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multistage stochastic programming for integrated network optimization in hurricane relief logistics and evacuation planning

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NETWORKS 2025年第1期85卷 3-37页

作者： Bhattarai, Sudhan Song, Yongjia Clemson Univ Dept Ind Engn Clemson SC 29634 USA

In this article, we study the integrated hurricane relief logistics and evacuation planning (IHRLEP) problem, integrating hurricane evacuation and relief item pre-positioning operations that are typically treated separately. We propose a fully adaptive multistage stochastic programming (MSSP) model and solution approaches based on two-stage stochastic programming (2SSP). Utilizing historical forecast errors modeled using the auto-regressive model of order one, we generate hurricane scenarios and approximate the hurricane process as a Markov chain, and each Markovian state is characterized by the hurricane's location and intensity attributes. We conduct a comprehensive numerical experiment based on case studies motivated by Hurricane Florence and Hurricane Ian. Through the computational results, we demonstrate the value of fully adaptive policies given by the MSSP model over static ones given by the 2SSP model in terms of the out-of-sample performance. By conducting an extensive sensitivity analysis, we offer insights into how the value of fully adaptive policies varies in comparison to static ones with key problem parameters.

关键词： disaster relief logistics network optimization hurricane evacuation Markov chain multistage stochastic programming

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A multistage stochastic programming approach for drone-supported last-mile humanitarian logistics system planning

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ADVANCED ENGINEERING INFORMATICS 2025年 65卷

作者： Jin, Zhongyi Ng, Kam K. H. Zhang, Chenliang Chan, Y. Y. Qin, Yichen Hong Kong Polytech Univ Dept Aeronaut & Aviat Engn Hung Hom Hong Kong Peoples R China Shanghai Maritime Univ Sch Econ & Management Shanghai Peoples R China

Drone-supported last-mile humanitarian logistics systems playa crucial role inefficiently delivering essential relief items during disasters. In contrast to conventional truck-based transportation methods, drones provide a versatile and rapid transportation alternative. They are capable of navigating challenging terrain and bypassing damaged infrastructure. However, establishing an effective drone-supported last-mile humanitarian logistics system faces various challenges. This study introduces a novel approach to address these challenges by proposing a drone-supported last-mile humanitarian logistics system planning (DLHLSP) problem. The DLHLSP problem involves decision-making for both pre-disaster and post-disaster phases, taking into account the unique characteristics of drone-based delivery operations and uncertain demands. In the pre-disaster phase, decisions include determining drone-supported relief facility locations, drone deployment strategies, and drone visit schedules to disaster sites. Post-disaster decisions focus on inventory management, relief item procurement, and drone-based delivery operations. To capture the demand uncertainty in chaotic disaster environment, we establish a multistage stochastic programming model incorporating nonanticipativity constraints to make decisions at each stage without knowledge of the demand information in future time periods. Next, we employ the Benders decomposition algorithm to obtain exact solutions. Furthermore, we perform numerical experiments to verify the exact algorithm using randomly generated numerical instances. The results show that the algorithm significantly outperforms the Gurobi solver and could solve the problem of practical scale. Finally, the study validates the proposed model based on a case study of the Lushan earthquake in China and provides several managerial implications and insights. Overall, this research contributes to the field of humanitarian logistics by offering a comprehensive framework

关键词： logistics system multistage stochastic programming Nonanticipativity constraints Benders decomposition

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multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第3期290卷 886-900页

作者： Sha, Yue Zhang, Junlong Cao, Hui Tsinghua Univ Dept Ind Engn Beijing Peoples R China Suning Com Artificial Intelligent Res Ctr Nanjing Peoples R China

Job scheduling incorporated with material ordering can better meet practical needs and lead to overall cost reduction. In this paper, we present a stochastic approach for this joint optimization problem, considering uncertainties in job processing times and resource consumptions. We formulate this integrated problem as a multistage stochastic mixed-integer program involving endogenous uncertainties. Several theoretical properties that can reduce the model size are studied. Based on this, a branch-and-bound exact algorithm and a sampling-based approximate method are designed as solution algorithms. The effectiveness of the integrated scheduling approaches and the efficiency of the proposed solution algorithms are evaluated via numerical experiments. It is shown that our approach can greatly reduce the overall cost compared with the traditional separate production planning approach, especially when production resources are not very restricted. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Job scheduling Material ordering multistage stochastic programming Endogenous uncertainties

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Value function gradient learning for large-scale multistage stochastic programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期308卷 321-335页

作者： Lee, Jinkyu Bae, Sanghyeon Kim, Woo Chang Lee, Yongjae Korea Adv Inst Sci & Technol KAIST Dept Ind & Syst Engn Daejeon South Korea Ulsan Natl Inst Sci & Technol UNIST Dept Ind Engn Ulsan South Korea

A stagewise decomposition algorithm called "value function gradient learning" (VFGL) is proposed for large-scale multistage stochastic convex programs. VFGL finds the parameter values that best fit the gra-dient of the value function within a given parametric family. Widely used decomposition algorithms for multistage stochastic programming, such as stochastic dual dynamic programming (SDDP), approximate the value function by adding linear subgradient cuts at each iteration. Although this approach has been successful for linear problems, nonlinear problems may suffer from the increasing size of each subprob-lem as the iteration proceeds. On the other hand, VFGL has a fixed number of parameters;thus, the size of the subproblems remains constant throughout the iteration. Furthermore, VFGL can learn the param-eters by means of stochastic gradient descent, which means that it can be easil0y parallelized and does not require a scenario tree approximation of the underlying uncertainties. VFGL was compared with a deterministic equivalent formulation of the multistage stochastic programming problem and SDDP ap-proaches for three illustrative examples: production planning, hydrothermal generation, and the lifetime financial planning problem. Numerical examples show that VFGL generates high-quality solutions and is computationally efficient.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Decision processes Large-scale optimization multistage stochastic programming Stagewise decomposition Value function approximation

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Approximation of multistage stochastic programming problems by smoothed quantization

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REVIEW OF MANAGERIAL SCIENCE 2024年第7期18卷 2079-2114页

作者： Smid, Martin Kozmik, Vaclav Czech Acad Sci Inst Informat Theory & Automat Vodarenskou Vezi 4 Prague 8 Czech Republic Charles Univ Prague Fac Math & Phys Dept Probabil & Math Stat Sokolovska 49-83 Prague Czech Republic

We present an approximation technique for solving multistage stochastic programming problems with an underlying Markov stochastic process. This process is approximated by a discrete skeleton process, which is consequently smoothed down by means of the original unconditional distribution. Approximated in this way, the problem is solvable by means of Markov stochastic Dual Dynamic programming. We state an upper bound for the nested distance between the exact process and its approximation and discuss its convergence in the one-dimensional case. We further propose an adjustment of the approximation, which guarantees that the approximate problem is bounded. Finally, we apply our technique to a real-life production-emission trading problem and demonstrate the performance of its approximation given the "true" distribution of the random parameters.

关键词： multistage stochastic programming Approximation Markov dependence SDDP C61

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Optimization of the cropping pattern under seasonal fluctuations of surface water using multistage stochastic programming

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WATER SUPPLY 2022年第6期22卷 5716-5728页

作者： Mirzaei, Abbas Azarm, Hassan Naghavi, Somayeh Agr Sci & Nat Resources Univ Khuzestan Dept Agr Econ Mollasani Iran Shiraz Univ Sch Agr Dept Agr Econ Shiraz Iran Univ Jiroft Sch Agr Dept Agr Econ Kerman Iran

Regarding the rapid socio-economic development, increasing food demand and decreasing available resources, this challenge has become a major problem in the agricultural sector, causing the change consumption from surface water to groundwater resources and reduction of farmers' income. Therefore, optimal programming of the cropping pattern is necessary to handle such challenges. To accomplish the mentioned aim, a model of irrigation water allocation was developed based on the cropping pattern using multistage stochastic programming in accordance with the surface water supply fluctuations. In this model, different stochastic states are considered for all irrigation seasons in the irrigation network of Jiroft plain in Kerman province, which faces a severe shortage of surface water resources and the tendency of farmers to overuse groundwater resources. By solving multistage stochastic model, it can be observed that by utilizing an appropriate programming of the cropping pattern, more benefits for the farmers could be realized in the conditions of available surface water fluctuations. The results also indicated that if the surface water released into the canals increased in the spring, the share of profitable with high water consumption crops in pattern will increase, which will strengthen farmers' profits and pressure on groundwater resources. However, it could not expect to receive a significant reduction of groundwater resource consumption and a significant increase of cropping intensity. According to the results obtained, surface water resources cannot meet the water needs of the region, even by using optimal cropping patterns, and this has led to overuse of groundwater resources in this area. Finally, such planning can help adoption of desired policies for irrigation water management through the proper release of these resources.

关键词： groundwater consumption multistage stochastic programming optimal cropping pattern surface water fluctuations

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multistage stochastic programming: Algorithms, Modelling and Applications

Multistage Stochastic Programming: Algorithms, Modelling and...

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作者： Siddig, Murwan Clemson University

学位级别：Ph.D., Doctor of Philosophy

This dissertation comprises four different topics related to multistage stochastic programming (MSP) algorithms, modeling, and applications. First, we extend the adaptive partition-based approach for solving two-stage stochastic programs with a fixed recourse matrix and a fixed cost vector to the MSP setting, where the stochastic process is assumed to be stage-wise independent. The proposed algorithms integrate the adaptive partition-based strategy with a popular approach for solving multistage stochastic programs, the stochastic dual dynamic programming (SDDP) algorithm, according to two main strategies. These two strategies are distinct from each other in the manner by which they refine the partitions during the solution process. In particular, we propose a refinement outside SDDP strategy whereby we iteratively solve a coarse scenario tree induced by the partitions and refine the partitions in a separate step outside of SDDP, only when necessary. We also propose a refinement within SDDP strategy where the partitions are refined in conjunction with the machinery of the SDDP algorithm. We then use, within the two different refinement schemes, different tree-traversal strategies, which allow us to have some control over the size of the partitions. Our numerical experiments on a hydro-thermal power generation planning problem show the effectiveness of the proposed algorithms in comparison to the standard SDDP algorithm. Moreover, the results show that the algorithms with the refinement outside SDDP strategy outperform the ones with the refinement within SDDP strategy. Second, we study an important question related to solving MSP problems with a large number of stages. A common approach to tackle MSP problems with a large number of stages is a rolling-horizon (RH) procedure, where one solves a sequence of MSP problems with a smaller number of stages. This leads to a delicate issue of how many stages to include in the smaller problems used in the RH procedure. We study

关键词： multistage stochastic programming stochastic Dual Dynamic programming Algorithms Hydrothermal power generation Logistics costs Decision making Planning

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On the impact of deep learning-based time-series forecasts on multistage stochastic programming policies

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INFOR 2022年第2期60卷 133-164页

作者： Wang, Juyoung Cevik, Mucahit Bodur, Merve Univ Toronto Dept Mech & Ind Engn Toronto ON Canada Ryerson Univ Dept Mech & Ind Engn Toronto ON Canada

multistage stochastic programming provides a modeling framework for sequential decision-making problems that involve uncertainty. One typically overlooked aspect of this methodology is how uncertainty is incorporated into modeling. Traditionally, statistical forecasting techniques with simple forms, e.g. (first-order) autoregressive time-series models, are used to extract scenarios to be added to optimization models to represent the uncertain future. However, often times, the performance of these forecasting models are not thoroughly assessed. Motivated by the advances in probabilistic forecasting, we incorporate a deep learning-based time-series forecasting method into multistage stochastic programming framework, and compare it with the cases where a traditional forecasting method is employed to model the uncertainty. We assess the impact of more accurate forecasts on the quality of two commonly used look-ahead policies, a deterministic one and a two-stage one, in a rolling-horizon framework on a practical problem. Our results illustrate that more accurate forecasts contribute substantially to the model performance, and enable obtaining high-quality solutions even from computationally cheap heuristics. They also show that the probabilistic forecasting capabilities of deep learning-based methods can be especially beneficial when used as a (conditional) sampling tool for scenario-based models, and to predict the worst-case scenario for risk-averse models.

关键词： multistage stochastic programming policy evaluation lot-sizing problem time-series forecasting deep learning autoregressive process

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Seasonal operation planning of hydrogen-enabled multi-energy microgrids through multistage stochastic programming

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JOURNAL OF ENERGY STORAGE 2024年 85卷

作者： Sun, Xunhang Cao, Xiaoyu Li, Miaomiao Zhai, Qiaozhu Guan, Xiaohong Xi An Jiao Tong Univ Sch Automat Sci & Engn Xian 710049 Peoples R China Xi An Jiao Tong Univ Natl Innovat Platform Ctr Ind Educ Integrat Energy Xian 710049 Peoples R China Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA Tsinghua Univ Ctr Intelligent & Networked Syst Dept Automat Beijing 100084 Peoples R China

As a carbon-free storage medium, hydrogen has advantages in large-scale and long -term energy shifting, thereby mitigating the seasonal imbalance between energy supply and demands. By integrating hydrogen, electricity, heating and cooling, the hydrogen-enabled multi -energy microgrid (HMM) provides a desirable test bed for decarbonizing the energy and power systems. In this paper, we study the networked HMMs operation planning (NHOP) that optimizes the multi-timescale synergy of seasonal and short -term energy storage. To hedge against the complex demand-supply uncertainties (e.g., seasonal fluctuation and hourly variation of renewable power generation and energy demands), the NHOP problem is recast as a multistage stochastic mixed-integer program (MS-MIP). Moreover, to overcome the computational challenges, a nested decomposition algorithm based on stochastic dual dynamic integer programming (SDDiP) is tailored and implemented. Case studies on a 33 -bus test network with multiple HMMs demonstrate the economic benefits of our operation planning strategy. The proposed NHOP model can well capture the seasonal and intra-day dynamics of multi -type storage operation, which helps improve the cost-benefits under versatile practical situations. Also, the customized SDDiP algorithm shows a strong scalable capacity for efficiently computing large-scale MS-MIPs.

关键词： Hydrogen-enabled microgrids Multi-energy synergy Operation planning Seasonal hydrogen storage multistage stochastic programming

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Solving multistage stochastic linear programming via regularized linear decision rules: An application to hydrothermal dispatch planning

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期309卷 345-358页

作者： Nazare, Felipe Street, Alexandre Pontifical Catholic Univ Rio DeJaneiro Elect Engn Dept LAMPS PUC Rio Rio De Janeiro Brazil

The solution of multistage stochastic linear problems (MSLPs) represents a challenge for many applications. Long-term hydrothermal dispatch planning (LHDP) materializes this challenge in a real-world problem that affects electricity markets, economies, and natural resources worldwide. No closed-form solutions are available for MSLP and the definition of non-anticipative policies with high-quality outof-sample performance is crucial. Linear decision rules (LDRs) provide an interesting simulation-based framework for finding high-quality policies for MSLP through two-stage stochastic models. In practical applications, however, the number of parameters to be estimated when using an LDR may be close to or higher than the number of scenarios of the sample average approximation problem, thereby generating an in-sample overfit and poor performances in out-of-sample simulations. In this paper, we propose a novel regularized LDR to solve MSLP based on the AdaLASSO (adaptive least absolute shrinkage and selection operator). The goal is to use the parsimony principle, as largely studied in high-dimensional linear regression models, to obtain better out-of-sample performance for a LDR applied to MSLP. Computational experiments show that overfitting is a non-negligible threat when using the classical non-regularized LDR to solve the LHDP, one of the most studied MSLP with relevant applications in industry. Our analysis highlights the following benefits of the proposed framework in comparison to the non-regularized benchmark: 1) significant reductions in the number of non-zero coefficients (model parsimony), 2) substantial cost reductions in out-of-sample evaluations, and 3) improved spot-price profiles. (c) 2022 Elsevier B.V. All rights reserved.

关键词： OR in energy AdaLASSO Long -term hydrothermal dispatch planning multistage stochastic programming Regularized linear decision rules

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