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Toward coordinated water allocation in urban agglomerations under joint supply-demand uncertainty: A distributionally robust bi-level multi-objective framework
Journal article   Peer reviewed

Toward coordinated water allocation in urban agglomerations under joint supply-demand uncertainty: A distributionally robust bi-level multi-objective framework

Yan Tu, Qian Li, Yiqian Ding, Yongzheng Lu and Benjamin Lev
Journal of hydrology (Amsterdam), v 678, 136084
Oct 2026
DOI: https://doi.org/10.1016/j.jhydrol.2026.136084
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Abstract

Bi-level multi-objective programming Joint supply-demand uncertainty Lexicographic priority Urban agglomeration Wasserstein distributionally robust optimization Water resource coordination
Coordinated water allocation is vital for urban agglomerations where high inter-city dependence amplifies systemic risks. However, traditional management faces strains from climate change and urbanization alongside conflicting interests across management levels. To this end, this study develops a distributionally robust bi-level multi-objective water allocation (DRBMWA) framework to facilitate coordination by integrating a Wasserstein-based distributionally robust representation of joint supply-demand uncertainty. The model features a bi-level multi-objective structure balancing economic cost, environmental load (COD), equity between cities (Gini coefficient), and systemic coordination, with lexicographic priorities (Living > Ecology > Production) reflecting social mandates. The original bi-level model is solved through a tractable single-level reformulation that embeds the lower-level lexicographic responses while preserving the hierarchical decision logic. Applied to the Shandong Peninsula urban agglomeration, results show that: (1) The DRO results reveal a robustness premium, as increasing the conservatism parameter α, which reflects the decision maker’s preference for uncertainty protection, from 1.0 to 1.5 raises the compromise cost by 34.88% while reducing the Gini coefficient from 0.034 to 0.018. (2) Under joint supply-demand stress, the deterministic compromise solution reaches a maximum city–sector shortage rate of 85.64%, whereas the DRBMWA solution maintains sectoral shortage levels within a more controllable range. (3) Compared with the single-level model, the bi-level model reduces the maximum city shortage rate from 21.16% to 14.19% and strengthens the protection of living and ecological water, although at higher transfer cost and COD discharge. (4) Scenario analysis shows that worsening supply-demand conditions substantially increase transfer costs and weaken coordination performance, indicating a greater need for earlier transfer activation and larger fiscal reserves. These findings support annual quota setting, transfer planning, sectoral allocation, and contingency preparation under uncertain water availability. •Building a framework toward synergistic water allocation in urban agglomerations.•Proposing a distributionally robust bi-level multi-objective optimization model.•Handling uncertainties using Wasserstein-metric distributionally robust optimization.•Ensuring tractability through lexicographic priorities and analytical reformulation.•Validating robustness under extreme shocks via a Shandong Peninsula case study.

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