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dynamic booking control for car rental revenue management: A decomposition approach

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第3期256卷 850-867页

作者： Li, Dong Pang, Zhan Univ York York Management Sch York YO10 5GD N Yorkshire England City Univ Hong Kong Dept Management Sci Hong Kong Hong Kong Peoples R China

This paper considers dynamic booking control for a single-station car rental revenue management problem. Different from conventional airline revenue management, car rental revenue management needs to take into account not only the existing bookings but also the lengths of the existing rentals and the capacity flexibility via fleet shuttling, which yields a high-dimensional system state space. In this paper, we formulate the dynamic booking control problem as a discrete-time stochastic dynamic program over an infinite horizon. Such a model is computationally intractable. We propose a decomposition approach and develop two heuristics. The first heuristic is an approximate dynamic program (ADP) which approximates the value function using the value functions of the decomposed problems. The second heuristic is constructed directly from the optimal booking limits computed from the decomposed problems, which is more scalable compared to the ADP heuristic. Our numerical study suggests that the performances of both heuristics are close to optimum and significantly outperform the commonly used probabilistic nonlinear programming (PNLP) heuristic in most of the instances. The dominant performance of our second heuristic is evidenced in a case study using sample data from a major car rental company in the UK. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Revenue management Car rental approximate dynamic programming Decomposition

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Markdown optimization for an apparel retailer under cross-price and initial inventory effects

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KNOWLEDGE-BASED SYSTEMS 2017年 120卷 186-197页

作者： Cosgun, Ozlem Kula, Ufuk Kahraman, Cengiz Wichita State Univ Ind Syst & Mfg Engn Dept 1845 Fairmount St Wichita KS 67260 USA Amer Univ Middle East Eqalia Kuwait Istanbul Tech Univ Istanbul Turkey

Apparel Retailers have been using markdowns as a means of revenue maximization with an increased frequency. Parallel to this increase, several authors have studied single product markdown optimization problem under various settings or assumed that the products are independent in case of multi -products. In this paper, we address the simultaneous determination of markdown prices and optimal initial inventory levels under the cross-price effects in a random demand setting for multi-product groups for an apparel retailer chain in Turkey. First, we formulate the problem as a Markov Decision Process that considers price-based substitution and complementary effects among products and maximizes the expected total profit over a finite horizon. Then, we find the approximate markdown policies of each product by using approximate dynamic programming algorithm. We investigate how cross-price elasticity affects the markdown policies of each product by considering several relationships among them, such as the products are all substitute or all are complement or some are substitute and some are complement. In addition to this, we provide insights on how they affect the expected revenues when non-optimal and optimal initial inventory levels are considered. When cross-price effects are considered in case of non-optimal initial inventory levels, average revenue increases about 32% while it increases to 50% when optimal initial inventory levels are in case. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Markdown optimization dynamic pricing Cross-price elasticity approximate dynamic programming Markov decision processes

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Comparison of least squares Monte Carlo methods with applications to energy real options

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期256卷 196-204页

作者： Nadarajah, Selvaprabu Margot, Francois Secomandi, Nicola Univ Illinois Coll Business Adm 601 South Morgan St Chicago IL 60607 USA Carnegie Mellon Univ Tepper Sch Business 5000 Forbes Ave Pittsburgh PA 15213 USA

Least squares Monte Carlo (LSM) is a state-of-the-art approximate dynamic programming approach used in financial engineering and real options to value and manage options with early or multiple exercise opportunities. It is also applicable to capacity investment and inventory/production management problems with demand/supply forecast updates arising in operations and hydropower-reservoir management. LSM has two variants, referred to as regress-now/later (LSMN/L), which compute continuation/value function approximations (C/VFAs). We provide novel numerical evidence for the relative performance of these methods applied to energy swing and storage options, two typical real options, using a common price evolution model. LSMN/L estimate C/VFAs that yield equally accurate (near optimal) and precise lower and dual (upper) bounds on the value of these real options. Estimating the LSMN/L C/VFAs and their associated lower bounds takes similar computational effort. In contrast, the estimation of a dual bound using the LSML VFA instead of the LSMN CFA takes seconds rather than minutes or hours. This finding suggests the use of LSML in lieu of LSMN when estimating dual bounds on the value of early or multiple exercise options, as well as of related capacity investment and inventory/production policies. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Energy Real options Least-squares Monte Carlo approximate dynamic programming Information relaxation and duality

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dynamic portfolio choices by simulation-and-regression: Revisiting the issue of value function vs portfolio weight recursions

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COMPUTERS & OPERATIONS RESEARCH 2017年 79卷 174-189页

作者： Denault, Michel Simonato, Jean-Guy HEC Montreal Dept Decis Sci Montreal PQ Canada Gerad Montreal PQ Canada HEC Montreal Dept Finance Montreal PQ Canada

Simulation-and-regression methods have been recently proposed to solve multi-period, dynamic portfolio choice problems. In the constant relative risk aversion (CRRA) framework, the "value function recursion vs portfolio weight recursion" issue was previously examined in van Binsbergen and Brandt [24] and Garlappi and Skoulakis [14]. We revisit this issue in the context of an alternative simulation-and-regression algorithmic approach which does not rely on Taylor series approximations of the value function. We find that, in this context and for the CRRA example examined here, both approach are capable of obtaining precise results, but that the portfolio weight recursion variant of the algorithm provides more accurate results for a similar level of computational complexity, especially for problems with long maturities and large risk-aversion levels.

关键词： dynamic portfolio choices Portfolio optimization approximate dynamic programming Least-squares Monte Carlo Simulation-and-regression

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Neural-network-based synchronous iteration learning method for multi-player zero-sum games

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NEUROCOMPUTING 2017年 242卷 73-82页

作者： Song, Ruizhuo Wei, Qinglai Song, Biao Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China

In this paper, a synchronous solution method for multi-player zero-sum games without system dynamics is established based on neural network. The policy iteration (PI) algorithm is presented to solve the Hamilton-Jacobi-Bellman (HJB) equation. It is proven that the obtained iterative cost function is convergent to the optimal game value. For avoiding system dynamics, off-policy learning method is given to obtain the iterative cost function, controls and disturbances based on Pl. Critic neural network (CNN), action neural networks (ANNs) and disturbance neural networks (DNNs) are used to approximate the cost function, controls and disturbances. The weights of neural networks compose the synchronous weight matrix, and the uniformly ultimately bounded (UUB) of the synchronous weight matrix is proven. Two examples are given to show that the effectiveness of the proposed synchronous solution method for multi-player ZS games. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Adaptive dynamic programming approximate dynamic programming Adaptive critic designs Multi-player Iteration learning Neural network

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Drift counteraction optimal control for deterministic systems and enhancing convergence of value iteration

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AUTOMATICA 2017年 83卷 108-115页

作者： Zidek, Robert A. E. Kolmanovsky, Ilya V. Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

The paper treats a class of optimal control problems for deterministic nonlinear discrete-time systems with the objective of maximizing the time or total yield until prescribed constraints are violated. Such problems are referred to as drift counteraction optimal control (DCOC) problems as the corresponding control policy may be viewed as optimally counteracting drift imposed by disturbances or system dynamics. We derive conditions for the existence of an optimal solution. The optimal control policy is characterized by the value function and a new algorithm based on proportional feedback is presented that obtains the value function faster than conventional dynamic programming algorithms. In addition, an approximate dynamic programming (ADP) approach using Gaussian process regression is formulated based on the new algorithm. Two numerical examples are reported, a time maximization problem for a van der Pol oscillator and a satellite life extension problem. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Optimal control Constrained nonlinear systems approximate dynamic programming Aerospace applications

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Meeting Inelastic Demand in Systems With Storage and Renewable Sources

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IEEE TRANSACTIONS ON SMART GRID 2017年第4期8卷 1619-1629页

作者： Kwon, Soongeol Xu, Yunjian Gautam, Natarajan Texas A&M Univ Dept Ind & Syst Engn College Stn TX 77843 USA Singapore Univ Technol & Design Engn Syst & Design Pillar Singapore 591401 Singapore

We consider a system where inelastic demand for electric power is met from three sources: 1) the grid;2) in-house renewables such as solar panels;and 3) an in-house energy storage device. In our setting, energy demand, renewable power supply, and cost for grid power are all time-varying and stochastic. Furthermore, there are limits and inefficiency associated with charging and discharging the energy storage device. We formulate the storage operation problem as a dynamic program with parameters estimated from real-world demand, supply, and cost data. As the dynamic program is computationally intensive for large-scale problems, we explore algorithms based on approximate dynamic programming (ADP) and apply them to a test data set. Using the real-world test data, we numerically compare the performance of two ADP-based algorithms against Lyapunov optimization-based algorithms that require no statistical knowledge. Our results ascertain the value of storage and the value of installing a renewable source.

关键词： approximate dynamic programming energy storage look-ahead policies renewable generation solar PV

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Data-driven approximate value iteration with optimality error bound analysis

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AUTOMATICA 2017年 78卷 79-87页

作者： Li, Yongqiang Hou, Zhongsheng Feng, Yuanjing Chi, Ronghu Zhejiang Univ Technol Coll Informat Engn Hangzhou Zhejiang Peoples R China Beijing Jiaotong Univ Sch Elect & Informat Engn Adv Control Syst Lab Beijing Peoples R China Qingdao Univ Sci & Technol Sch Automat & Elect Engn Qingdao Peoples R China

Features of the data-driven approximate value iteration (AVI) algorithm, proposed in Li et al. (2014) for dealing with the optimal stabilization problem, include that only process data is required and that the estimate of the domain of attraction for the closed-loop is enlarged. However, the controller generated by the data-driven AVI algorithm is an approximate solution for the optimal control problem. In this work, a quantitative analysis result on the error bound between the optimal cost and the cost under the designed controller is given. This error bound is determined by the approximation error of the estimation for the optimal cost and the approximation error of the controller function estimator. The first one is concretely determined by the approximation error of the data-driven dynamic programming (DP) operator to the DP operator and the approximation error of the value function estimator. These three approximation errors are zeros when the data set of the plant is sufficient and infinitely complete, and the number of samples in the interested state space is infinite. This means that the cost under the designed controller equals to the optimal cost when the number of iterations is infinite. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Data-driven control approximate dynamic programming Domain of attraction Asymptotic stabilization

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Mixed Iterative Adaptive dynamic programming for Optimal Battery Energy Control in Smart Residential Microgrids

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2017年第5期64卷 4110-4120页

作者： Wei, Qinglai Liu, Derong Lewis, Frank L. Liu, Yu Zhang, Jie Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Univ Texas Arlington UTA Res Inst Arlington TX 76118 USA Chinese Acad Sci Inst Automat Beijing 100190 Peoples R China Qingdao Acad Intelligent Ind Qingdao 266000 Shandong Peoples R China

In this paper, a novel mixed iterative adaptive dynamic programming (ADP) algorithm is developed to solve the optimal battery energy management and control problem in smart residential microgrid systems. Based on the data of the load and electricity rate, two iterations are constructed, which are P-iteration and V-iteration, respectively. The V-iteration is implemented based on value iteration, which aims to obtain the iterative control law sequence in each period. The P-iteration is implemented based on policy iteration, which updates the iterative value function according to the iterative control law sequence. Properties of the developed mixed iterative ADP algorithm are analyzed. It is shown that the iterative value function is monotonically nonincreasing and converges to the solution of the Bellman equation. In each iteration, it is proven that the performance index function is finite under the iterative control law sequence. Finally, numerical results and comparisons are given to illustrate the performance of the developed algorithm.

关键词： Adaptive critic designs adaptive dynamic programming (ADP) approximate dynamic programming mixed iteration optimal control policy iteration smart grid value iteration

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Discrete-Time Optimal Control via Local Policy Iteration Adaptive dynamic programming

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IEEE TRANSACTIONS ON CYBERNETICS 2017年第10期47卷 3367-3379页

作者： Wei, Qinglai Liu, Derong Lin, Qiao Song, Ruizhuo Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China

In this paper, a discrete-time optimal control scheme is developed via a novel local policy iteration adaptive dynamic programming algorithm. In the discrete-time local policy iteration algorithm, the iterative value function and iterative control law can be updated in a subset of the state space, where the computational burden is relaxed compared with the traditional policy iteration algorithm. Convergence properties of the local policy iteration algorithm are presented to show that the iterative value function is monotonically nonincreasing and converges to the optimum under some mild conditions. The admissibility of the iterative control law is proven, which shows that the control system can be stabilized under any of the iterative control laws, even if the iterative control law is updated in a subset of the state space. Finally, two simulation examples are given to illustrate the performance of the developed method.

关键词： Adaptive critic designs adaptive dynamic programming (ADP) approximate dynamic programming local policy iteration neuro-dynamic programming nonlinear systems optimal control

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