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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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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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Comparative Study of Real-Time HEV Energy Management Strategies

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2017年第12期66卷 10875-10888页

作者： Jiang, Qi Ossart, Florence Marchand, Claude Grp Elect Engn Paris F-91192 Gif Sur Yvette France

An adequate energy management strategy is the key to optimizing hybrid electric vehicle fuel efficiency. Various real-time controls have been recently developed. As each study is performed in a specific context, a comparative analysis is critically needed to point out their pros and cons. This paper proposes a comparison between three promising real-time strategies: adaptive equivalent consumption minimization strategy (A-ECMS), optimal control law (OCL), and stochastic dynamic programming (SDP). Two offline algorithms are used as benchmark: Pontryagin's minimum principle and dynamic programming. Implementation and parameters setting issues are discussed for each strategy. The real-time strategies robustness is then evaluated over several types of driving cycles and a statistical analysis is conducted using random cycles generated by Markov process. Simulation results show that OCL needs improvement. A-ECMS reaches the best fuel saving performance when used with parameter sets adjusted to the driving environment, while SDP better respects the charge sustaining constraint.

关键词： A-ECMS hybrid electric vehicle Markov chain OCL optimal control Pontryagin minimum principle real-time energy management stochastic dynamic programming

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Water storage in a changing environment: The impact of allocation institutions on value

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WATER RESOURCES RESEARCH 2017年第1期53卷 672-687页

作者： Maas, Alexander Dozier, Andre Manning, Dale T. Goemans, Christopher Colorado State Univ Dept Agr & Resource Econ Ft Collins CO 80523 USA Colorado State Univ Dept Civil Engn Ft Collins CO 80523 USA

As populations increase in arid regions of the world, investment in water infrastructure improves resource management by increasing control over the location and timing of water allocation. Many studies have explored freer trade as a substitute for additional infrastructure investment. We instead quantify how water allocation institutions, reservoir management objectives, and storage capacity influence the value derived from a reservoir system. We develop a stochastic dynamic programming model of a reservoir system that faces within-year variation in weather-dependent water demand as well as stochastic semiannual inflows. We parameterize the model using the Colorado-Big Thompson system, which transports stored water from the West Slope of the Rocky Mountains to the East Slope. We then evaluate the performance of the system under five institutional settings. Our results suggest that rigid allocation mechanisms and inefficient management objectives result in a decrease of up to 13% in the value generated from stored water when compared to a free trade scenario, an impact on par with predicted losses associated with climate-change-induced inflow reductions. We also find that under biased management objectives, increasing storage capacity can decrease the social value obtained from stored water.

关键词： stochastic dynamic programming water infrastructure water management

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Methodology for forecasting in the Swedish-Norwegian market for el-certificates

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ENERGY 2015年 88卷 322-333页

作者： Wolfgang, Ove Jaehnert, Stefan Mo, Birger SINTEF Energy Res NO-7034 Trondheim Norway

In this paper we describe a novel methodology for forecasting in the Swedish Norwegian el-certificate market, which is a variant of a tradable green certificate scheme. For the forecasting, the el-certificate market is integrated in the electricity-market model EMPS, which has weekly to hourly time-step length, whereas the planning horizon can be several years. Strategies for the certificate inventory are calculated by stochastic dynamic programming, whereas penalty-rates for non-compliance during the annual settlement of certificates are determined endogenously. In the paper the methodology is described, and we show the performance of the model under different cases that can occur in the el-certificate market. The general results correspond to theoretical findings in previous studies for tradable green certificate markets, in particular that price-scenarios spread out in such a way that the unconditional expected value of certificates is relatively stable throughout the planning period. In addition the presented methodologies allows to assess the actual dynamics of the certificate price due to climatic uncertainty. Finally, special cases are indentified where the certificate price 'becomes excessively high respectively zero, due the design-specific dynamics of the penalty rate. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： El-certificates TGC Electricity Forecasting RES-E stochastic dynamic programming

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Managing Volunteers and Paid Workers in a Nonprofit Operation

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MANAGEMENT SCIENCE 2024年第8期70卷 5298-5316页

作者： Berenguer, Gemma Haskell, William B. Li, Lei Univ Carlos III Madrid Dept Business Adm Getafe 28903 Madrid Spain Purdue Univ Mitchell E Daniels Jr Sch Business W Lafayette IN 47907 USA Hong Kong Polytech Univ Fac Business Logist & Maritime Studies Hung Hom Hong Kong Peoples R China

Some nonprofit organizations (NPOs) manage a complex workforce composed of a mix of volunteers, part-time workers, and full-time workers. We study the NPO's finite-horizon staffing problem to determine the optimal initial staff planning decisions and per period optimal hiring and assignment decisions given a budget, capacity constraints, and an uncertain supply of volunteers and part-time workers. Our main goal is to solve this problem in a way that is effective and easy to implement while obtaining interesting managerial insights. To this end, we first demonstrate that the optimal staffing policies are computationally challenging to identify in general. However, we demonstrate that a prioritization assignment policy and a hire-up-to policy for part-time workers can be conveniently applied and are close to optimal. These policies are, in fact, optimal under staff scarcity and staff sufficiency. In our numerical analysis, we study the value and impact of the general optimal solution that considers flexibility and turnover of part-time workers versus the prioritization assignment policy and a constant hire-up-to policy that omit flexibility and turnover behaviors. We further suggest two easy-to-implement heuristics and theoretically analyze them and run a numerical performance study. We observe that both heuristics have low relative optimality gaps. Finally, we extend our analysis by studying how the optimal policy varies under three different practical considerations: a concave social value objective, nonzero volunteer costs, and dynamic volunteer behaviors.

关键词： volunteers staffing problem nonprofit operations management stochastic dynamic programming

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Can culling a threatened species increase its chance of persisting?

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ECOLOGICAL MODELLING 2007年第1期201卷 11-18页

作者： Bode, Michael Possingham, Hugh P. Univ Queensland Ctr Ecol St Lucia Qld 4072 Australia

Many interacting predator-prey populations have a natural tendency to exhibit persistent limit-cycles or damped oscillations, especially in the presence of environmental stochasticity. The restriction of populations into small conservation reserves reduces the scale of ecosystems, and can induce cycling in previously stable predator-prey relationships. During the course of these cycles, the abundance of both predator and prey regularly decrease to low levels. At these times, environmental and demographic stochasticity may cause the extinction of one of the populations. Could culling one or both species at critical times reduce their probability of extinction? we use stochastic dynamic programming to determine the optimal management strategy for oscillation-prone species pairs. Remarkably, if the interventions are enacted at the appropriate time, infrequent culling of a small number of individuals significantly reduces the probability of extinction of the predator. Our approach can be applied to many different ecosystems, and can incorporate more complex system dynamics without a significant increase in computational time. (c) 2006 Elsevier B.V. All rights reserved.

关键词： predator-prey relationships stochastic dynamic programming culling optimal control

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Optimal production planning in a multi-product stochastic manufacturing system with long-run average cost

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DISCRETE EVENT dynamic SYSTEMS-THEORY AND APPLICATIONS 1998年第1期8卷 37-54页

作者： Sethi, SP Suo, W Taksar, MI Yan, H Univ Texas Dallas Sch Management Richardson TX USA Univ Toronto Fac Management Toronto ON Canada SUNY Stony Brook Dept Appl Math Stony Brook NY 11794 USA Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong

This paper is concerned with the problem of production planning in a flexible manufacturing system consisting of a single or parallel failure-prone machines producing a number of different products. The objective is to choose the rates of production of the various products over time in order to meet their demands at the minimum long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellman equation in terms of directional derivatives has a solution consisting of the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem, and in specifying an optimal control policy in terms of the potential function. The results settle a hitherto open problem as well as generalize known results.

关键词： production planning stochastic dynamic programming vanishing discount approach optimal control long-run average cost

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Spinning plates and squad systems: Policies for bi-directional restless bandits

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ADVANCES IN APPLIED PROBABILITY 2006年第1期38卷 95-115页

作者： Glazebrook, KD Kirkbride, C Ruiz-Hernandez, D Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England Univ Lancaster Dept Management Sci Lancaster LA1 4YF England Univ Pompeu Fabra Dept Econ & Business E-08005 Barcelona Spain

This paper concerns two families of Markov decision problem that fall within the family of (bi-directional) restless bandits, an intractable class of decision processes introduced by Whittle. The spinning plates problem concerns the optimal management of a portfolio of reward-generating assets whose yields grow with investment but otherwise tend to decline. In the model of asset exploitation called the squad system, the yield from an asset tends to decline when it is used but will recover when the asset is at rest. In all cases, simply stated conditions are given that guarantee indexability of the problem, together with conditions necessary and sufficient for its strict indexability. The index heuristics for asset activation that emerge from the analysis are assessed numerically and found to perform very strongly.

关键词： index policy Lagrangian method Markov decision problem restless bandit stochastic dynamic programming

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Redesign policy for a system with uncertain failure rates

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OPERATIONS RESEARCH LETTERS 2024年 54卷

作者： Ge, Qianru Atan, Zuembuel van Jaarsveld, Willem Dongbei Univ Finance & Econ Sch Management Sci & Engn Dalian Peoples R China Eindhoven Univ Technol Dept Ind Engn & Innovat Sci Eindhoven Netherlands

Consider a newly developed system sold under a performance based contract (PBC), and subject to failures following various failure modes. Redesign may address certain failure modes. To trade-off redesign costs and costs associated with the PBC, we find the optimal failure modes to redesign based on the current beliefs on the failure rate per failure mode, and the amount of time remaining under the PBC. We develop analytic insights into the structure of the optimal policy. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

关键词： Multiple failure modes Redesign policy stochastic dynamic programming Bayesian inference

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