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A Two-stage stochastic programming for the Integrated Emergency Mobility Facility Allocation and Road Network Design Under Uncertainty

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NETWORKS & SPATIAL ECONOMICS 2024年 1-42页

作者： Gong, Huatian Yang, Xiaoguang Tongji Univ Urban Mobil Inst Shanghai 201804 Peoples R China Tongji Univ Sch Traff & Transportat Engn Shanghai 201804 Peoples R China

Emergency Mobility Facilities (EMFs) possess the capability to relocate dynamically, providing adequate responses to fluctuations in emergent demand patterns across temporal and spatial dimensions. This study proposes a two-stage stochastic programming model that integrates the EMF allocation problem and the road network design problem for disaster preparedness. The model takes into account uncertainties arising from emergency demand and road network congestion levels under various sizes and timings of disaster occurrences. The first-stage decision involves determining the fleet size of EMFs and identifying which road links' travel time should be reduced. The second-stage decision pertains to the routing and schedule of each EMF for each disaster scenario. Due to considering various sources of uncertainty, the resulting model takes the form of a non-convex mixed-integer nonlinear program (MINLP). This poses computational challenges due to the inclusion of bilinear terms, implicit expressions, and the double-layered structure in the second-stage model, along with integer decision variables. A comprehensive set of techniques is applied to solve the model efficiently. This includes employing linearization techniques, converting the second-stage model into a single-level equivalent, transforming an integer variable into multiple binary variables, and utilizing other methods to equivalently reformulate the model into a mixed-integer linear programming problem (MILP). These transformations render the model amenable to solutions using the integer L-shaped method. A simplified example clarifies the solution procedures of the model and algorithm, establishing the theoretical foundation for their practical implementation. Subsequently, to empirically demonstrate the practicality of the proposed model and algorithm, a real-world case study is conducted, effectively validating their utility.

关键词： EMF allocation Road network design Uncertainties stochastic programming Integer L-shaped method

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Models and applications of stochastic programming with decision-dependent uncertainty in power systems: A review

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IET RENEWABLE POWER GENERATION 2024年第14期18卷 2819-2834页

作者： Yin, Wenqian Hou, Yunhe Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China HKU Shenzhen Inst Res & Innovat Shenzhen Peoples R China

stochastic programming is a competitive tool in power system uncertainty management. Traditionally, stochastic programming assumes uncertainties to be exogenous and independent of decisions. However, there are situations where statistical features of uncertain parameters are not constant but dependent on decisions, classifying such uncertainties as decision-dependent uncertainty (DDU). This is particularly the case with future power systems highly penetrated by multi-source uncertainties, where planning or operation decisions might exert unneglectable impacts on uncertainty features. This paper reviews the stochastic programming with DDU, especially those applied in the field of power systems. Mathematical properties of diversified types of DDU in stochastic programming are introduced, and a comprehensive review on sources and applications of DDU in power systems is presented. Then, focusing on a specific type of DDU, that is, decision-dependent probability distributions, a taxonomy of available modelling techniques and solution approaches for stochastic programming with this type of DDU and different structural features are presented and discussed. Eventually, the outlook of two-stage stochastic programming with DDU for future power system uncertainty management is explored, including both exploring the applications and developing efficient modelling and solution tools. This paper reviews the stochastic programming with decision-dependent uncertainty (DDU), especially those applied in the field of power systems. Mathematical properties of diversified types of DDU in stochastic programming are introduced, and a taxonomy of available modelling techniques and solution approaches for stochastic programming are presented and discussed. Eventually, insights of two-stage stochastic programming with DDU for future power system optimization are explored. image

关键词： power system operation and planning stochastic programming

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Carsharing equitable relocation problem: A two-stage stochastic programming approach with learning-embedded endogenous uncertainty in demand

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2024年 179卷

作者： Zhang, Si Sun, Huijun Liu, Yang Lv, Ying Wu, Jianjun Feng, Xiaoyan Beijing Jiaotong Univ Sch Syst Sci Beijing Peoples R China Natl Univ Singapore Dept Civil & Environm Engn Singapore Singapore Natl Univ Singapore Dept Ind Syst Engn & Management Singapore Singapore

Uncertain demand may exacerbate the imbalance of the supply-demand for a one-way carshar-ing system and complicate vehicle relocation decisions. To consider the effect of the uncertainty, this study proposes a two-stage stochastic nonlinear programming model, integrating long-term and short-term decisions and maximizing the profit of the carsharing companies. Specifically, in the first stage, tactical decisions of fleet sizing and initial vehicle distribution are determined before the realization of the uncertain demand. Operational decisions of both operator-based and user-based relocation are optimized in the second stage. Moreover, this paper first studies the user-based relocation incentives, which affect the distribution of uncertain demand with an endogenous relationship. A learning-embedded optimization method is introduced to learn such a distribution, enabling the decision-making optimization model to achieve higher performance under the guidance of the demand uncertainty. Second, we envision an equitable relocation issue that considers an uneven distribution of the unsatisfied demand with two different equity criteria measured from the aspects of stations and OD pairs, respectively. Third, the large problem scale, the nonlinear objective function and constraints, and the endogenous demand uncertainty constitute the nontrivial challenges to the feasible solution. For solving the problem efficiently, we linearize the nonlinear terms and develop a dedicated two-phase solution algorithm with a learning-embedded trust-region method in phase I to solve the continuous relaxation problem and a mixed-integer linear programming guided iterative rounding in phase II to obtain the integer solutions of carsharing operations. The solution algorithm adaptively bridges the learning and optimization process via the trust-region method with flexible sample generation. Finally, we conduct numerical experiments based on a real -world one-way carsharing system in Beijing to de

关键词： One-way carsharing relocation stochastic programming Endogenous uncertainty Discount Equity

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A stochastic programming model for ambulance (re)location-allocation under equitable coverage and multi-interval response time

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EXPERT SYSTEMS WITH APPLICATIONS 2024年第PartC期249卷

作者： Gago-Carro, Imanol Aldasoro, Unai Ceberio, Josu Merino, Maria BCAM Basque Ctr Appl Math Bilbao Spain Univ Basque Country UPV EHU Dept Math Leioa Spain Univ Basque Country UPV EHU Dept Appl Math Lejona Spain Univ Basque Country UPV EHU Dept Comp Sci & Artificial Intelligence Gipuzkoa 20018 Spain Barrio Sarriena S-N Leioa 48940 Spain

Emergency Medical Services are essential for health systems as their effective management can improve patient prognosis. Nevertheless, designing an optimized distribution of resources is a difficult task due to the complex nature of these systems. Moreover, locating the resources is particularly challenging in heterogeneous density territories where, in addition to their efficient management, the equity principle in the medical access of inhabitants of rural areas is also desirable. This paper approaches the ambulance (re)location-allocation problem in the geographical area of the Basque Country. The area has three major cities, which account for a third of the emergencies, while there are few emergencies in rural areas, with a sparse population. To that end, a two-stage stochastic 0-1 integer linear programming model that balances the response time between densely populated and isolated areas is proposed. Specifically, the model incorporates two relevant principles: (1) optimizing emergency attendance through the option of allocating ambulances via a multi-interval response time and (2) equitably responding to emergencies so remote areas are not neglected. Conducted experiments have been validated and indicate that the proposed model can improve the success rate in rural areas by 23 percentage points, while reducing the overall success rate by less than 9 percentage points.

关键词： stochastic programming Location-allocation OR in health services Regional equity Multi-interval response time

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Urban transit decarbonization via stochastic programming and statistical inference under uncertainty

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TRANSPORTATION RESEARCH PART D-TRANSPORT AND ENVIRONMENT 2025年 142卷

作者： Wang, Jing Shirkoohi, Majid Gholami Akter, Rubina Merida, Walter Univ British Columbia Clean Energy Res Ctr 2360 East Mall Vancouver BC V6T 1Z3 Canada

Urban transit decarbonization is integral to achieving a net-zero public transportation systems. This work proposes an optimization model for bus fleet transition planning, involving purchases and allocation to routes, fueling and charging infrastructure, and financing. The model adopts stochastic programming to address decision-making under uncertainty and is formulated as a mixed-integer linear program. A confidence interval estimation method is derived to accommodate diverse decision values and non-uniform scenario probabilities, alongside an efficient scenario construction approach. A case study of the Metro Vancouver regional bus network is conducted to explore transition pathways for adopting battery electric and hydrogen fuel cell buses. Results indicate that shifting to a battery electric fleet is more cost-effective overall, while the hydrogen pathway demands smaller infrastructure investments. The competitiveness of hydrogen could significantly improve if the substantial potential for cost reductions is realized. A mixed fleet can integrate the advantages of both pathways.

关键词： Transit decarbonization Optimization under uncertainty stochastic programming Statistical inference Battery electric bus Hydrogen fuel cell bus

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Distribution-free algorithms for predictive stochastic programming in the presence of streaming data

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2024年第2期87卷 355-395页

作者： Diao, Shuotao Sen, Suvrajeet Univ Southern Calif Daniel J Epstein Dept Ind & Syst Engn 3715 McClintock Ave Los Angeles CA 90089 USA

This paper studies a fusion of concepts from stochastic programming and non-parametric statistical learning in which data is available in the form of covariates interpreted as predictors and responses. Such models are designed to impart greater agility, allowing decisions under uncertainty to adapt to the knowledge of predictors (leading indicators). This paper studies two classes of methods for such joint prediction-optimization models. One of the methods may be classified as a first-order method, whereas the other studies piecewise linear approximations. Both of these methods are based on coupling non-parametric estimation for predictive purposes, and optimization for decision-making within one unified framework. In addition, our study incorporates several non-parametric estimation schemes, including k nearest neighbors (kNN) and other standard kernel estimators. Our computational results demonstrate that the new algorithms proposed in this paper outperform traditional approaches which were not designed for streaming data applications requiring simultaneous estimation and optimization as important design features for such algorithms. For instance, coupling kNN with stochastic Decomposition (SD) turns out to be over 40 times faster than an online version of Benders Decomposition while finding decisions of similar quality. Such computational results motivate a paradigm shift in optimization algorithms that are intended for modern streaming applications.

关键词： stochastic programming Non-parametric statistical estimation

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Enhancing explainability of stochastic programming solutions via scenario and recourse reduction

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OPTIMIZATION AND ENGINEERING 2024年第2期25卷 605-+页

作者： Rathi, Tushar Gupta, Rishabh Pinto, Jose M. M. Zhang, Qi Univ Minnesota Dept Chem Engn & Mat Sci Minneapolis MN 55455 USA Linde plc Linde Digital Amer Danbury CT 06810 USA

stochastic programming (SP) is a well-studied framework for modeling optimization problems under uncertainty. However, despite the significant advancements in solving large SP models, they are not widely used in industrial practice, often because SP solutions are difficult to understand and hence not trusted by the user. Unlike deterministic optimization models, SP models generally involve recourse variables that can take different values for different scenarios (i.e. uncertainty realizations), which makes interpreting their solutions a challenge when large numbers of scenarios and recourse variables are considered. In this work, we propose scenario and recourse reduction methods that can help enhance the explainability of SP solutions. Focusing on two-stage linear SP, the goal is to build reduced models, with much smaller sets of scenarios and recourse variables, that are easier to analyze yet still capture the key features of the original problems. Specifically, we explicitly search for reduced models that generate the same or close to the same first-stage decisions as the original SP models. The efficacy of the proposed methods is demonstrated in computational case studies involving problems of industrial relevance and size.

关键词： stochastic programming Explainability Scenario reduction Recourse reduction

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A two-stage stochastic programming model and parallel Master-Slave adaptive GA for flexible Seru system formation

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2024年第4期62卷 1144-1161页

作者： Ren, Yuhong Tang, Jiafu Yu, Yang Li, Xiaolong Dongbei Univ Finance & Econ Sch Management Sci & Engn Dalian Peoples R China Northeastern Univ Dept Intelligent Data & Syst Engn State Key Lab Synthet Automation Proc Ind Shenyang Peoples R China

High flexibility is an important feature of seru system that has received less attention. In this paper, we discuss how to do such flexible seru system formation, especially focusing on the strategic decision phase. We formulate the flexible seru system formation problem (FSFP) as a nonlinear programming model to evaluate flexibility performance in terms of flexibility-investment cost and flexibility-loss cost. To exactly obtain the optimal solution of the FSFP, we transform the nonlinear model into a linear one and solve it with Gurobi solver. For the large-scale problem, we proposed a parallel Master-Slave adaptive genetic algorithm (PMSA-GA) by transforming it into a two-stage stochastic programming model. The adaptive selection is used to improve the quality of solutions in PMSA-GA. To reduce the computational time, multiple populations of seru formation evolve in parallel with the assistance of the Master-Slave mechanism. Extensive experiments are tested to evaluate the performance of the proposed model and algorithm, and the effect of cost parameters on the system performance is discussed. The results show that the FSFP model takes the property of dynamic demand into account and is more suitable for dynamic demand environments than the task-oriented seru formation (TOSF) strategy from the previous literature.

关键词： Seru system flexibility seru system formation stochastic programming Gurobi solver

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Two-stage stochastic programming approach for fleet sizing and allocating rail wagon under uncertain demand

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COMPUTERS & INDUSTRIAL ENGINEERING 2024年 188卷

作者： Karmanesh, Yasin Bagheri, Morteza Hasany, Reza Mohammad Pishvaee, Mir Saman Iran Univ Sci & Technol Sch Railway Engn Tehran 16846 Iran Iran Univ Sci & Technol Sch Ind Engn Tehran 16846 Iran

In this paper, a scenario-based two-stage stochastic programming model has been developed to determine the optimal number of wagons and allocation of full and empty wagons during different time periods to optimize profit. In allocating wagons, when the wagon arrives at a station, it is not possible to reallocate the wagon at the moment of arrival, this issue has not been addressed before. In addition, the possibility of renting wagons to/ from other companies is concerned in the railway planning. These two actions have not been addressed before. In this paper, firstly, the research problem is formulated in the form of an integer programming model with deterministic data. Due to the inherent uncertainty in the transportation demands of the real case study, the deterministic model has been transformed into a scenario-based two-stage stochastic programming model with recourse. Then the L-shaped method was proposed to solve the stochastic model and by using it for 34 instances, its better efficiency than CPLEX software was shown. The stochastic model was solved using the L-shaped method and the results show that the studied company should rent 749 wagons to meet the demands, and on average, the stochastic model is expected to have about 1.1% added value in the company's profit compared to the deterministic model.

关键词： L-shaped method Optimization stochastic programming Integer programming Fleet sizing Fleet allocation

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SAMPLE AVERAGE APPROXIMATION FOR stochastic programming WITH EQUALITY CONSTRAINTS

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SIAM JOURNAL ON OPTIMIZATION 2024年第4期34卷 3506-3533页

作者： Lew, Thomas Bonalli, Riccardo Pavone, Marco Stanford Univ Dept Aeronaut & Astronaut Stanford CA 94305 USA Univ Paris Saclay Lab Signals & Syst CNRS CentraleSupelec Gif Sur Yvette France

We revisit the sample average approximation (SAA) approach for nonconvex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic optimality guarantees as the sample size increases. To address this issue, we relax the equality constraints. Then, we prove the asymptotic optimality of the modified SAA approach under mild smoothness and boundedness conditions on the equality constraint functions. Our analysis uses random set theory and concentration inequalities to characterize the approximation error from the sampling procedure. We apply our approach and analysis to the problem of stochastic optimal control for nonlinear dynamical systems under external disturbances modeled by a Wiener process. Numerical results on relevant stochastic programs show the reliability of the proposed approach. Results on a rocket-powered descent problem show that our computed solutions allow for significant uncertainty reduction compared to a deterministic baseline.

关键词： stochastic programming sampling methods concentration inequalities random set theory stochastic optimal control

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