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Asymptotically optimal production policies in dynamic stochastic jobshops with limited buffers

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2006年第2期317卷 398-428页

作者： Hou, YM Sethi, SP Zhang, HQ Zhang, Q Univ Texas Sch Management Richardson TX 75083 USA Acad Sinica Acad Math & Syst Sci Beijing 100080 Peoples R China Univ Georgia Dept Math Athens GA 30602 USA

We consider a production planning problem for a jobshop with unreliable machines producing a number of products. There are upper and lower bounds on intermediate parts and an upper bound on finished parts. The machine capacities are modelled as finite state Markov chains. The objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production. Finding an optimal control policy for this problem is difficult. Instead, we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity. The asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities. The value function for the original problem is shown to converge to the value function of the limiting problem. The convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established. (C) 2006 Elsevier Inc. All rights reserved.

关键词： optimal production policy stochastic manufacturing systems stochastic dynamic programming discounted cost asymptotic analysis

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Rate control for low delay H.264/AVC transmission over channels with burst error

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IMACS Multiconference on Computational Engineering in Systems Applications (CESA 2006)

作者： Wang, Wensheng Lu, Yang Cui, Huijuan Tang, Kun Tsinghua Univ Dept Elect Engn State Key Lab Microwave & Digital Commun Beijing 100084 Peoples R China

ISBN: (纸本)9787302139225

A rate control approach is proposed to deal with the low delay H.264/AVC video transmission over channels with burst errors by applying stochastic optimization technique. Based on the exponential rate-distortion and the linear variance prediction model, the one pass rate control algorithm will take into account the channel state and round trip delay, and make an immediate decision on the optimal rate allocation for the video frame. Simulation results show that for different end to end delay constraints and round trip delay, the number of lost frames is significantly reduced, and the average reconstruction peek sinal to noise ratio is improved by 0.5 similar to 1.6dB, compared with the reference rate control scheme [ARA, 01].

关键词： rate control stochastic dynamic programming burst error H.264/AVC

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Farsighted sensor management for feature-aided tracking

Farsighted sensor management for feature-aided tracking

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Conference on Signal Processing, Sensor Fusion, and Target Recognition XV

作者： Nedich, Angelia Schneider, Michael K. Shen, Xinzhuo Lea, Djuana BAE Syst 6 New England Execut Pk Burlington MA 01803 USA US Air Force Res Lab Wright Patterson AFB OH 45433 USA

ISBN: (纸本)0819462918

We consider the sensor management problem arising in air-to-ground tracking of moving targets. The sensing-tracking system includes a radar and a feature-aided tracker. The radar collects target-signature data in high-resolution-radar (HRR) mode. The tracker is using the collected HRR-signature data to create and maintain target-track identification information. More specifically, the tracker is learning target-track profiles from the collected signature data, and is using these profiles to resolve the potential report-to-track or track-to-track association ambiguities. In this paper, we focus on the management of the HRR-signature data collection. Specifically, the sensor management problem is to determine where to collect signature data on targets in time so as to optimize the utility of the collected data. As with other sensor management problems, determining the optimal data collection is a hard combinatorial problem due to many factors including the large number of possible sensor actions and the complexity of the dynamics. The complexity of the dynamics stems in part from the presence of the sensor slew time. A distinguishing feature of the sensor management problem considered here is that the HRR-signature data collected during the learning phase has no immediate value. To optimize the data collections, a sensor manager must look sufficiently far into the future to adequately trade-off alternative plans. Here, we propose some farsighted algorithms, and evaluate them against a sequential scanning and a greedy algorithm. We present our simulation results obtained by applying these algorithms to a problem of managing a single sensor providing HRR-signature data.

关键词： feature-aided tracking HRR-signature data collection sensor management stochastic dynamic programming farsighted strategy

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Optimal exploitation of renewable resources under uncertainty and the extinction of species

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ECONOMIC THEORY 2006年第1期28卷 1-23页

作者： Mitra, T Roy, S Cornell Univ Dept Econ Ithaca NY 14853 USA So Methodist Univ Dept Econ Dallas TX 75275 USA

We consider an optimally managed renewable resource with stochastic non-concave growth function. We characterize the conditions under which the optimal policy leads to global extinction, global conservation and the existence of a safe standard of conservation. Our conditions are specified in terms of the economic and ecological primitives of the model: the biological growth function, the welfare function, the distribution of shocks and the discount rate. Our results indicate that, unlike deterministic models, extinction and conservation in stochastic models are not determined by a simple comparison of the growth rate and the discount rate;the welfare function plays an important role.

关键词： renewable resources extinction biological species safe standard of conservation optimal resource management stochastic dynamic programming

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The stochastic lake game: A numerical solution

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JOURNAL OF ECONOMIC dynamicS & CONTROL 2006年第9-10期30卷 1569-1587页

作者： Dechert, W. D. O'Donnell, S. I. Baylor Coll Med Childrens Nutr Res Ctr Houston TX 77030 USA Univ Wisconsin Madison WI 53706 USA

In this paper, we numerically solve a stochastic dynamic programming problem for the solution of a stochastic dynamic game for which there is a potential function. The players select a mean level of control. The state transition dynamics is a function of the current state of. the system and a multiplicative noise factor on the control variables of the players. The particular application is for lake water usage. The control variables are the levels of phosphorus discharged (typically by farmers) into the watershed of the lake, and the random shock is the rainfall that washes the phosphorus into the lake. The state of the system is the accumulated level of phosphorus in the lake. The system dynamics are sufficiently nonlinear so that there can be two Nash equilibria. A Skiba-like point can be present in the optimal control solution. We analyze (numerically) how the dynamics and the Skiba-like point change as the variance of the noise (the rain) increases. The numerical analysis uses a result of Dechert (1978. Optimal control problems from second order difference equations. Journal of Economic Theory 19, 50-63) to construct a potential function for the dynamic game. This greatly reduces the computational burden in finding Nash equilibria solutions for the dynamic game. (c) 2006 Elsevier B.V. All rights reserved.

关键词： stochastic optimal control Markov processes stochastic dynamic programming lake water pollution dynamic games with a potential function

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The Jointed Decision Model on a Newsboy-type Ordering and Pricing for Retailer

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Journal of Systems Science and Information 2006年第3期4卷 467-475页

作者： Bin Liu Hui Zhang Sifeng Liu College of Information and Management Science Henan Agricultural UniversityZhengzhou 450002 China College of Economics and Management Nanfing University of Aeronautics andAstronautics Nanjing 210016 China

This paper deals with the jointed decision question on ordering and pricing for a short-life-cycle product under stochastic multiplicative demand depended selling price. According to the marketing practices, which retailers sell their products in different periods with the different marketing policies, we depict the jointed decision question with a stochastic dynamic programming model from the view of the centralized system. Then, we prove that the expected profit function are concave on decision vectors respectively, and develop the decision method for ordering and pricing. Lastly, we design the iterative search arithmetic to find the optimal decision vectors.

关键词： newsboy model jointed decision stochastic dynamic programming iterative search arithmetic multiplicative demand

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Reservoir operation using grey fuzzy stochastic dynamic programming

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HYDROLOGICAL PROCESSES 2002年第12期16卷 2395-2408页

作者： Chang, FJ Hui, SC Chen, YC Natl Taiwan Univ Dept Bioenvironm Syst Engn Taipei Taiwan

This paper presents an optimal regulation programme, grey fuzzy stochastic dynamic programming (GFSDP), for reservoir operation. It is composed of a grey system, fuzzy theory and dynamic programming. The grey system represents data by covering the whole range without loss of generality, and the fuzzy arithmetic takes charge of the rules of reservoir operation. The GFSDP deals with the multipurpose decision-making problem by fuzzy optimization theorem. The practicability and effectiveness of the proposed approach is tested on the operation of the Shiman reservoir in Taiwan. The current M5 operating rule curves of this reservoir also are evaluated. The simulation results demonstrate that this new approach, in comparison with the M5 rule curves, has superior performance with regard to the total water deficit and number of monthly deficits. Copyright (C) 2002 John Wiley Sons, Ltd.

关键词： fuzzy arithmetic grey system reservoir operation stochastic dynamic programming

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Optimum constrained portfolio rules in a diffusion market

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Applied Mathematical Finance 2006年第4期13卷 285-307页

作者： Durrell, Fernando J. Department of Mathematics and Applied Mathematics University of Cape Town South Africa Department of Mathematics and Applied Mathematics University of Cape Town Rondebosch 7700 Cape Town South Africa

A portfolio selection model is derived for diffusions where inequality constraints are imposed on portfolio security weights. Using the method of stochastic dynamic programming Hamilton-Jacobi-Bellman (HJB) equations are obtained for the problem of maximizing the expected utility of terminal wealth over a finite time horizon. Optimal portfolio weights are given in feedback form in terms of the solution of the HJB equations and its partial derivatives. An analysis of the no-constraining (NC) region of a portfolio is also conducted. © 2006 Taylor & Francis.

关键词： Constraints Hamilton-Jacobi-Bellman equation stochastic dynamic programming Utility

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The costate variable in a stochastic renewable resource model

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Natural Resource Modeling 2006年第1期19卷 45-66页

作者： Lyon, Kenneth S. Pande, Saket Economics Department Utah State University Logan UT 84322-3530 3530 Old Main Hill United States Center for World Food Studies (SOW-VU) Vrije Universiteit Amsterdam Netherlands

In this paper we discuss the costate variable in a stochastic optimal control model of a renewable natural resource, which we call a fishery. The role of the costate variable in deterministic control models has been discussed extensively in the literature. See for example Lyon [1999], Clark [1990, pp. 102 107] and Arrow and Kurz [1970, pp. 35 37];however, there is little discussion of this variable for stochastic models, even though thecostate variable has similar roles in the two models. In both models the costate variableis a shadow value of the associated state variable, and as such has the role of rationingthe use of the state variable. In addition, as has been shown in Lyon [1999], in natural resource problems the costate variable can be partitioned into a scarcity effect and a cost effect. We show that this same partitioning can be done in the stochastic renewable resource problem. We discuss and contrast the similarities and differences in these concepts for deterministic and stochastic models. In addition, we present a numerical example to help solidify the results. © 2006 Rocky Mountain Mathematics Consortium.

关键词： Costate variable Deterministic dynamic programming Renewable resource model Simulation stochastic dynamic programming

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Linking genetic algorithms with stochastic dynamic programming to the long-term operation of a multireservoir system

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WATER RESOURCES RESEARCH 2002年第12期38卷 40-1-40-9页

作者： Huang, WC Yuan, LC Lee, CM Natl Taiwan Ocean Univ Dept Harbor & River Engn Chilung 202 Taiwan

[1] The objective of this paper is to present a genetic algorithm-based stochastic dynamic programming (GA-based SDP) to cope with the dimensionality problem of a multiple-reservoir system. The joint long-term operation of a parallel reservoir system in the Feitsui and Shihmen reservoirs in northern Taiwan demonstrates the successful application of the proposed GA-based SDP model. Within the case study system it is believed that GA is a useful technique in supporting optimization. Though the employment of GA-based SDP may be time consuming as it proceeds through generation by generation, the model can overcome the "dimensionality curse'' in searching solutions. Simulation results show Feitsui's surplus water can be utilized efficiently to fill Shihmen's deficit water without affecting Feitsui's main purpose as Taipei city's water supply. The optimal joint operation suggests that Feitsui, on average, can provide 650,000 m(3)/day and 920,000 m(3)/day to Shihmen during the wet season and dry season, respectively.

关键词： genetic algorithms stochastic dynamic programming multireservoir system dimensionality water supply

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