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Mid-Term stochastic Scheduling of a Price-Maker Hydro Producer With Pumped Storage

IEEE TRANSACTIONS ON POWER SYSTEMS 2011年第4期26卷 1856-1865页

作者： Baslis, Costas G. Bakirtzis, Anastasios G. Aristotle Univ Thessaloniki Dept Elect & Comp Engn GR-54124 Thessaloniki Greece

A yearly stochastic self-scheduling model for a price-maker hydro producer is presented. In the short term, the producer aims at maximizing profits in the day-ahead market. Residual demand curves model the producer's interaction with his competitors and the load demand. A modification of the residual demand curve is proposed to enable the definition of optimal pumped-hydro bids. Multistage stochastic programming provides hedging against the mid-term uncertainty of inflows, load demand, and competitors' offers. The proposed method models the impact of short-term profit maximization decisions on mid-term scheduling within a compact stochastic mixed integer linear programming (MILP) approach. A test case with a three-stage, 90-scenario stochastic tree and data of the Greek Power System is presented. Results provide insight on both mid-term reservoir management and short-term market-based operation and indicate the feasibility of solving a very large-scale scheduling problem as a unique MILP using a commercial solver. The role of forward contracts in mitigating market power is also analyzed.

关键词： Hydro producer market power mid-term scheduling price-maker pumped storage stochastic mixed-integer programming

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Metamodel-based simulation optimisation for bed allocation

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2020年第20期58卷 6315-6335页

作者： Wang, Xiuxian Gong, Xuran Geng, Na Jiang, Zhibin Zhou, Liping Shanghai Jiao Tong Univ Dept Ind Engn & Management Shanghai Peoples R China Shanghai Jiao Tong Univ Sino US Global Logist Inst Shanghai Peoples R China Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai Peoples R China

Hospital beds are one of the most critical resources in healthcare institutions. In practice, beds are usually allocated to different departments in advance to accommodate different kinds of patients. Inappropriate decisions in the allocation may lead to the idleness of beds or the high rejection ratio of patients. Hospital managers are under pressure to allocate beds to different departments. High variability in patient arrivals and service times make the allocation problem complex and challenging to solve. To address this problem, a mixed-integer non-linear programming model is formulated, with the objective of minimising the weighted cost of rejecting patients and holding them waiting. To solve this model, a data-driven metamodel simulation optimisation method is proposed, in which metamodels, based on an analytical queuing model and a general function, are proposed and embedded into a general-purpose algorithm Adaptive Hyperbox Algorithm. The metamodels designated for local and global approximation are separately fitted using different sets of simulation observations, which can combine structural information and simulation information, and can provide insightful guidance in solution improvements. A case study is conducted based on the real data collected from a public hospital in Shanghai. Numerical results demonstrate the efficiency of the proposed method.

关键词： beds allocation metamodel simulation optimisation adaptive hyperbox algorithm stochastic mixed-integer programming

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Resilience-Oriented Design of Distribution Systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2019年第4期34卷 2880-2891页

作者： Ma, Shanshan Li, Shiyang Wang, Zhaoyu Qiu, Feng Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA CSG State Key Lab HVDC Elect Power Res Inst Guangzhou 510663 Guangdong Peoples R China Argonne Natl Lab Div Energy Syst 9700 S Cass Ave Argonne IL 60439 USA

Climatic hazards, such as hurricanes and ice storms, pose a top threat to power distribution systems. This paper pro poses a resilience-enhancing strategy to make distribution systems more resilient to climatic hazards. The proposed strategy consists of three resilience-oriented design (ROD) measures, namely line hardening, installing backup distributed generators (DGs), and adding automatic switches. The main challenges of this problem are modeling the spatio-temporal correlation among ROD decisions and uncertainties, capturing the entire failure-recovery-cost process, and solving the resultant large-scale mixed-integer stochastic problem efficiently. To deal with these challenges, we propose a hybrid stochastic process with deterministic casual structure to model the spatio-temporal correlations of uncertainties. A new two-stage stochastic mixed-integer linear program is formulated to capture the impacts of ROD decisions and uncertainties on system's responses to climatic hazards. The objective is to minimize the ROD investment cost in the first stage and the expected costs of loss of load, DC: operation, and damage repairs in the second stage. A dual decomposition algorithm with branch-and-bound is developed to solve the proposed model with binary variables in both stages. Case studies on the IEEE 123-bus test feeder show the proposed approach can improve the system resilience at minimum costs.

关键词： Distribution systems dual decomposition spatio-temporal correlated uncertainty resilience-oriented design stochastic mixed-integer programming

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A comparative study of decomposition algorithms for stochastic combinatorial optimization

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2008年第3期40卷 299-319页

作者： Ntaimo, Lewis Sen, Suvrajeet Texas A&M Univ Dept Ind & Syst Engn College Stn TX 77843 USA Ohio State Univ Dept Ind & Syst Engn Columbus OH 43210 USA

This paper presents comparative computational results using three decomposition algorithms on a battery of instances drawn from two different applications. In order to preserve the commonalities among the algorithms in our experiments, we have designed a testbed which is used to study instances arising in server location under uncertainty and strategic supply chain planning under uncertainty. Insights related to alternative implementation issues leading to more efficient implementations, benchmarks for serial processing, and scalability of the methods are also presented. The computational experience demonstrates the promising potential of the disjunctive decomposition (D-2) approach towards solving several large-scale problem instances from the two application areas. Furthermore, the study shows that convergence of the D-2 methods for stochastic combinatorial optimization (SCO) is in fact attainable since the methods scale well with the number of scenarios.

关键词： stochastic mixed-integer programming disjunctive decomposition stochastic server location strategic supply chain planning

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Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

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MATHEMATICAL programming 2016年第1期157卷 47-67页

作者： Gade, Dinakar Hackebeil, Gabriel Ryan, Sarah M. Watson, Jean-Paul Wets, Roger J. -B. Woodruff, David L. Sabre Holdings Southlake TX 76092 USA Sandia Natl Labs POB 5800 Albuquerque NM 87185 USA Texas A&M Univ College Stn TX 77843 USA Iowa State Univ Ames IA 50011 USA Univ Calif Davis Davis CA 95616 USA

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

关键词： stochastic mixed-integer programming Decomposition algorithms Lower bounding

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A scenario decomposition approach for stochastic production planning in sawmills

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2013年第1期64卷 48-59页

作者： Zanjani, M. Kazemi Nourelfath, M. Ait-Kadi, D. Concordia Univ Dept Mech & Ind Engn Montreal PQ H3H 1M8 Canada Univ Laval Quebec City PQ Canada Interuniv Res Ctr Enterprise Networks Logist & Tr Montreal PQ Canada

This study considers a real world stochastic multi-period, multi-product production planning problem. Motivated by the challenges encountered in sawmill production planning, the proposed model takes into account two important aspects: (i) randomness in yield and in demand;and (ii) set-up constraints. Rather than considering a single source of randomness, or ignoring set-up constraints as is typically the case in the literature, we retain all these characteristics while addressing real life-size instances of the problem. Uncertainties are modelled by a scenario tree in a multi-stage environment. In the case study, the resulting large-scale multi-stage stochastic mixed-integer model cannot be solved by using the mixed-integer solver of a commercial optimization package, such as CPLEX. Moreover, as the production planning model under discussion is a mixed-integer programming model lacking any special structure, the development of decomposition and cutting plane algorithms to obtain good solutions in a reasonable time-frame is not straightforward. We develop a scenario decomposition approach based on the progressive hedging algorithm, which iteratively solves the scenarios separately. CPLEX is then used for solving the sub-problems generated for each scenario. The proposed approach attempts to gradually steer the solutions of the sub-problems towards an implementable solution by adding some penalty terms in the objective function used when solving each scenario. Computational experiments for a real-world large-scale sawmill production planning model show the effectiveness of the proposed solution approach in finding good approximate solutions. Journal of the Operational Research Society (2013) 64, 48-59. doi:10.1057/jors.2012.28 Published online 4 April 2012

关键词： production planning stochastic mixed-integer programming scenario tree progressive hedging sawmills

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Lagrange dual bound computation for stochastic service network design

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期302卷 1097-1112页

作者： Jiang, Xiaoping Bai, Ruibin Ren, Jianfeng Li, Jiawei Kendall, Graham Univ Nottingham Ningbo China Sch Comp Sci Ningbo 315100 Peoples R China Natl Univ Def Technol Coll Elect Engn Hefei 230009 Peoples R China Univ Nottingham Sch Comp Sci Nottingham NG7 2RD England Univ Nottingham Sch Comp Sci Malaysia Campus Semenyih 43500 Malaysia

Information on lower bounds plays an important role in the development of exact and heuristic methods for stochastic service network design (SSND). In this paper, we consider the Lagrange dual problem of SSND for computing lower bounds. The Lagrange dual problem is obtained by introducing scenario bundling into scenario-wise decomposition of the SSND model and dualizing the non-anticipativity constraints in a Lagrangian fashion. Our theoretical analysis establishes the superiority of the resulting optimal Lagrange dual bound over that in the case of scenario-wise decomposition. The Lagrange dual problem is solved from the primal perspective by employing the recently proposed FW-PH algorithm, which combines Progressive Hedging with a Frank-Wolfe-like method. To improve the computing efficiency, scenario-wise decomposition in the FW-PH algorithm is replaced with bundle-wise decomposition, which divides the problem by scenario bundles into multiple-scenario subproblems, rather than by individual scenarios into single-scenario subproblems. Scenario bundles are constructed using Gaussian mixture models. Our convergence analysis shows that this improvement retains the desirable theoretical property of FW-PH about convergence to the optimal Lagrange dual value. Computational experiments on SSND instances demonstrate that the improved FW-PH algorithm is far superior to the basic version, providing either a dramatic saving in the run-time required to achieve convergence or a much tighter lower bound when terminated due to the time limit. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Transportation Service network design stochastic mixed-integer programming Lagrangian relaxation Progressive hedging

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Relating single-scenario facets to the convex hull of the extensive form of a stochastic single-node flow polytope

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OPERATIONS RESEARCH LETTERS 2020年第3期48卷 342-349页

作者： Mildebrath, David Gonzalez, Victor Hemmati, Mehdi Schaefer, Andrew J. Rice Univ Dept Computat & Appl Math Houston TX 77005 USA MIT Operat Res Ctr 77 Massachusetts Ave Cambridge MA 02139 USA

We study when a facet-defining inequality for a deterministic, single-scenario subproblem is also facet-defining for the extensive form of a two-stage stochastic mixed-integer linear program (SMIP). To answer this question, we introduce a novel stochastic variant of the well-known single-node flow (SNF) polytope, and present necessary and sufficient conditions for single-scenario facet-defining inequalities to be facet-defining for the extensive form. We further demonstrate that our stochastic SNF polytope is a relaxation of a broad subclass of SMIPs, illustrating its generality. (C) 2020 Published by Elsevier B.V.

关键词： stochastic mixed-integer programming Facets Polyhedral combinatorics

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On the robust decision-making in a supply chain under disruption risks

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2014年第22期52卷 6760-6781页

作者： Sawik, Tadeusz AGH Univ Sci & Technol Dept Operat Res & Informat Technol Krakow Poland

This paper considers a robust decision-making problem associated with supplies of parts and deliveries of finished products in a customer driven supply chain under disruption risks. The robustness refers to an equitably efficient performance of a supply chain in average-case as well as in the worst-case, which reflects the decision-makers common requirement to maintain an equally good performance of a supply chain under different conditions. Given a set of customer orders for products, the decision-maker needs to select suppliers of parts required to complete the orders, allocate the demand for parts among the selected suppliers and schedule the orders over the planning horizon, to equitably optimise average and worst-case performance of the supply chain. The supplies are subject to independent random local and regional disruptions. The obtained combinatorial stochastic optimisation problem is formulated as a mixed-integer program with conditional value-at-risk as a risk measure. The ordered weighted averaging aggregation of the expected value and the conditional value-at-risk of the selected optimality criterion is applied to obtain a robust solution. The risk-neutral, risk-averse and robust solutions that optimise, respectively average, worst-case and equitable average and worst-case performance of a supply chain are determined and compared for cost and customer service level objective functions. Numerical examples and computational results, in particular comparison with the mean-risk approach, are presented and some managerial insights are reported.

关键词： supplier selection customer order scheduling disruption risks equitable optimisation stochastic mixed-integer programming

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Strategic reliable supply chain network design: determining tradeoffs between cost and risk

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2023年第11期61卷 3621-3633页

作者： Meng, Lingpeng He, Junliang Hu, Shaolong Han, Chuanfeng Shanghai Maritime Univ China Inst FTZ Supply Chain Room 427Container Supply Chain Bldg Shanghai Peoples R China Southwest Jiaotong Univ Sch Econ & Management Chengdu Peoples R China Tongji Univ Sch Econ & Management Shanghai Peoples R China

The design of a supply chain network (SCN) should address two conflicting objectives, i.e. inexpensive yet reliable operation. This paper presents models to choose supply facilities and determine distribution options while considering the expected risk of not serving customers attributed to supply shortages. The goal is to design a reliable network with a lower cost under traditional cost objectives. We formulate a stochastic mixed-integer biobjective programming model considering the protection of facilities and solve this problem with a progressive hedging algorithm (PHA). We examine the tradeoff curve between the cost and risk through a case study involving Shanghai in China. The results indicate that substantial improvements in reliability can be reached with a limited increase in the total cost.

关键词： Supply chain network disruption stochastic mixed-integer programming multiobjective optimisation progressive hedging algorithm

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