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Scenario tree reduction in stochastic programming with recourse for hydropower operations

WATER RESOURCES RESEARCH 2015年第8期51卷 6359-6380页

作者： Xu, Bin Zhong, Ping-An Zambon, Renato C. Zhao, Yunfa Yeh, William W. -G. Hohai Univ Coll Hydrol & Water Resources Nanjing Jiangsu Peoples R China Univ Calif Los Angeles Dept Civil & Environm Engn Los Angeles CA 90095 USA Hohai Univ Natl Engn Res Ctr Water Resources Efficient Utili Nanjing Jiangsu Peoples R China Univ Sao Paulo Dept Hydraul & Environm Engn Polytech Sch Sao Paulo Brazil China Three Gorges Corp Beijing Peoples R China Univ Calif Los Angeles Dept Civil & Environm Engn Los Angeles CA USA

A stochastic programming with recourse model requires the consequences of recourse actions be modeled for all possible realizations of the stochastic variables. Continuous stochastic variables are approximated by scenario trees. This paper evaluates the impact of scenario tree reduction on model performance for hydropower operations and suggests procedures to determine the optimal level of scenario tree reduction. We first establish a stochastic programming model for the optimal operation of a cascaded system of reservoirs for hydropower production. We then use the neural gas method to generate scenario trees and employ a Monte Carlo method to systematically reduce the scenario trees. We conduct in-sample and out-of-sample tests to evaluate the impact of scenario tree reduction on the objective function of the hydropower optimization model. We then apply a statistical hypothesis test to determine the significance of the impact due to scenario tree reduction. We develop a stochastic programming with recourse model and apply it to real-time operation for hydropower production to determine the loss in solution accuracy due to scenario tree reduction. We apply the proposed methodology to the Qingjiang cascade system of reservoirs in China. The results show: (1) the neural gas method preserves the mean value of the original streamflow series but introduces bias to variance, cross variance, and lag-one covariance due to information loss when the original tree is systematically reduced;(2) reducing the scenario number by as much as 40% results in insignificant change in the objective function and solution quality, but significantly reduces computational demand.

关键词： hydropower operation stochastic programming with recourse neural gas method scenario tree reduction numerical experiments

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A Proposed Multi-Objective, Multi-Stage stochastic programming with recourse Model for Reservoir Management and Operation

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WATER RESOURCES RESEARCH 2021年第10期57卷 e2020WR029200-e2020WR029200页

作者： Li, Jinshu Zhang, Wei Yeh, William W-G Univ Calif Los Angeles Dept Civil & Environm Engn Los Angeles CA 90095 USA China Three Gorges Corp Beijing Peoples R China Wuhan Univ Wuhan Peoples R China

We present a multi-objective, multi-stage stochastic programming with recourse model for reservoir management and operation, where we use utility theory to select the best compromise solution from the Pareto front. A multi-stage streamflow scenario tree is generated first by the neural gas method. Then the Pareto front at each stage is produced by a modified constrained NSGA-II. A single best compromise solution on the Pareto front must be selected for the immediate stage and the model moves forward one stage and is re-optimized over a moving planning horizon of fixed duration. A key contribution of this study is the selection of the best compromise solution, which is achieved by a proposed linear spline utility function allied with regression. Our proposed utility function has the following advantages: (a) It satisfies the law of diminishing marginal rate of substitution, (b) it does not rely on the pre-specified weight or goal, and (c) it selects the best compromise solution that is likely to fall in the "knee regions" of the Pareto front. We apply the proposed optimization model to the Three Gorges Reservoir in China. The two conflicting objectives are (a) maximizing the total expected energy output in the planning horizon, and (b) maximizing the average expected ecological benefits in the planning horizon. The results show that the proposed model produces the optimal water release policy successfully under different hydrological scenarios, considering both the inflow uncertainty and the tradeoff between the two conflicting objectives.

关键词： stochastic multi-objective optimization stochastic programming with recourse reservoir operation utility function Three Gorges Reservoir

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Location configuration design for Dynamic Message Signs under stochastic incident and ATIS scenarios

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2007年第1期15卷 33-50页

作者： Chiu, Yi-Chang Huynh, Nathan Univ Arizona Dept Civil Engn & Engn Mech Tucson AZ 85721 USA N Carolina Agr & Tech State Univ Dept Civil Architectural Agr & Environm Engn Greensboro NC 27411 USA

This paper proposes a methodology for deploying permanent Dynamic Message Signs (DMS) in a vehicular traffic network. Of particular interest is the planning problem to optimize the number of DMS to deploy in conjunction with Advanced Traveler Information Systems (ATIS), operating and maintenance cost of DMS, and incident-related user cost under random traffic incident situations. The optimal DMS location design problem discussed herein is formulated as a two-stage stochastic program with recourse (SPR). A Tabu search algorithm combined with dynamic traffic simulation and assignment approaches are employed to solve this problem. A case study performed on the Fort-Worth, Texas network highlights the effectiveness of the proposed framework and illustrates the affect factors such as demand, network structure, DMS response rate, and incident characteristics have on the solution. The numerical results suggest that designing and deploying DMS and ATIS jointly is more cost-effective and efficient than the sequential build-out of the two from the system management perspective. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： dynamic message signs stochastic programming with recourse dynamic traffic assignment advanced traveler information systems DYNASMART-P Tabu search

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Parametric Forecasting and stochastic programming Models for Call-Center Workforce Scheduling

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M&SOM-MANUFACTURING & SERVICE OPERATIONS MANAGEMENT 2015年第4期17卷 571-588页

作者： Gans, Noah Shen, Haipeng Zhou, Yong-Pin Korolev, Nikolay McCord, Alan Ristock, Herbert Univ Penn Wharton Sch Operat Informat & Decis Dept Philadelphia PA 19104 USA Univ N Carolina Dept Stat & Operat Res Chapel Hill NC 27599 USA Univ Hong Kong Sch Business Innovat & Informat Management Pok Fu Lam Hong Kong Peoples R China Univ Washington Michael G Foster Sch Business Dept Informat Syst & Operat Management Seattle WA 98195 USA Genesys Telecommun Labs Daly City CA 94014 USA

We develop and test an integrated forecasting and stochastic programming approach to workforce management in call centers. We first demonstrate that parametric forecasts, discretized using Gaussian quadrature, can be used to drive stochastic programs whose results are stable with relatively small numbers of scenarios. We then extend our approach to include forecast updates and two-stage stochastic programs with recourse and provide a general modeling framework for which recent, related models are special cases. In our formulations, the inclusion of multiple arrival-rate scenarios allows call centers to meet long-run average quality-of-service targets, and the use of recourse actions helps them to lower long-run average costs. Experiments with two large sets of call-center data highlight the complementary nature of these elements.

关键词： call-center management production planning and scheduling service operations distributional forecast updating stochastic programming with recourse

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A vehicle routing problem with time windows and stochastic demands

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JOURNAL OF THE CHINESE INSTITUTE OF ENGINEERS 2005年第5期28卷 783-794页

作者： Chang, MS Chung Hua Univ Dept Business Adm Hsinchu 300 Taiwan

This study presents an approach for considering a vehicle routing problem where customers' pickup demands are uncertain and require serving within some settled time windows. Customers' demands are assumed to follow given discrete probability distributions. This study proposes a nonlinear stochastic integer program with recourse to formulate the vehicle routing problem with stochastic demands and time windows (VRPTW-SD, for short). The objective of the VRPTW-SD is to minimize the total cost of the first-stage solution and expected recourse cost of the second-stage solution. The total cost of the first-stage problem includes the total travel cost for all links and the total waiting cost at all nodes. When a vehicle capacity is attained or exceeded, recourse actions are needed and recourse costs incurred in order to finish the planned route schedules. Two categories of schedule failure are introduced in this work;the recourse costs derive from the variations in travel time travel time, waiting time, and penalties of late arrival for time windows. In addition, an optimization algorithm is developed for solving the VRPTW-SD, according to the framework of the L-shaped method. Numerical results are given to demonstrate its validity.

关键词： stochastic programming with recourse optimization algorithm optimality cuts

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QUANTITATIVE STABILITY IN stochastic-programming

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MATHEMATICAL programming 1994年第1期67卷 99-108页

作者： SHAPIRO, A 1. School of Industrial and Systems Engineering Georgia Institute of Technology 30332-0205 Atlanta Georgia USA

In this paper we study stability of optimal solutions of stochastic programming problems with fixed recourse. An upper bound for the rate of convergence is given in terms of the objective functions of the associated deterministic problems. As an example it is shown how it can be applied to derivation of the Law of Iterated Logarithm for the optimal solutions. It is also shown that in the case of simple recourse this upper bound implies upper Lipschitz continuity of the optimal solutions with respect to the Kolmogorov-Smirnov distance between the corresponding cumulative probability distribution functions.

关键词： stochastic programming with recourse QUANTITATIVE STABILITY LIPSCHITZ CONTINUITY LAW OF ITERATED LOGARITHM KOLMOGOROV-SMIRNOV DISTANCE

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An Adaptive Large Neighbourhood Search Heuristic for the Capacitated Arc-Routing Problem with stochastic Demands

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TRANSPORTATION SCIENCE 2010年第1期44卷 125-135页

作者： Laporte, Gilbert Musmanno, Roberto Vocaturo, Francesca HEC Montreal Montreal PQ H3T 2A7 Canada Univ Calabria Dipartimento Elettr Informat & Sistemist I-87036 Arcavacata Di Rende CS Italy Univ Calabria Dipartimento Econ & Stat I-87036 Arcavacata Di Rende CS Italy

The capacitated arc-routing problem with stochastic demands (CARPSD) is an extension of the well-known capacitated arc-routing problem (CARP) in which demands are stochastic. This leads to the possibility of route failures whenever the realized demand exceeds the vehicle capacity. This paper presents the CARPSD in the context of garbage collection. It describes an adaptive large-scale neighbourhood search heuristic for the problem. Computational results show the superiority of this algorithm over an alternative solution approach.

关键词： capacitated arc-routing problem stochastic programming with recourse a priori optimization adaptive large neighbourhood search

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The capacitated vehicle routing problem with evidential demands

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2018年第Apr.期95卷 124-151页

作者： Helal, Nathalie Pichon, Frederic Porumbel, Daniel Mercier, David Lefevre, Eric Univ Artois EA 3926 Lab Genie Informat & Automat Artois LGI2A F-62400 Bethune France Conservatoire Natl Arts & Metiers EA 4629 F-75003 Paris France

We propose to represent uncertainty on customer demands in the Capacitated Vehicle Routing Problem (CVRP) using the theory of evidence. To tackle this problem, we extend classical stochastic programming modelling approaches. Specifically, we propose two models for this problem. The first model is an extension of the chance-constrained programming approach, which imposes certain minimum bounds on the belief and plausibility that the sum of the demands on each route respects the vehicle capacity. The second model extends the stochastic programming with recourse approach: for each route, it represents by a belief function the uncertainty on its recourses, i.e., corrective actions performed when the vehicle capacity is exceeded, and defines the cost of a route as its classical cost (without recourse) plus the worst expected cost of its recourses. We solve the proposed models using a metaheuristic algorithm and present experimental results on instances adapted from a well-known CVRP data set. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Vehicle routing problem Chance constrained programming stochastic programming with recourse Belief function

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Comparative Statics Analysis of Multiproduct Newsvendor Networks Under Responsive Pricing

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OPERATIONS RESEARCH 2012年第5期60卷 1111-1124页

作者： Bish, Ebru K. Zeng, Xin Liu, Juqi Bish, Douglas R. Virginia Tech Grado Dept Ind & Syst Engn Blacksburg VA 24061 USA

We propose a novel analytic approach for the comparative statics analysis of multiproduct multiresource newsvendor networks under responsive pricing. Our approach involves exploiting the properties of the primal mathematical programming formulation and of the dual variables and linking those properties to the concept of convex orders and to properties of the underlying demand function. The use of convex orders allows us to establish our main results without restriction to a specific demand distribution. A major strength of our approach is that it is "scalable," i.e., it applies to newsvendor networks with any number of "nonindependent" (i.e., demand or resource sharing) products and resources, without an exponential increase in effort as problem size increases. This is unlike the current approaches commonly used in the operations management literature, which typically involve a parametric analysis of the recourse problem, followed by the use of Jacobians and the implicit function theorem. Providing a rigorous framework for comparative statics analysis, which can be applied to other problems that are not amenable to traditional parametric analysis, is our main contribution. We demonstrate this approach on the optimal capacity decision problem in multiproduct newsvendor networks under responsive pricing, formulated as a two-stage stochastic programming problem with recourse: The firm determines the resource capacities ex ante, in the first stage, when demand intercepts are uncertain, and makes the pricing and production decisions ex post. in the second stage, when demand intercepts (e.g., market conditions) are fully observed. This particular problem and its variants are well studied in the operations management literature. A comparative statics analysis is integral to the study of the capacity investment decision, as it allows answers to important questions such as the following: "Does the firm acquire more or less of the different resources available as demand uncer

关键词： comparative statics analysis capacity planning responsive pricing resource flexibility substitutable products stochastic programming with recourse convex orders

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AN UPPER BOUND ON THE EXPECTATION OF SIMPLICIAL FUNCTIONS OF MULTIVARIATE RANDOM-VARIABLES

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MATHEMATICAL programming 1992年第1期55卷 69-80页

作者： DULA, JH 1. Southern Methodist University 75275-0112 Dallas TX USA

We introduce an upper bound on the expectation of a special class of sublinear functions of multivariate random variables defined over the entire Euclidean space without an independence assumption. The bound can be evaluated easily requiring only the solution of systems of linear equations thus permitting implementations in high-dimensional space. Only knowledge on the underlying distribution means and second moments is necessary. We discuss pertinent techniques on dominating general sublinear function, by using simpler sublinear and polyhedral functions and second order quadratic functions.

关键词： UPPER BOUNDS stochastic programming with recourse SEMI-INFINITE programming MOMENT PROBLEM

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