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Accounting for parametric uncertainty in Markov decision processes

ECOLOGICAL MODELLING 2013年 254卷 15-21页

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

Markov decision processes have become the standard tool for modeling sequential decision-making problems in conservation. In many real-world applications, however, it is practically infeasible to accurately parameterize the state transition function. In this study, we introduce a new way of dealing with ambiguity in the state transition function. In contrast to existing methods, we explore the effects of uncertainty at the level of the policy, rather than at the level of decisions within states. We use information-gap decision theory to ask the question of how much uncertainty in the state transition function can be tolerated while still delivering a specified expected value given by the objective function. Accordingly, the goal of the optimization problem is no longer to maximize expected value, but to maximize local robustness to uncertainty (while still meeting the desired level of performance). We analyze a simple land acquisition problem, using info-gap decision theory to propagate uncertainties and rank alternative policies. Rather than requiring information about the extent of parameter uncertainty at the outset, info-gap addresses the question of how much uncertainty is permissible in the state transition function before the optimal policy would change. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Information-gap Markov decision process Reserve selection stochastic dynamic programming Uncertainty

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Fluctuating quota and management costs under multiannual adjustment of fish quota

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ECOLOGICAL MODELLING 2013年第1期265卷 230-238页

作者： van Dijk, Diana Haijema, Rene Hendrix, Eligius M. T. Groeneveld, Rolf A. van Ierland, Ekko C. Wageningen Univ Environm Econ & Nat Resources Grp NL-6706 KN Wageningen Netherlands Wageningen Univ NL-6706 KN Wageningen Netherlands Univ Malaga ETSI Informat Dept Comp Architecture E-29071 Malaga Spain

North Sea fisheries are managed by the European Union (EU) through a system of annual quota. Due to uncertainty about future fish stocks, yearly revisions of these policies lead to fluctuation in quota, which in turn affects harvest and investment decisions of fishermen. Determination of quota requires high management costs in terms of obtaining information and negotiations between experts and policy makers. To reduce both quota fluctuation and management costs, the EU has proposed a system of multiannual quota. In this paper we study the effect of multiannual quota on quota volatility and resource rents, while accounting for management costs. We develop a bi-level stochastic dynamic programming model, where at level one, the EU determines the quota that maximizes resource rents. At level two, fishermen decide myopically on their harvest and investment levels, subject to the quota. Results show that policy makers can reduce quota volatility and improve resource rents from the fishery with multiannual quota. Important trade-offs are involved in the accomplishment of these objectives: fish stock and investments become more volatile, which leads to more overcapacity. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Fisheries management Multiannual quota Management costs stochastic dynamic programming

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The economic value of coordination in large-scale multireservoir systems: The Parana River case

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WATER RESOURCES RESEARCH 2013年第11期49卷 7546-7557页

作者： Marques, Guilherme Fernandes Tilmant, A. Ctr Fed Educ Tecnol Minas Gerais Dept Civil Engn BR-30510000 Belo Horizonte MG Brazil Univ Laval Dept Civil & Water Engn Quebec City PQ Canada

The coordination of reservoir operation is critical for water systems' efficiency. Improved coordination requires sharing information, demanding a clear understanding of the potential gains and its distribution among the users to motivate engagement in coordinated operations and bearing of transaction costs. In a multiuser, multireservoir system, the evaluation of the potential coordination gains is not trivial because it requires the simultaneous evaluation of numerous trade offs. This paper presents a methodology to identify the likely upper and lower bounds in multireservoir system benefits, providing a reference framework for analyzing the economic value of coordination. The methodology is applied to a large-scale multireservoir system in Brazil. The methods rely on the comparison between two management scenarios. The first one mimics typical system operation based on individually designed rule curves, which are likely to perform on the lower bound. This is compared with fullscale system-wide optimization through an stochastic Dual dynamic programming algorithm to represent fully coordinated reservoir operation (upper bound). For our case study, results indicate that better coordination reduced spills and improved releases timing according to reservoirs characteristics and location, allowing overall gains between 3% and 8% in energy and 7.9% in revenues, with revenues mostly improved by coordination in dry years. Larger reservoirs presented the highest gains in absolute terms, while the smaller ones presented the highest relative increases. By indicating individual gains at each reservoir, valuable information is produced to support future negotiations and benefit sharing among different agents, being water agencies or power companies.

关键词： reservoir operation hydropower optimization stochastic dynamic programming water systems coordination stochastic dual dynamic programming

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Optimal production control policy in unreliable batch processing manufacturing systems with transportation delay

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2013年第1期51卷 264-280页

作者： Bouslah, B. Gharbi, A. Pellerin, R. Hajji, A. Univ Quebec Ecole Technol Super Automated Prod Engn Dept Quebec City PQ Canada Ecole Polytech Dept Math & Ind Engn Montreal PQ H3C 3A7 Canada Univ Laval Dept Operat & Decis Syst Quebec City PQ Canada

This paper considers the problem of production planning of unreliable batch processing manufacturing systems. The finished goods are produced in lots, and are then transported to a storage area in order to continuously meet a constant demand rate. The main objective of this work is to jointly determine the optimal lot sizing and optimal production control policy that minimise the total expected cost of inventory/backlog and transportation, over an infinite time horizon. The decision variables are the lot sizing and the production rate. The problem is formulated with a stochastic dynamic programming model and the impulse control theory is applied to establish the Hamilton-Jacobi-Bellman (HJB) equations. Based on a numerical resolution of the HJB equations, it is shown that the optimal control policy is governed by a base stock policy for production rate control and economic lot size for batch processing. A thorough analysis and practical issues are addressed with a simulation-based approach. Thus, a combined discrete-continuous simulation model is developed to determine the optimal parameters of the proposed policy when the failure and repair times follow general distributions. The results are illustrated with numerical examples and confirmed through sensitivity analysis.

关键词： unreliable manufacturing systems economic production quantity feedback production planning stochastic dynamic programming simulation

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Evaluation of optimization operation models for cascaded hydropower reservoirs to utilize medium range forecasting inflow

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Science China(Technological Sciences) 2013年第10期56卷 2540-2552页

作者： XU Wei PENG Yong WANG BenDe School of Hydraulic Engineering Dalian University of Technology

This paper evaluates the performances of the models that incorporate forecasting inflow for cascaded hydropower reservoirs operation. These models are constructed separately on the concepts of explicit stochastic optimization （ESO） and implicit sto- chastic optimization （ISO） as well as parametefization-simulation-optimization （PSO）. Firstly, the aggregation-disaggregation method is implemented in ESO models to reduce the complexity of stochastic dynamic programming （SDP）. And the aggre- gate flow SDP （AF-SDP） and aggregation-disaggregation SDP （AD-SDP） are constructed respectively. Secondly, in ISO mod- el, decision tree is the well-known and widespread algorithm. The algorithm C 5.0 is selected to extract the if-then-else rules for reservoir operation. Thirdly, based on the PSO model, the hedging rule curves （HRCs） are pre-defined by fusing the storage and inflow as state variable. The parameters of the HRCs are determined by using the simulation-optimization model. Finally, China＇s Hun River cascade hydropower reservoirs system is taken as an example to illustrate the efficiency and reliability of the models. In addition, the values of quantitative precipitation forecasts of the global forecast system （10 days lead-time） are implemented to forecast the 10 days inflow.

关键词： cascaded hydropower reservoirs forecasting inflow stochastic dynamic programming decision tree hedging rule

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On the value and price-responsiveness of ramp-constrained storage

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ENERGY CONVERSION AND MANAGEMENT 2013年 76卷 472-482页

作者： Faghih, Ali Roozbehani, Mardavij Dahleh, Munther A. MIT Elect Engn & Comp Sci EECS Dept Cambridge MA 02139 USA MIT Lab Informat & Decis Syst Cambridge MA 02139 USA

The primary concerns of this paper are twofold: understanding the value of storage in the presence of ramp constraints and exogenous energy prices, and understanding the implications of the associated optimal storage management policy for qualitative and quantitative characteristics of storage response to real-time prices. The optimal policy, along with the associated finite-horizon time-averaged value of storage, are analytically characterized in this paper. An analytical upper bound on the infinite-horizon time-averaged value of storage is also derived. This bound is valid for any achievable realization of prices when the support of the distribution is fixed, and highlights the dependence of the value of storage on ramp constraints and storage capacity. It is shown that while the value of storage is a non-decreasing function of price volatility, due to the finite ramp rate, the value of storage saturates quickly as the capacity increases, regardless of volatility. To study the implications of the optimal policy, computational experiments are presented that suggest optimal utilization of storage can, in expectation, induce a considerable amount of price elasticity near the average price. Then, a computational framework is presented for characterization of the behavior of storage as a function of price and the state of charge, which illustrates a steep buy/sell phase transition in the price-state plane. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Ramp-constrained energy storage stochastic dynamic programming Control systems

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Optimal production and admission control for a stochastic SOM system with demands for product and PSS

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2013年第23-24期51卷 7270-7288页

作者： Wang, Kangzhou Jiang, Zhibin Li, Na Geng, Na Shanghai Jiao Tong Univ Sino US Global Logist Inst Shanghai 200030 Peoples R China Shanghai Jiao Tong Univ Sch Mech Engn Dept Ind Engn & Logist Management Shanghai 200030 Peoples R China Shanghai Jiao Tong Univ Res Ctr Serv Sci & Enterprise Innovat Shanghai 200030 Peoples R China

In decades, many traditional manufacturing firms are making the transition from products manufacturers to the providers of product-service systems (PSSs). The new business mode to support this transition is termed service-oriented manufacturing (SOM) paradigm by researchers and practitioners. In this paper, we address the problem of optimal control for a SOM system in which one factory manufactures products in the first stage and then one service centre realises PSSs by adding some product-based services on the products in the second stage. There are two-class external demands: demands for products and PSSs. The PSSs orders have higher priority and are fully accepted whereas the product orders can either be accepted or rejected. The optimal dynamic admission control of the product orders and the optimal dynamic production control of products are examined simultaneously. We first model the system in the context of a simple production-inventory-queue system and formulate the optimal integrated control problem as a continuous Markov decision process in which the objective is to maximise the profit of the firm. Then we characterise the optimal integrated dynamic control by two state-dependent threshold functions. The monotonicity of two optimal control curves verifies that, to achieve an effective management for the SOM system, the controls of manufacturing subsystem and service subsystem in the SOM system must be coo. We also illustrate the impacts of the revenues of both product orders and PSS orders on the optimal policy numerically. It is interesting that the optimal control policy is independent of the revenue of PSS order.

关键词： service-oriented manufacturing inventory control yield management stochastic dynamic programming Markov decision process

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On traveling wave solutions to a Hamilton-Jacobi-Bellman equation with inequality constraints

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2013年第1期30卷 51-67页

作者： Ishimura, Naoyuki Sevcovic, Daniel Hitotsubashi Univ Grad Sch Econ Kunitachi Tokyo 1868601 Japan Comenius Univ Dept Appl Math & Stat Fac Math Phys & Informat Bratislava 84248 Slovakia

The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear parabolic partial differential equation for the optimal response function. We construct monotone traveling wave solutions and identify parametric regions for which the traveling wave solution has a positive or negative wave speed.

关键词： Hamilton-Jacobi-Bellman equation Traveling wave solution Riccati transformation stochastic dynamic programming

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Optimal gear shift strategies for fuel economy and driveability

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART D-JOURNAL OF AUTOMOBILE ENGINEERING 2013年第10期227卷 1398-1413页

作者： Viet Dac Ngo Navarrete, Jose A. Colin Hofman, Theo Steinbuch, Maarten Serrarens, Alex Eindhoven Univ Technol NL-5600 MB Eindhoven Netherlands Drivetrain Innovat BV Eindhoven Netherlands

This paper aims at designing optimal gear shift strategies for conventional passenger vehicles equipped with discrete ratio transmissions. In order to study quantitatively an optimal trade-off between the fuel economy and the driveability, the vehicle driveability is addressed in a fuel-optimal gear shift algorithm based on dynamic programming by three methods: method 1, weighted inverse of power reserve;method 2, constant power reserve;method 3, variable power reserve. Furthermore, another method based on stochastic dynamic programming is proposed to derive an optimal gear shift strategy over a number of driving cycles in an average sense, hence taking into account the vehicle driveability. In contrast with the dynamic-programming-based strategy, the obtained gear shift strategy based on stochastic dynamic programming is real time implementable. A comparative analysis of all proposed gear shift methods is given in terms of the improvements in the fuel economy and the driveability. The variable-power-reserve method achieves the highest fuel economy without sacrificing the driveability.

关键词： Gear shift strategy automated manual transmission power reserve optimal control dynamic programming fuel economy driveability stochastic dynamic programming

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Dual sourcing using capacity reservation and spot market: Optimal procurement policy and heuristic parameter determination

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第2期225卷 298-309页

作者： Inderfurth, Karl Kelle, Peter Kleber, Rainer Univ Magdeburg Fac Econ & Management Chair Prod & Logist D-39016 Magdeburg Germany Louisiana State Univ Dept Informat Syst & Decis Sci Baton Rouge LA 70803 USA

This contribution focuses on the cost-effective management of the combined use of two procurement options: the short-term option is given by a spot market with random price, whereas the long-term alternative is characterized by a multi period capacity reservation contract with fixed purchase price and reservation level. A reservation cost, proportional with the reservation level, has to be paid for the option of receiving any amount per period up to the reservation level. A long-term decision has to be made regarding the reserved capacity level, and then it has to be decided - period by period - which quantities to procure from the two sources. Considering the multi-period problem with stochastic demand and spot price, the structure of the optimal combined purchasing policy is derived using stochastic dynamic programming. Exploiting these structural properties, an advanced heuristic is developed to determine the respective policy parameters. This heuristic is compared with two rolling-horizon approaches which use the one-period and two-period optimal solution. A comprehensive numerical study reveals that the approaches based on one-period and two-period solutions have considerable drawbacks, while the advanced heuristic performs very well compared to the optimal solution. Finally, by exploiting our numerical results we give some insights into the system's behavior under problem parameter variations. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Dual sourcing Capacity reservation Spot market Procurement policy stochastic dynamic programming Heuristics

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