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A Multi-Quantile Approach for Open-Loop stochastic dynamic programming Problems *

IFAC Proceedings Volumes 2009年第2期42卷 52-57页

作者： Rodrigo T.N. Cardoso Ricardo H.C. Takahashi Frederico R.B. Cruz Carlos M. Fonseca Department of Physics and Mathematics Centro Federal de Educação Tecnológica de Minas Gerais MG Brazil Department of Mathematics Universidade Federal de Minas Gerais Department of Statistics Universidade Federal de Minas Gerais Faculty of Science and Technology Universidade do Algarve Portugal CEG-IST Instituto Superior Técnico Universidade Técnica de Lisboa Portugal

This paper proposes a multi-quantile approach for solving open-loop continuous-variable discrete-time stochastic dynamic programming problems in systems with non-standard probability distribution functions. Instead of using the expected value of the objective function for building the optimization criterion, the decision maker performs a choice on the decision variables over the objective function value quantiles. The proposed procedure relies on a Monte Carlo simulation of the unknown process input outcomes, associated with an open-loop multiobjective optimization. The optimal control comes from a trade-off analysis that considers, for instance, the risk associated with each policy versus its yield.

关键词： stochastic dynamic programming Multiobjective Optimization Model Predictive Control

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stochastic optimal control of manufacturing systems under production-dependent failure rates

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2014年 150卷 174-187页

作者： Francie, Kouedeu Annie Jean-Pierre, Kenne Pierre, Dejax Victor, Songmene Vladimir, Polotski Univ Quebec Ecole Technol Super Lab Integrated Prod Technol Dept Mech Engn Montreal PQ H3C 1K3 Canada Ecole Mines Nantes LUNAM F-44307 Nantes 3 France

A production system consisting of two parallel machines with production-dependent failure rates is investigated in this paper. The machines produce one type of final product and unmet demand is backlogged. The objective of the system is to find a productivity policy for both machines that will minimize the inventory and shortage costs over an infinite horizon. The failure rate of the main machine depends on its productivity, while the failure rate of the second machine is constant. In the proposed model, the main machine is characterized by a higher productivity. This paper proposes a stochastic dynamic programming formulation of the problem and derives the optimal policies numerically. A numerical example is included and sensitivity analyses with respect to the system parameters are examined to illustrate the importance and effectiveness of the proposed methodology. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Production planning stochastic dynamic programming Numerical methods

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On the optimal control of manufacturing and remanufacturing activities with a single shared server

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第1期234卷 86-98页

作者： Flapper, Simme Douwe Gayon, Jean-Philippe Lim, Lam Laurent Grenoble INP UJF Grenoble 1 CNRS G SCOP UMR5272 F-38031 Grenoble France Tech Univ Eindhoven NL-5600 MB Eindhoven Netherlands

We consider a single-product make-to-stock manufacturing-remanufacturing system. Returned products require remanufacturing before they can be sold. The manufacturing and remanufacturing operations are executed by the same single server, where switching from one activity to another does not involve time or cost and can be done at an arbitrary moment in time. Customer demand can be fulfilled by either newly manufactured or remanufactured products. The times for manufacturing and remanufacturing a product are exponentially distributed. Demand and used products arrive via mutually independent Poisson processes. Disposal of products is not allowed and all used products that are returned have to be accepted. Using Markov decision processes, we investigate the optimal manufacture-remanufacture policy that minimizes holding, backorder, manufacturing and remanufacturing costs per unit of time over an infinite horizon. For a subset of system parameter values we are able to completely characterize the optimal continuous-review dynamic preemptive policy. We provide an efficient algorithm based on quasi-birth-death processes to compute the optimal policy parameter values. For other sets of system parameter values, we present some structural properties and insights related to the optimal policy and the performance of some simple threshold policies. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Manufacturing Remanufacturing Shared server Inventory control stochastic dynamic programming

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A decision support system for mean-variance analysis in multi-period inventory control

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DECISION SUPPORT SYSTEMS 2014年第0期57卷 285-295页

作者： Basu, Preetam Nair, Suresh K. Indian Inst Management Calcutta Operat Management Grp Kolkata 700104 India Univ Connecticut Sch Business Operat & Informat Management Dept Storrs CT 06269 USA

Traditionally inventory management models have focused on risk-neutral decision making with the objective of maximizing the expected rewards or minimizing costs over a specified time horizon. However, for items marked by high demand volatility such as fashion goods and technology products, this objective needs to be balanced against the risk associated with the decision. Depending on how the product performs vis-a-vis the seller's original forecast, the seller could end up with losses due to either short or surplus supply. Unfortunately, traditional models do not address this issue. stochastic dynamic programming models have been extensively used for sequential derision making in the context of multi-period inventory management, but in the traditional way where one either minimizes costs or maximizes profits. Risk is implicitly considered by accounting for stock-out costs. Considering risk and reward simultaneously and explicitly in a stochastic dynamic setting is a cumbersome task and often difficult to implement for practical purposes, since dynamic programming is designed to optimize on one variable, not two. In this paper we develop an algorithm, Variance-Retentive stochastic dynamic programming that tracks variance as well as expected reward in a stochastic dynamic programming model for inventory control. We use the mean-variance solutions in a heuristic. RiskTrackr, to construct efficient frontiers which could be an ideal derision support tool for risk-reward analysis. (C) 2013 Elsevier B.V. All rights reserved.

关键词： stochastic dynamic programming Risk-reward heuristic Mean-variance analysis Efficient frontier analysis Inventory management

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Generation Expansion Planning Considering Mass Penetration of Renewable Energy Generation and Supply Reliability

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ELECTRICAL ENGINEERING IN JAPAN 2014年第3期189卷 1-12页

作者： Manabe, Yusuke Hara, Ryoichi Kita, Hiroyuki Hokkaido Univ Sapporo Hokkaido 060 Japan Hokkaido Univ Grad Sch Informat Sci & Technol Sapporo Hokkaido 060 Japan Hokkaido Univ Grad Sch Engn Sapporo Hokkaido 060 Japan

In the future, renewable energy (RE) generation systems will be constructed and interconnected to the power system by nonutility entities such as generation companies and residential customers. Therefore, generation expansion planning (GEP) should consider the effects of RE generation. The purpose of this paper is to discuss the best GEP from the economic, supply reliability, and environmental aspects considering the penetration of RE generation. For this purpose, this paper proposes a model of a utility's GEP process considering RE generation. The proposed method is based on stochastic dynamic programming (SDP) in which long-term uncertainties are modeled by geometric Brownian motion (GBM) and the binomial lattice process. The variation of RE generation output due to the weather conditions (short-term uncertainty) is also considered in the proposed method by means of the net load curve.

关键词： generation expansion planning renewable energy reliability assessment uncertainty stochastic dynamic programming

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Active Classification for POMDPs: A Kalman-Like State Estimator

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2014年第23期62卷 6209-6224页

作者： Zois, Daphney-Stavroula Levorato, Marco Mitra, Urbashi Univ So Calif Dept Elect Engn Los Angeles CA 90089 USA Univ Calif Irvine Donald Bren Sch Informat & Comp Sci Dept Comp Sci Irvine CA 92697 USA

The problem of state tracking with active observation control is considered for a system modeled by a discrete-time, finite-state Markov chain observed through conditionally Gaussian measurement vectors. The measurement model statistics are shaped by the underlying state and an exogenous control input, which influence the observations' quality. Exploiting an innovations approach, an approximate minimum mean-squared error (MMSE) filter is derived to estimate the Markov chain system state. To optimize the control strategy, the associated mean-squared error is used as an optimization criterion in a partially observable Markov decision process formulation. A stochastic dynamic programming algorithm is proposed to solve for the optimal solution. To enhance the quality of system state estimates, approximate MMSE smoothing estimators are also derived. Finally, the performance of the proposed framework is illustrated on the problem of physical activity detection in wireless body sensing networks. The power of the proposed framework lies within its ability to accommodate a broad spectrum of active classification applications, including sensor management for object classification and tracking, estimation of sparse signals, and radar scheduling.

关键词： Active classification controlled sensing active state tracking partially observable Markov decision processes (POMDP) nonlinear POMDPs Kalman-like filter Kalman-like smoothers innovations approach approximate MMSE estimation stochastic dynamic programming discrete state Markov chains Martingale difference sequence body sensing network application

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Optimal charging of an electric vehicle using a Markov decision process

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APPLIED ENERGY 2014年 123卷 1-12页

作者： Iversen, Emil B. Morales, Juan M. Madsen, Henrik Tech Univ Denmark DTU Compute DK-2800 Lyngby Denmark

The combination of electric vehicles and renewable energy is taking shape as a potential driver for a future free of fossil fuels. However, the efficient management of the electric vehicle fleet is not exempt from challenges. It calls for the involvement of all actors directly or indirectly related to the energy and transportation sectors, ranging from governments, automakers and transmission system operators, to the ultimate beneficiary of the change: the end-user. An electric vehicle is primarily to be used to satisfy driving needs, and accordingly charging policies must be designed primarily for this purpose. The charging models presented in the technical literature, however, overlook the stochastic nature of driving patterns. Here we introduce an efficient stochastic dynamic programming model to optimally charge an electric vehicle while accounting for the uncertainty inherent to its use. With this aim in mind, driving patterns are described by an inhomogeneous Markov model that is fitted using data collected from the utilization of an electric vehicle. We show that the randomness intrinsic to driving needs has a substantial impact on the charging strategy to be implemented. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Electric vehicles Driving patterns Optimal charging Markov processes stochastic dynamic programming

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Coordination of manufacturing, remanufacturing and returns acceptance in hybrid manufacturing/remanufacturing systems

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2014年 148卷 62-70页

作者： Vercraene, Samuel Gayon, Jean-Philippe Flapper, Simme Douwe Inst Natl Sci Appl DISP F-69621 Villeurbanne France Grenoble INP UJF Grenoble 1 CNRS G SCOP UMR5272 F-38031 Grenoble France Tech Univ Eindhoven NL-5600 MB Eindhoven Netherlands

This paper deals with the coordination of manufacturing, remanufacturing and returns acceptance control in a hybrid production-inventory system. We use a queuing control framework, where manufacturing and remanufacturing are modelled by single servers with exponentially distributed processing times. Customer demand and returned products arrive in the system according to independent Poisson processes. A returned product can be either accepted or rejected. When accepted, a return is placed in a remanufacturable product inventory. Customer demand can be satisfied as well by new and remanufactured products. The following costs are included: stock keeping, backorder, manufacturing, remanufacturing, acceptance and rejection costs. We show that the optimal policy is characterized by two state-dependent base-stock thresholds for manufacturing and remanufacturing and one state-dependent return acceptance threshold. We also derive monotonicity results for these thresholds. Based on these theoretical results, we introduce several relevant heuristic control rules for manufacturing, remanufacturing and returns acceptance. In an extensive numerical study we compare these policies with the optimal policy and provide several insights. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Remanufacturing Manufacturing Returns acceptance control Inventory control stochastic dynamic programming Optimal policy Heuristic policies

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Maximizing a new quantity in sequential reserve selection

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ENVIRONMENTAL CONSERVATION 2014年第2期41卷 198-205页

作者： Schapaugh, Adam W. Tyre, Andrew J. Univ Nebraska Sch Nat Resources Lincoln NE 68510 USA

The fundamental goal of conservation planning is biodiversity persistence, yet most reserve selection methods prioritize sites using occurrence data. Numerous empirical studies support the notion that defining and measuring objectives in terms of species richness (where the value of a site is equal to the number of species it contains, or contributes to an existing reserve network) can be inadequate for maintaining biodiversity in the long-term. An existing site-assessment framework that implicitly maximized the persistence probability of multiple species was integrated with a dynamic optimization model. The problem of sequential reserve selection as a Markov decision process was combined with stochastic dynamic programming to find the optimal solution. The approach represents a compromise between representation-based approaches (maximizing occurrences) and more complex tools, like spatially-explicit population models. The method, the inherent problems and interesting conclusions are illustrated with a land acquisition case study on the central Platte River.

关键词： reserve selection Bayesian network Markov decision process stochastic dynamic programming reserve adequacy

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FULLY POLYNOMIAL TIME APPROXIMATION SCHEMES FOR stochastic dynamic PROGRAMS

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2014年第4期28卷 1725-1796页

作者： Halman, Nir Klabjan, Diego Li, Chung-Lun Orlin, James Simchi-Levi, David Hebrew Univ Jerusalem Jerusalem Israel MIT Cambridge MA 02139 USA Northwestern Univ Evanston IL 60208 USA Hong Kong Polytech Univ Hong Kong Hong Kong Peoples R China

We present a framework for obtaining fully polynomial time approximation schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely, the calculus of K-approximation functions and the calculus of K-approximation sets. Using our framework, we provide the first FPTASs for several NP-hard problems in various fields of research such as knapsack models, logistics, operations management, economics, and mathematical finance. Extensions of our framework via the use of the newly established computational rules are also discussed.

关键词： fully polynomial time approximation schemes stochastic dynamic programming K-approximation

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