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Solving nonlinear dynamic games via orthogonal collocation: An application to international commodity markets

ANNALS OF OPERATIONS RESEARCH 1996年第1期68卷 89-108页

作者： Rui, XW Miranda, MJ OHIO STATE UNIV DEPT AGR ECONCOLUMBUSOH 43210

We develop methods for solving nonlinear stochastic dynamic difference games using orthogonal polynomial collocation techniques. The methods are applied to models of world commodity markets in which governments compete against each other using storage as a strategy variable. The rational expectations equilibrium outcomes under four different game structures are derived numerically and compared using stochastic simulation techniques.

关键词： stochastic dynamic games stochastic dynamic programming Chebyshev orthogonal collocation rational expectations commodity storage

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A dual sourcing inventory model for modal split transport: Structural properties and optimal solution

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第3期283卷 883-900页

作者： Dong, Chuanwen Transchel, Sandra ESCP Europe Berlin Campus Berlin Germany Kuehne Logist Univ Hamburg Germany

Shifting freight volumes from road to rail transport increases the economic performances of freight logistics. However, compared to road transport, rail transport generally lacks the flexibility in delivery quantity and frequency, and exhibits economies of scale in its shipment volume. This often leads to high inventory levels in the destination after deliveries. We generalize the tailored base-surge dual sourcing inventory model by introducing a fixed cost in rail transport, adding an extra decision in its delivery frequency, and relaxing the assumption of the base stock control of road transport, to support firms' modal split transport optimization. The objective is to optimize the controls of the two transport modes and the corresponding inventory management at the destination, which minimize the combined average transport and inventory costs per period in the steady state. Using stochastic dynamic programming, we find that when the delivery quantity and frequency of rail transport is fixed, the optimal shipment volume via the road transport indeed follows a base stock control. This allows to solve the relevant Bellman equation via an efficient policy iteration approach. We also find that the total cost is convex in the delivery quantity of rail transport, and a bi-section search can be applied. Finally, we analyze the sensitivity and robustness of our model using values suggested by a consumer goods firm. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Inventory Modal split transport Dual sourcing stochastic dynamic programming Optimization

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An optimal statistical testing policy for software reliability demonstration of safety-critical systems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第3期137卷 544-557页

作者： Tal, O McCollin, C Bendell, A Nottingham Trent Univ Dept Math Stat & Operat Res Nottingham NG1 4BU England RAFAEL IL-31021 Haifa Israel Univ Leicester Ctr Management Leicester LE1 7RH Leics England

When software reliability demonstration of safety-critical systems by statistical testing is treated as a Test, Analyse and Fix (TAAF) process, an optimal testing policy can be found, which maximises the probability of p success of the whole process, over a pre-determined period of time. The optimisation problem is formulated, solved by stochastic dynamic programming, and demonstrated by two numerical examples. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： reliability software reliability demonstration statistical testing safety-critical systems stochastic dynamic programming

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An approximate dynamic programming approach for sequential pig marketing decisions at herd level

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第3期276卷 1056-1070页

作者： Pourmoayed, Reza Nielsen, Lars Relund Aarhus Univ Dept Econ & Business Econ Fuglesangs Alle 4 DK-8210 Aarhus V Denmark

One of the most important operations in the production of growing/finishing pigs is the marketing of pigs for slaughter. While pork production can be managed at different levels (animal, pen, section, or herd), it is beneficial to consider the herd level when determining the optimal marketing policy due to inter-dependencies, such as those created by fixed transportation costs and cross-level constraints. In this paper, we consider sequential marketing decisions at herd level. A high-dimensional infinite horizon Markov decision process (MDP) is formulated which, due to the curse of dimensionality, cannot be solved using standard MDP optimization techniques. Instead, approximate dynamic programming (ADP) is applied to solve the model and find the best marketing policy at herd level. Under the total expected discounted reward criterion, the proposed ADP approach is first compared with a standard solution algorithm for solving an MDP at pen level to show the accuracy of the solution procedure. Next, numerical experiments at herd level are given to confirm how the marketing policy adapts itself to varying costs (e.g., transportation cost) and cross-level constraints. Finally, a sensitivity analysis for some parameters in the model is conducted and the marketing policy found by ADP is compared with other well-known marketing polices, often applied at herd level. (C) 2019 Elsevier B.V. All rights reserved.

关键词： OR in agriculture Approximate dynamic programming Markov decision process Herd management stochastic dynamic programming

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Finding the K best policies in a finite-horizon Markov decision process

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第2期175卷 1164-1179页

作者： Nielsen, Lars Relund Kristensen, Anders Ringgaard Royal Vet & Agr Univ Dept Large Anim Sci DK-1870 Frederiksberg C Denmark

Directed hypergraphs represent a general modelling and algorithmic tool, which have been successfully used in many different research areas such as artificial intelligence, database systems, fuzzy systems, propositional logic and transportation networks. However, modelling Markov decision processes using directed hypergraphs has not yet been considered. In this paper we consider finite-horizon Markov decision processes (MDPs) with finite state and action space and present an algorithm for finding the K best deterministic Markov policies. That is, we are interested in ranking the first K deterministic Markov policies in non-decreasing order using an additive criterion of optimality. The algorithm uses a directed hypergraph to model the finite-horizon MDP. It is shown that the problem of finding the optimal policy can be formulated as a minimum weight hyperpath problem and be solved in linear time, with respect to the input data representing the MDP, using different additive optimality criteria. (c) 2005 Elsevier B.V. All rights reserved.

关键词： finite-horizon Markov decision processes stochastic dynamic programming directed hypergraphs hyperpaths K best policies

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Shared Steering Torque Control for Lane Change Assistance: A stochastic Game-Theoretic Approach

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2019年第4期66卷 3093-3105页

作者： Ji, Xuewu Yang, Kaiming Na, Xiaoxiang Lv, Chen Liu, Yahui Tsinghua Univ State Key Lab Automot Safety & Energy Beijing 100084 Peoples R China Univ Cambridge Dept Engn Cambridge CB2 1PZ England Nanyang Technol Univ Sch Mech & Aerosp Engn Singapore 639798 Singapore Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

The challenging issue of "human-machine copilot" opens up a new frontier to enhancing driving safety. However, driver-machine conflicts and uncertain driver/external disturbances are significant problems in cooperative steering systems, which degrade the system's path-tracking ability and reduce driving safety. This paper proposes a novel stochastic game-based shared control framework to model the steering torque interaction between the driver and the intelligent electric power steering (IEPS) system. A six-order driver-vehicle dynamic system, including driver/external uncertainty, is established for path-tracking. Then, the affine linear-quadratic-based path-tracking problem is proposed to model the maneuvers of the driver and IEPS. Particularly, the feedback Nash and Stackelberg frameworks to the affine-quadratic problem are derived by stochastic dynamic programming. Two cases of copilot lane change driving scenarios are studied via computer simulation. The intrinsic relation between the stochastic Nash and Stackelberg strategies is investigated based on the results. And the steering-in-the-loop experiment reveals the potential of the proposed shared control framework in handling driver-IEPS conflicts and uncertain driver/external turbulence. Finally, the copiloting experiments with a human driver further demonstrate the rationality of the game-based pattern between both the agents.

关键词： Affine-quadratic game driver-machine conflicting shared steering control stochastic dynamic programming

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Practical dual-control guidance using adaptive intermittent maneuver strategy

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JOURNAL OF GUIDANCE CONTROL AND dynamicS 2001年第5期24卷 1009-1015页

作者： Lee, HI Tahk, MJ Sun, BC Korea Adv Inst Sci & Technol Div Aerosp Engn Taejon 305701 South Korea Korea Aerosp Res Inst Guidance & Control Dept Taejon 305333 South Korea

A new adaptive intermittent maneuver strategy is proposed, which has switching threshold levels dependent on the estimated time-to-go for dual-control guidance of passive homing missiles. Guidance performance in terms of control effort and target observability for the adaptive intermittent maneuver strategy are also analyzed, as well as proportional navigation guidance. With intermittent maneuvers the guidance command is occasionally disabled to intentionally increase guidance errors. When provided with suitable switching threshold levels, this intermittent maneuver strategy improves target observability and, consequently, intercept performance. Statistical simulations for an atmospheric engagement demonstrate the effectiveness of the proposed intermittent maneuver strategy.

关键词： Control Guidance Proportional Navigation Homing Missile Guidance Algorithms Homing Guidance stochastic dynamic programming Polar Coordinate System Switching Mechanisms stochastic Control Command Missile

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Project management under risk: Using the real options approach to evaluate flexibility in R&D

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MANAGEMENT SCIENCE 2001年第1期47卷 85-101页

作者： Huchzermeier, A Loch, CH WHU Otto Beisheim Hsch D-56179 Vallendar Germany INSEAD F-77305 Fontainebleau France

Managerial flexibility has value in the context of uncertain R&D projects, as management can repeatedly gather information about uncertain project and market characteristics and, based on this information, change its course of action. This value is now well accepted and referred to as "real option value." We introduce, in addition to the familiar real option of abandonment, the option of corrective action that management can take during the project. The intuition from options pricing theory is that higher uncertainty in project pay offs increases the real option value of managerial decision flexibility. However, R&D managers face uncertainty not only in payoffs, but also from many other sources. We identify five example types of R&D uncertainty, in market payoffs, project budgets, product performance, market requirements, and project schedules. How do they influence the value from managerial flexibility? We find that if uncertainty is resolved or costs/revenues occur after all decisions have been made, more variability may "smear out" contingencies and thus reduce the value of flexibility In addition, variability may reduce the probability of flexibility ever being exercised, which also reduces its value. This result runs counter to established option pricing theory intuition and contributes to a better risk management in R&D projects. Our model builds intuition for R&D managers as to when it is and when it is not worthwhile to delay commitments-for example, by postponing a design freeze, thus maintaining flexibility in R&D projects.

关键词： real options R&D projects project evaluation decision trees stochastic dynamic programming managerial flexibility project management

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OPTIMAL RECONFIGURATION STRATEGIES FOR RECONFIGURABLE COMPUTER-SYSTEMS WITH NO REPAIR

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IEEE TRANSACTIONS ON COMPUTERS 1986年第3期35卷 278-280页

作者： RAMAMOORTHY, CV MA, YWE UNIV PENN DEPT COMP & INFORMAT SCIPHILADELPHIAPA 19104

In this correspondence, we study the problem of finding optimal reconfiguration strategies for a class of reconfigurable fault- tolerant computer systems in which there is no repair in failed components. The problem of finding optimal reconfiguration strategies consists of determining, for each failed state of the system, the operational state into which the system should reconfigure itself. We presented a stochastic model for the above class of reconfigurable computer systems. Based on this model, we construct a polynomial-time algorithm for finding optimal reconfiguration strategies.

关键词： Fault-tolerance long-life systems optimization polynomial-time algorithm reconfiguration stochastic dynamic programming systems with postponed maintenance

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OPTIMIZATION IN A CLASS OF PRIORITY-DISCARDING POLICIES FOR FINITE QUEUES

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1994年第5期39卷 1020-1024页

作者： PETR, DW Department of Electrical and Computer Engineering Telecommunications and Information Sciences Laboratory University of Kansas Lawrence KS USA

We consider an optimization problem for finite queues governed by priority-discarding control policies. We develop an analytical model for systems that defer discarding decisions until service completion instants, but then may expel any waiting jobs. Using stochastic dynamic programming techniques, we obtain closed-form optimization results for systems constrained to retain at most one job. Numerical performance examples are included.

关键词： dynamic programming queueing theory stochastic programming analytical model closed-form optimization finite queues priority-discarding policies service completion stochastic dynamic programming queueing theory jobs stochastic programming dynamic programming stochastic models ANALYSIS MODELS

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