiple uncertainties including fuzziness, randomness and their interaction in reservoir operation management (ROM). FFS-DP is framed on the integration of stochastic dynamic programming, fuzzy-Markov chain, vertex analysis and factorial analysis techniques. It can not only deal with the conventional optimization problem for reflecting dynamic and uncertain features in ROM, but also obtain detailed effects of uncertain parameters and their interactions on the system performance. The developed method is applied to a case study of a reservoir operation system, where the local authority is in charge of allocating relative scant water to the downstream municipality. The results obtained can help the local authority identify desired water release policies under uncertain system conditions. Besides, the results simultaneously indicate that significant factors and their interactions can be identified in ROM. Moreover, the results can be further analyzed for generating optimal parameter inputs to obtain maximized system benefits.

关键词： Factorial analysis Fuzzy Markov chain Reservoir operation management stochastic dynamic programming Vertex analysis Uncertainty

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Availability maximization under partial observations

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OR SPECTRUM 2013年第3期35卷 691-710页

作者： Jiang, Rui Kim, Michael J. Makis, Viliam Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada

In this paper, we propose a new model for availability maximization under partial observations for maintenance applications. Compared with the widely studied cost minimization models, few structural results are known about the form of the optimal control policy for availability maximization models. We consider a failing system with unobservable operational states. Only the failure state is observable. System deterioration is driven by an unobservable, continuous-time homogeneous Markov process. Multivariate condition monitoring data which is stochastically related to the unobservable state of the system is collected at equidistant sampling epochs and is used to update the posterior state distribution for decision making. Preventive maintenance can be carried out at any sampling epoch, and corrective maintenance is carried out upon system failure. The objective is to determine the form of the optimal control policy that maximizes the long-run expected average availability per unit time. We formulate the problem as an optimal stopping problem with partial information. Under standard assumptions, we prove that a control limit policy is optimal. A computational algorithm is developed, illustrated by numerical results.

关键词： Availability maximization Optimal stopping stochastic dynamic programming Partially observable system Control limit structure

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Influence of Guiding Curves in the Optimal Management of a Hydropower System

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WATER RESOURCES MANAGEMENT 2013年第15期27卷 4989-5001页

作者： Arganis-Juarez, Maritza L. Mendoza-Ramirez, Rosalva Dominguez-Mora, Ramon Hernandez-Ruiz, Alma A. Berezowsky-Verduzco, Moises Univ Nacl Autonoma Mexico Inst Ingn Mexico City 04510 DF Mexico

Optimal operating policies for hydropower generation in a system of dams were obtained by means of a modified algorithm of stochastic dynamic programming that incorporates the guiding curve concept and other operating requirements defined by the Mexican agency in charge of electricity generation. These operating policies were used to simulate the long term system behavior and to analyze the influence of the guiding curves in the energy generation, the volume spilled and the possible deficit. The results show that by trying different curves it is possible to obtain a range of results that will enable decision makers to choose those that best fit their needs.

关键词： Guiding curves Optimal operating policies stochastic dynamic programming Hydropower system

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Production planning optimization for manufacturing and remanufacturing system in stochastic environment

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JOURNAL OF INTELLIGENT MANUFACTURING 2013年第4期24卷 717-728页

作者： Naeem, Mohd Arshad Dias, Dean J. Tibrewal, Rupak Chang, P. C. Tiwari, M. K. Indian Inst Technol Dept Ind Engn & Management Kharagpur 721302 W Bengal India Coll Informat Dept Informat Management Chungli Taiwan

This article studies a single item dynamic lot sizing problem with manufacturing and remanufacturing provisions. The demands and returns are considered as both stochastic and deterministic. There are two inventories recoverable and serviceable inventory. We developed a dynamic programming based model with objective to determine the quantities that have to be manufactured or re-manufactured at each period in order to minimize the total cost, including production cost, holding cost for returns and finished goods, and backlog cost. Also, unit production cost is also taken as variable in case of deterministic case. Finally, a numerical example for each of deterministic and stochastic model is worked out to illustrate how the model is applied and to prove its feasibility.

关键词： Inventory control Manufacturing-remanufacturing hybrid system Lot sizing stochastic dynamic programming

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Active Adaptive Management for Reintroduction of an Animal Population

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JOURNAL OF WILDLIFE MANAGEMENT 2013年第6期77卷 1135-1144页

作者： Runge, Michael C. US Geol Survey Patuxent Wildlife Res Ctr Laurel MD 20708 USA

Captive animals are frequently reintroduced to the wild in the face of uncertainty, but that uncertainty can often be reduced over the course of the reintroduction effort, providing the opportunity for adaptive management. One common uncertainty in reintroductions is the short-term survival rate of released adults (a release cost), an important factor because it can affect whether releasing adults or juveniles is better. Information about this rate can improve the success of the reintroduction program, but does the expected gain offset the costs of obtaining the information? I explored this question for reintroduction of the griffon vulture (Gyps fulvus) by framing the management question as a belief Markov decision process, characterizing uncertainty about release cost with 2 information state variables, and finding the solution using stochastic dynamic programming. For a reintroduction program of fixed length (e.g., 5 years of releases), the optimal policy in the final release year resembles the deterministic solution: release either all adults or all juveniles depending on whether the point estimate for the survival rate in question is above or below a specific threshold. But the optimal policy in the earlier release years 1) includes release of a mixture of juveniles and adults under some circumstances, and 2) recommends release of adults even when the point estimate of survival is much less than the deterministic threshold. These results show that in an iterated decision setting, the optimal decision in early years can be quite different from that in later years because of the value of learning. (c) 2013 The Wildlife Society.

关键词： active adaptive management belief Markov decision process griffon vulture Gyps fulvus reintroduction stochastic dynamic programming

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