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Strong Formulations for Multistage stochastic Self-Scheduling Unit Commitment

OPERATIONS RESEARCH 2016年第6期64卷 1482-1498页

作者： Pan, Kai Guan, Yongpei Hong Kong Polytech Univ Fac Business Dept Logist & Maritime Studies Kowloon Hong Kong Peoples R China Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

With the increasing penetration of renewable energy into the power grid system, the volatility of real-time electricity prices increases significantly. This brings challenges for independent power producers to provide optimal bidding strategies. The traditional approaches of only attending the day-ahead market might not be profitable enough without taking advantage of real-time price volatility. In this paper, we study the optimal bidding strategies for the independent power producers utilizing self-scheduling strategies to participate in the real-time market considering real-time electricity price volatility, with the objective of maximizing the total expected profit. Considering the correlations of renewable energy generation outputs among different time periods, the correlations of real-time prices are captured in our modeling framework, in which we explore a multistage stochastic scenario tree to formulate the price uncertainties. Accordingly, the derived multistage stochastic self-scheduling unit commitment problem is transformed as a deterministic equivalent mixed-integer linear programming formulation. To overcome the curse of dimensionality, we develop strong valid inequalities for the derived stochastic unit commitment polytope to speed up the algorithms to solve the problem. In particular, we derive strong valid inequalities that can provide the convex hull descriptions for the two-period case and a special class of the three-period cases with rigorous proofs provided. Furthermore, strong valid inequalities, including facet-defining proofs, for multistage cases are proposed to further strengthen the model. Finally, numerical experiments verify the effectiveness of our derived strong valid inequalities by incorporating them in a branch-and-cut framework.

关键词： stochastic integer programming cutting planes self-scheduling unit commitment

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A stochastic Optimization Model for Designing Last Mile Relief Networks

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TRANSPORTATION SCIENCE 2016年第3期50卷 1092-1113页

作者： Noyan, Nilay Balcik, Burcu Atakan, Semih Sabanci Univ Ind Engn Program TR-34956 Istanbul Turkey Ozyegin Univ Dept Ind Engn TR-34794 Istanbul Turkey

In this study, we introduce a distribution network design problem that determines the locations and capacities of the relief distribution points in the last mile network, while considering demand- and network-related uncertainties in the post-disaster environment. The problem addresses the critical concerns of relief organizations in designing last mile networks, which are providing accessible and equitable service to beneficiaries. We focus on two types of supply allocation policies and propose a hybrid version considering their different implications on equity and accessibility. Then, we develop a two-stage stochastic programming model that incorporates the hybrid allocation policy and achieves high levels of accessibility and equity simultaneously. We devise a branch-and-cut algorithm based on Benders decomposition to solve large problem instances in reasonable times and conduct a numerical study to demonstrate the computational effectiveness of the solution method. We also illustrate the application of our model on a case study based on real-world data from the 2011 Van earthquake in Turkey.

关键词： distribution network design post-disaster humanitarian relief accessibility equity stochastic integer programming L-shaped method branch-and-cut

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Optimization of Integrated Design and Operation of Microgrids Under Uncertainty 19

Optimization of Integrated Design and Operation of Microgrid...

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19th Power Systems Computation Conference (PSCC)

作者： Moshi, Godfrey Gladson Bovo, Cristian Berizzi, Alberto Taccari, Leonardo Politecn Milan Dipartimento Energia Via La Masa 34 Milan Italy Politecn Milan DEIB Operat Res Grp Piazza Leonardo da Vinci 32 I-20133 Milan Italy

ISBN: (纸本)9788894105124

We present two Mixed-integer Linear programming (MILP) models for a complete microgrid planning problem which consider uncertainties in the main input data (hourly solar irradiance, wind speed and electricity demand). The first model adopts a Two-Stage stochastic integer programming (2SSIP) formulation with discrete scenarios, whereas the second model adopts a Robust Optimization (RO) formulation with polyhedral uncertainty sets. The aim is to determine the optimal combination, capacities, and number of components to install in the microgrid considering long-term operations and uncertainty in the main input data. The 2SSIP model offers the possibility to obtain a planning solution using discrete scenarios sampled from appropriate probability distributions. The RO model gives a planning solution which is guaranteed to be feasible for any realization of input data within specified uncertainty sets. To show and compare the effectiveness of these models, we present a case study in which we apply the two models to plan a standalone microgrid in Singida, Tanzania. The proposed models can be applied for planning and detailed feasibility studies on generic microgrids with renewables, storage batteries and diesel generators.

关键词： microgrid planning optimization robust optimization stochastic integer programming uncertainty

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Appointment Scheduling of Diagnostic Facilities Subject to Non-stationary Emergency Demand and Waiting Time Targets 21

Appointment Scheduling of Diagnostic Facilities Subject to N...

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21st IEEE International Conference on Emerging Technologies and Factory Automation (ETFA)

作者： Wen, Jing Geng, Na Xie, Xiaolan Shanghai Jiao Tong Univ Shanghai 200240 Peoples R China Ecole Natl Super Mines F-42023 St Etienne France

ISBN: (纸本)9781509013142

Diagnostic facility is one of the most important critical resources in the hospital. Patient scheduling plays an important role in managing these facilities, especially when they are shared between regular and emergency patients. Due to the non-stationary emergency arrival and waiting time targets of emergency patients, it is challenging for hospital managers to make appointment scheduling decision and real time scheduling decisions, i.e., how many regular patients could reserve the service and how to coordinate the service of both types of patients. To deal with this problem, this paper proposes a stochastic integer programming model by considering the uncertainty of emergency patients and their waiting time requirement. The objective is to minimize the weighted idle time, overtime, and patients' waiting time. Monte Carlo optimization is used to solve this model. Numerical experiments are proposed to show the usefulness of the proposed model for investigation of the influence of different parameters.

关键词： healthcare appointment scheduling stochastic integer programming Monte Carlo optimization

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Decomposition Algorithms and Parallel Computing for Chance-Constrained and stochastic integer Programs with Applications

Decomposition Algorithms and Parallel Computing for Chance-C...

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作者： Deng, Yan University of Michigan

学位级别：Ph.D.

The focus of this dissertation is to develop solution methods for stochastic programs with binary decisions and risk-averse features such as chance constraint or risk-minimizing objective. We approach these problems through scenario-based reformulations, which are often of intractable scale due to the use of a large number of scenarios to represent the uncertainty. Our goal is to develop specialized decomposition algorithms for solving the problem in reasonable time. We first study a surgery planning problem with uncertainty in surgery durations. A common practice is to first assign operating rooms to surgeries and then to develop schedules. We propose a chance-constrained model that integrates these two steps. A branch-and-cut algorithm is developed, which exploits valid inequalities derived from a bin packing problem and single-machine scheduling problems. We also discuss models and solutions given ambiguous distributional information. Computational results demonstrate the efficacy of the proposed algorithm and provide insights into enhancing performance by the proposed model. Next, we study general chance-constrained 0-1 programs, where decisions made before realization of uncertainty are binary. We develop dual decomposition algorithms that find solutions through bounds and cuts efficiently. We derive a proposition about computing the Lagrangian dual whose application substantially reduces the number of subproblems to solve, and deploy cut aggregation that accelerates the solution of subproblems. We also explore parallel schemes to implement our algorithms in a distributed system. All of them improve the efficacy effectively. We then study dual decomposition for risk-averse stochastic 0-1 programs, which minimize the risk of some random outcome measured by a coherent risk function. Using generic dual representations for coherent risk measures, we derive equivalent risk-neutral minimax reformulations, to which dual decomposition methods apply. We investigate how

关键词： stochastic integer programming Decomposition algorithms Chance-constrained programming Risk-averse stochastic programming Parallel computing Thesis

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Block-based outpatient clinic appointments scheduling under open-access policy

Block-based outpatient clinic appointments scheduling under ...

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作者： Fu, Yu Texas A&M University

学位级别：Ph.D.

Outpatient clinic appointment scheduling is an important topic in OR/IE studies. Open-access policy shows its strength in improving patient access and satisfaction, as well as reducing no-show rate. The traditional far-in-advance scheduling plays an important role in handling chronic and follow-up care. This dissertation discusses a hybrid policy under which a clinic deals with three types of patients. The first type of patients are those who request their appointments before the visit day. The second type of patients schedule their appointment on the visit day. The third type of patients are walk-in patients who go to the clinic without appointments and wait to see the physician in turn. In this dissertation, the online scheduling policy is addressed for the Type 2 and Type 3 patients, and the offline scheduling policy is used for the Type 1 patients. For the online scheduling policy, two stochastic integer programming (SIP) models are built under two different sets of assumptions. The first set of assumptions ignores the endogenous uncertainty in the problem. An aggregate assigning method is proposed with the deterministic equivalent problem (DEP) model. This method is demonstrated to be better than the traditional one-at-a-time assignment through both overestimation and underestimation numerical examples. The DEP formulations are solved using the proposed bound-based sampling method, which provides approximated solutions and reasonable sample size with the least gap between lower and upper bound of the original objective value. On the basis of the first set of assumptions and the SIP model, the second set of assumptions considers patient no-shows, preference, cancellations and lateness, which introduce endogenous uncertainty into the SIP model. A modified L-shaped method and aggregated multicut L-shaped method are designed to handle the model with decision dependent distribution parameter. Distinctive optimality cut generation schemes are proposed for three types

关键词： appointment scheduling open-access policy stochastic integer programming endogenous uncertainty L-shaped method aggregated multicut L-shaped method job shop maximum independent set bin packing GRASP simulated annealing Thesis

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A stochastic programming Model for Fuel Treatment Management

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FORESTS 2015年第6期6卷 2148-2162页

作者： Kabli, Mohannad Gan, Jianbang Ntaimo, Lewis Texas A&M Univ Dept Ind & Syst Engn College Stn TX 77843 USA Texas A&M Univ Dept Ecosyst Sci & Management College Stn TX 77843 USA

This work considers a two-stage stochastic integer programming (SIP) approach for optimizing fuel treatment planning under uncertainty in weather and fire occurrence for rural forests. Given a set of areas for potentially performing fuel treatment, the problem is to decide the best treatment option for each area under uncertainty in future weather and fire occurrence. A two-stage SIP model is devised whose objective is to minimize the here-and-now cost of fuel treatment in the first-stage, plus the expected future costs due to uncertain impact from potential fires in the second-stage calculated as ecosystem services losses. The model considers four fuel treatment options: no treatment, mechanical thinning, prescribed fire, and grazing. Several constraints such as budgetary and labor constraints are included in the model and a standard fire behavior model is used to estimate some of the parameters of the model such as fuel levels at the beginning of the fire season. The SIP model was applied to data for a study area in East Texas with 15 treatment areas under different weather scenarios. The results of the study show, for example, that unless the expected ecosystem services values for an area outweigh fuel treatment costs, no treatment is the best choice for the area. Thus the valuation of the area together with the probability of fire occurrence and behavior strongly drive fuel treatment choices.

关键词： fuel treatment wildfire behavior wildfire risk optimization stochastic integer programming

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Optimization of stochastic virus detection in contact networks

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OPERATIONS RESEARCH LETTERS 2015年第1期43卷 59-64页

作者： Lee, Jinho Hasenbein, John J. Morton, David P. Korea Naval Acad Dept Management Sci Changwon Si 645797 Kyungsangnam Do South Korea Univ Texas Austin Dept Mech Engn Grad Program Operat Res & Ind Engn Austin TX 78712 USA Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

We develop network models to represent the dynamics of a virus spreading in a contact network. Based on the resulting dynamics governing the spread, we present optimization models to rapidly detect the virus. We consider two goals, maximizing the probability of detecting a virus by a time threshold and minimizing the expected time to detection. We establish submodularity results for these objective functions and, using data from a mobile service provider, we show that a greedy heuristic performs surprisingly well. (C) 2014 Elsevier B.V. All rights reserved.

关键词： stochastic spread model Submodular optimization stochastic integer programming

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The Wartime Portfolio Selection Problem

The Wartime Portfolio Selection Problem

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作者： Woodaman, Ronald F. A. George Mason University

学位级别：Ph.D.

This thesis describes the research conducted to support the optimal selection of a portfolio of military solutions during wartime. During peacetime, the United States military selects a portfolio of military solutions holistically as part of an annual budgetary planning cycle supported by long-term planning. During wartime, this annual review and decision process is not responsive to the rapid cycles of battlefield adaptation and the resulting exploitation of opposing capability gaps by adversaries. The long-running vulnerability of U.S. forces in Iraq and Afghanistan to Improvised Explosive Device (IED) attacks, as the threat's tactics and techniques evolved during these conflicts, provides a poignant example. During conflict, opportunities to improve the force arrive irregularly over time and are difficult to anticipate. When potential solutions are identified, these must be rapidly pursued, subject to resource constraints. Bad decisions early rob resources from better opportunities that arrive later, while good opportunities unduly delayed may lead to lost opportunities on the battlefield. We develop quantitative methods to support decision makers in the optimal selection of solutions in this context, employing as our motivating case study the challenges faced by the United States Department of Defense's Joint Improvised Explosive Device Defeat Organization (JIEDDO). For example, in fiscal year 2013, the JIEDDO budget was $1.6 billion. This organization had to make counter-IED solution selection decisions continuously as these arrived, without knowing precisely what other opportunities might occur in the future months. Two key aspects of this problem are how to measure the military value of potential solutions, and how to make the best choices as opportunities arrive. Correspondingly, this dissertation examines these two sides: valuation of war-fighting solutions in an uncertain and time-sensitive context, and, given a valuation method, methods for optimal sequen

关键词： Operations research Statistics Computer science approximate dynamic programming dynamic stochastic knapsack problem multi-objective decision analysis sequential decision analysis stochastic integer programming stochastic optimization

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On multistage stochastic integer programming for incorporating logical constraints in asset and liability management under uncertainty

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COMPUTATIONAL MANAGEMENT SCIENCE 2009年第3期6卷 307-327页

作者： Escudero, Laureano F. Garin, Araceli Merino, Maria Perez, Gloria Univ Miguel Hernandez Ctr Invest Operat Elche Alicante Spain Univ Basque Country Dept Econ Aplicada 3 Bilbao Vizcaya Spain Univ Basque Country Dept Matemat Aplicada Estadist & IO Leioa Vizcaya Spain

We present a model for optimizing a mean-risk function of the terminal wealth for a fixed income asset portfolio restructuring with uncertainty in the interest rate path and the liabilities along a given time horizon. Some logical constraints are considered to be satisfied by the assets portfolio. Uncertainty is represented by a scenario tree and is dealt with by a multistage stochastic mixed 0-1 model with complete recourse. The problem is modelled as a splitting variable representation of the Deterministic Equivalent Model for the stochastic model, where the 0-1 variables and the continuous variables appear at any stage. A Branch-and-Fix Coordination approach for the multistage 0-1 program solving is proposed. Some computational experience is reported.

关键词： Multistage scenario tree Assets and liabilities stochastic integer programming Branch-and-Fix Coordination Mean-risk function

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