Cloud seeding optimization under uncertainty: A Markov chain approach in a two-stage fuzzy-stochastic framework

•Proposing an integrated two-stage stochastic framework for cloud seeding decisions.•Modeling of cloud seeding impact using a Markov chain framework.•Lagrangian relaxation enhances solution efficiency for large-scale problems.•Valid inequalities reduce the complexity of binary variables.•Scenario-ba...

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Veröffentlicht in:Operations Research Perspectives Jg. 15; S. 100356
Hauptverfasser: Sadeghi, Mohammad, Yaghoubi, Saeed
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.12.2025
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ISSN:2214-7160, 2214-7160
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Abstract •Proposing an integrated two-stage stochastic framework for cloud seeding decisions.•Modeling of cloud seeding impact using a Markov chain framework.•Lagrangian relaxation enhances solution efficiency for large-scale problems.•Valid inequalities reduce the complexity of binary variables.•Scenario-based model achieves 11.7 % VSS and 16.5 % EVPI in decision-making. The occurrence of sequential droughts and various forms of water shortages globally underscores the urgent need for sustainable water management solutions. In this context, cloud seeding has gained attention for its potential to enhance precipitation, yet its effectiveness is often uncertain due to complex cloud microphysics and atmospheric conditions. Acknowledging the inherent uncertainty in this endeavor, in this study, we employ a two-stage stochastic framework, integrating strategic decisions (facility location and network design) and operational realizations (seeding planning according to storm trajectories). Additionally, our model also considers fuzzy nature of seeding parameters. Above all, we develop a Markov chain procedure to mathematically model the prediction of expected increase in precipitation across cloud seeding decision-making processes. The integration of these stochastic methods into existing deterministic models from the literature results in a multi-objective Mixed-Integer Linear Programming (MILP) model designed to maximize rain probability and coverage while minimizing system-wide costs. To enhance the scalability and efficiency of the model, valid inequalities are developed to reduce the domain of binary variables. Additionally, a Lagrangian relaxation technique is proposed, yielding exact optimal solutions within reasonable timeframes and facilitating the handling of continuous space instances. Finally, a real-world case study in Iran demonstrates significant enhancements in precipitation predictions, with the Markov chain procedure showing an average 55 % increase in expected rain probability based on optimized seeding decisions. Scenario-based stochastic programming yields an 11.7 % value of stochastic solution and 16.5 % expected value of perfect information for cloud seeding initiatives.
AbstractList •Proposing an integrated two-stage stochastic framework for cloud seeding decisions.•Modeling of cloud seeding impact using a Markov chain framework.•Lagrangian relaxation enhances solution efficiency for large-scale problems.•Valid inequalities reduce the complexity of binary variables.•Scenario-based model achieves 11.7 % VSS and 16.5 % EVPI in decision-making. The occurrence of sequential droughts and various forms of water shortages globally underscores the urgent need for sustainable water management solutions. In this context, cloud seeding has gained attention for its potential to enhance precipitation, yet its effectiveness is often uncertain due to complex cloud microphysics and atmospheric conditions. Acknowledging the inherent uncertainty in this endeavor, in this study, we employ a two-stage stochastic framework, integrating strategic decisions (facility location and network design) and operational realizations (seeding planning according to storm trajectories). Additionally, our model also considers fuzzy nature of seeding parameters. Above all, we develop a Markov chain procedure to mathematically model the prediction of expected increase in precipitation across cloud seeding decision-making processes. The integration of these stochastic methods into existing deterministic models from the literature results in a multi-objective Mixed-Integer Linear Programming (MILP) model designed to maximize rain probability and coverage while minimizing system-wide costs. To enhance the scalability and efficiency of the model, valid inequalities are developed to reduce the domain of binary variables. Additionally, a Lagrangian relaxation technique is proposed, yielding exact optimal solutions within reasonable timeframes and facilitating the handling of continuous space instances. Finally, a real-world case study in Iran demonstrates significant enhancements in precipitation predictions, with the Markov chain procedure showing an average 55 % increase in expected rain probability based on optimized seeding decisions. Scenario-based stochastic programming yields an 11.7 % value of stochastic solution and 16.5 % expected value of perfect information for cloud seeding initiatives.
The occurrence of sequential droughts and various forms of water shortages globally underscores the urgent need for sustainable water management solutions. In this context, cloud seeding has gained attention for its potential to enhance precipitation, yet its effectiveness is often uncertain due to complex cloud microphysics and atmospheric conditions. Acknowledging the inherent uncertainty in this endeavor, in this study, we employ a two-stage stochastic framework, integrating strategic decisions (facility location and network design) and operational realizations (seeding planning according to storm trajectories). Additionally, our model also considers fuzzy nature of seeding parameters. Above all, we develop a Markov chain procedure to mathematically model the prediction of expected increase in precipitation across cloud seeding decision-making processes. The integration of these stochastic methods into existing deterministic models from the literature results in a multi-objective Mixed-Integer Linear Programming (MILP) model designed to maximize rain probability and coverage while minimizing system-wide costs. To enhance the scalability and efficiency of the model, valid inequalities are developed to reduce the domain of binary variables. Additionally, a Lagrangian relaxation technique is proposed, yielding exact optimal solutions within reasonable timeframes and facilitating the handling of continuous space instances. Finally, a real-world case study in Iran demonstrates significant enhancements in precipitation predictions, with the Markov chain procedure showing an average 55 % increase in expected rain probability based on optimized seeding decisions. Scenario-based stochastic programming yields an 11.7 % value of stochastic solution and 16.5 % expected value of perfect information for cloud seeding initiatives.
ArticleNumber 100356
Author Sadeghi, Mohammad
Yaghoubi, Saeed
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Keywords Markov chain
Cloud seeding
Water management
Valid inequalities
Water resources
Two-stage stochastic programming
Language English
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Snippet •Proposing an integrated two-stage stochastic framework for cloud seeding decisions.•Modeling of cloud seeding impact using a Markov chain...
The occurrence of sequential droughts and various forms of water shortages globally underscores the urgent need for sustainable water management solutions. In...
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StartPage 100356
SubjectTerms Cloud seeding
Markov chain
Two-stage stochastic programming
Valid inequalities
Water management
Water resources
Title Cloud seeding optimization under uncertainty: A Markov chain approach in a two-stage fuzzy-stochastic framework
URI https://dx.doi.org/10.1016/j.orp.2025.100356
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