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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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Scenario tree reduction in stochastic programming with recourse for hydropower operations

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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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Multi-sourcing under supply uncertainty and Buyer's risk aversion

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EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2021年 9卷

作者： Chintapalli, Prashant Western Univ Ivey Business Sch London ON N6A 3K7 Canada

We address the combined problem of supplier (or vendor) selection and ordering decision when a buyer can choose to procure from multiple suppliers whose yields are uncertain and potentially correlated. We model this problem as a stochastic program with recourse in which the buyer purchases from the suppliers in the first period and, if needed, chooses to purchase from the spot market or from the suppliers with excess supply, whichever is beneficial, in the second period in order to meet the target procurement quantity. We solve the above problem using sample average approximation (SAA) technique that enables us to solve the problem easily in practice. We compare the performance of our solution with the certainty equivalent problem, which is practiced widely and which we use as the benchmark, to evaluate the efficacy of our approach. Next, we extend our model to incorpo-rate buyer's risk aversion with respect to the quantity procured. We reformulate the multi-sourcing problem as a mixed integer linear program (MILP) and adopt a statistical approach to account for buyer's risk aversion. Thus, we design a simple computational technique that provides an optimal sourcing policy from a set of suppliers when each supplier's yield is uncertain with a generic probability distribution.

关键词： Purchasing Supplier/vendor selection Supply/yield uncertainty Approximate dynamic programming stochastic programming with recourse

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A Complex Algorithm for Solving a Kind of stochastic programming

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Journal of Applied Mathematics and Physics 2020年第6期8卷 1016-1030页

作者： Yunpeng Luo Xinshun Ma Department of Mathematics and Physics North China Electric Power University Baoding China

Considering that the probability distribution of random variables in stochastic programming usually has incomplete information due to a perfect sample data in many real applications, this paper discusses a class of two-stage stochastic programming problems modeling with maximum minimum expectation compensation criterion (MaxEMin) under the probability distribution having linear partial information (LPI). In view of the nondifferentiability of this kind of stochastic programming modeling, an improved complex algorithm is designed and analyzed. This algorithm can effectively solve the nondifferentiable stochastic programming problem under LPI through the variable polyhedron iteration. The calculation and discussion of numerical examples show the effectiveness of the proposed algorithm.

关键词： stochastic programming with recourse Probability Distribution with Linear Partial Information Maximized Minimum Expectation Complex Algorithm

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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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A recourse Approach for the Capacitated Vehicle Routing Problem with Evidential Demands 14th

A Recourse Approach for the Capacitated Vehicle Routing Prob...

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14th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU)

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

ISBN: (纸本)9783319615813;9783319615806

The capacitated vehicle routing problem with stochastic demands can be modelled using either the chance-constrained approach or the recourse approach. In previous works, we extended the former approach to address the case where uncertainty on customer demands is represented by belief functions, that is where customers have so-called evidential demands. In this paper, we propose an extension of the recourse approach for this latter case. We also provide a technique that makes computations tractable for realistic situations. The feasibility of our approach is then shown by solving instances of this difficult problem using a metaheuristic algorithm.

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

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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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Customer allocation and production optimization under plant outages

Customer allocation and production optimization under plant ...

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5th International Conference on Industrial Engineering and Systems Management (IEEE IESM)

作者： Dubedout, Hugues Negau, Nicoleta Dejax, Pierre Yeung, Thomas Air Liquide Claude Delorme Res Ctr Jouy En Josas France Ecole Mines Nantes IRCCyN Nantes France

ISBN: (纸本)9782960053241

We consider the allocation of customers and optimization of production planning over a single time period (e.g., 1 year). The problem consists of deciding customer allocation to production plants coupled to the decision on the production level for each plant in order to satisfy the customers' demand. The decisions are taken under supply, production, distribution and contractual constraints. The main objective is to minimize the total estimated cost which includes production, distribution and contractual costs. The solution approach proposed is based on a stochastic programming with recourse formulation. We apply the proposed methodology to a real-world, large scale production and distribution problem under supply uncertainty occurring within the bulk supply chain of Air Liquide.

关键词： production planning customer allocation supply disruption stochastic programming with recourse MIP

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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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Incorporating geo-metallurgical information into mine production scheduling

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2011年第1期62卷 60-68页

作者： Kumral, M. Inonu Univ Sch Engn TR-44280 Malatya Turkey

Economic characterization ofmining parcels depends upon geo-metallurgical properties, which vary throughout orebody. Mine production scheduling should aim to obtain maximum utility from orebody in such a way as to ensure mine-mill reconciliation. As heterogeneity of geo-metallurgical variables increases, the scheduling will be a very complicated task. Geo-metallurgical and financial data used in the mine production scheduling are based on simulation and/or estimation generated from sparse drilling and unknown future events. Therefore, the scheduling process involves a significant degree of uncertainty. In order to deal with the uncertainty stemmed from geo-metallurgical and financial variables, two approaches are recommended in this paper. Firstly, mine production scheduling is formulated as a problem of stochastic programming with recourse. The extraction periods of mining blocks are treated as the first-stage variables and the block destinations represents a recourse vector. It is observed that the solution is implicitly robust. Secondly, the scheduling is expressed as a maximin problem to extract more uniform metal quantity in periods to coincide with mill requirements instead of maximization of net present value because the blending constraint in the traditional approach forces more uniform production. In the case where there is correlation between grade and geo-metallurgical variables, this model generates reasonably good results. Journal of the Operational Research Society (2011) 62, 60-68. doi:10.1057/jors.2009.174 Published online 10 February 2010

关键词： geo-metallurgical variables uncertainty stochastic programming with recourse mine production scheduling maximin problem

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