Pith. sign in

REVIEW 3 major objections 7 minor 87 references

Risk-Aware Pump Control in Water Supply Systems Using Probabilistic Water Demand and Electricity Price Forecasts

T0 review · 3 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Probabilistic pump schedules cut water-supply power costs up to 9 percent.

desk verdict The qualitative findings are credible, but the headline 9% savings rest on price forecasts that leak future information; re-run without RES regressors before trusting the numbers. read the letter →

arxiv 2608.08790 v1 pith:SF24WOD4 submitted 2026-08-09 stat.AP

Jens Kley-Holsteg This is my paper · ORCID
classification stat.AP
keywords pumpschedulingwatersupplyprobabilisticforecastingstochasticoptimizationconditionalvalue-at-riskimbalancemarketday-aheadelectricitypricescenarioreduction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a drinking-water utility can cut operating cost by up to 9 percent relative to a price-insensitive benchmark by scheduling pumps with probabilistic forecasts of water demand and electricity prices, while explicitly accounting for day-ahead procurement and imbalance-market settlement. The central finding is that the main gain from stochastic optimization is operational robustness: stochastic policies reduce imbalance energy, delay constraint violations, and improve reliability, while expected costs are only slightly lower than deterministic alternatives. The paper also reports that water demand uncertainty is the dominant driver of policy quality, and that further improvements in electricity-price forecasts add little value because the economically exploitable price signal is already captured. If correct, the results imply that utilities should invest in demand forecasting and risk-aware control rather than chasing ever-more-accurate price forecasts.

What carries the argument

The load-bearing mechanism is a stochastic lookahead policy solved as a mixed-integer linear program over a multistage scenario tree. Probabilistic forecasts of water demand, day-ahead prices, and imbalance prices are generated by naive, LASSO-autoregressive (LEAR), and GAMLSS distributional-regression models, merged into a 1,000-member joint ensemble, reduced to five scenarios by energy-distance forward selection, and branched only on the water-demand process. The objective is lexicographic: expected economic cost plus Conditional Value-at-Risk (the average loss in the worst-performing cost scenarios), pump-smoothing penalties, and two-regime exceedance-risk penalties for storage and head violations. This structure lets the optimizer trade a controlled increase in imbalance exposure against cheaper day-ahead procurement while keeping reliability constraints binding.

What would settle it

Re-run the numerical study with day-ahead price models estimated strictly from information available before gate closure (dropping RES forecast covariates), keeping everything else fixed. If the best stochastic policy's saving over the price-invariant benchmark falls well below 9 percent, the claimed economic benefit depends on the non-anticipativity violation; if the saving is unchanged, the violation is immaterial.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that a lexicographic, risk-aware formulation of the multi-stage pump-scheduling problem—combining expected cost, Conditional Value-at-Risk of cost, and exceedance-risk penalties for storage and pump-head violations—translates forecasting skill into operational value. In a numerical study on real-world data from a German water supplier (2021–2025, with 2025 held out), the best stochastic policy achieves normalized costs of about 6,097 EUR per optimization run versus 6,595 EUR for the price-invariant fall-back benchmark, an extrapolated annual saving of roughly 236,356 EUR, i.e., about 9 percent. The paper emphasizes that the benefit is primarily risk reduction: stochastic policies cut imbalance energy and delay first constraint violations by several hours relative to deterministic forecasts, even though expected costs are similar.

Load-bearing premise

The headline saving assumes the day-ahead price forecasts can use renewable-generation forecasts that are only published after the day-ahead market closes; if that leaked information materially improves the price forecasts, the simulated schedules and the 9 percent saving are better than what a real operator could achieve in real time.

Editorial extensions

If this is right

  • Utilities that adopt stochastic, risk-aware scheduling can expect cost savings on the order of 9 percent relative to conventional price-invariant operation, with most of the gain coming from reduced imbalance exposure and delayed reliability violations rather than lower expected procurement cost.
  • Improvements in water-demand forecasts matter more for policy quality than equally-sized improvements in electricity-price forecasts, so forecast-development effort should be weighted toward demand.
  • Because deterministic policies incur substantially more imbalance energy and earlier violations, using deterministic point forecasts in place of probabilistic ones sacrifices robustness even when average costs look similar.
  • Scenario reduction that preserves the overall distribution does not automatically preserve the tail events that drive CVaR- and exceedance-risk-based decisions; set sizes and reduction criteria should be chosen with the downstream risk objective in mind.
  • The framework is transferable: because the hydraulic model is deliberately simplified to a storage mass balance plus affine pump curves, the same forecasting-and-optimization pipeline can be extended to site-specific networks without changing the core approach.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the renewable-forecast non-anticipativity violation were corrected (training price models only on information available before gate closure), the 9 percent saving might shrink; a natural test is to re-estimate the day-ahead price models without the leaked RES covariates and re-run the policy comparison.
  • A decision-aware scenario-reduction criterion that targets the cost tail rather than the full distribution could recover part of the gap between reduced-set and full-ensemble performance and is a direct, testable extension of the energy-distance approach used here.
  • The finding that price-forecast improvements have limited marginal value is conditional on the studied market (German day-ahead plus imbalance settlement); in markets with different imbalance-price dynamics or stronger price spikes, price-forecast skill may matter more.
  • Because the paper assumes zero-mean imbalance deviations (no deliberate arbitrage), the 9 percent figure is a conservative estimate of what a fully optimizing trader could achieve if allowed to take intentional imbalance positions; extending the market-neutrality constraint is a natural next step.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. The paper develops a sequential decision-making framework for pump scheduling in a drinking water supply system, integrating probabilistic forecasts of water demand, day-ahead electricity prices, and imbalance prices into a risk-aware stochastic optimization problem. The objective function is lexicographic, combining expected operational costs, Conditional Value-at-Risk of economic costs, and reliability penalties based on exceedance risk measures. The framework explicitly models day-ahead procurement with subsequent imbalance settlement and uses scenario reduction and a MILP reformulation for tractability. In a numerical study with data from a German water supplier, the authors compare forecast-driven policies (Naive, LEAR, GAMLSS) against a price-invariant fall-back policy and perfect-foresight baselines, report cost savings of up to 9% versus the fall-back, and conclude that the primary benefit of stochastic optimization lies in improved operational robustness rather than lower expected costs.

Significance. If the quantitative findings are robust, the paper is a valuable methodological contribution at the interface of probabilistic forecasting and stochastic optimal control for water systems. It offers a detailed integration of forecast ensembles with a risk-aware, imbalance-aware scheduling model, a careful evaluation of scenario reduction methods, and a clean separation of forecast and policy evaluation. The explicit treatment of the imbalance market and the lexicographic risk objective are strengths. However, the headline quantitative claims currently rest on an acknowledged non-anticipativity violation in the price forecast models and on policy performance figures reported without any measures of uncertainty, which limits the confidence that can be placed in the reported rankings and the 9% savings figure.

major comments (3)
  1. [Section 1.2, Eqs. (29) and (30)] The day-ahead price forecasting models include dRES (forecast renewable generation) as a regressor, while the paper itself states that RES forecasts are published only after day-ahead gate closure and that their inclusion violates non-anticipativity. Since day-ahead procurement decisions for delivery day d+1 are fixed at 12:00 on day d, price forecasts used in the optimization are informed by information that a real operator would not possess at decision time. This leakage can inflate the reported 9% cost savings relative to the price-invariant benchmark and can also distort the conclusion that further price-forecast improvements have limited value, because the leaked information may already capture part of the exploitable price signal. The paper's acknowledgment of the violation does not address its materiality. I request a robustness analysis in which the dRES terms are removed from the DAPF models, the forecasts are regenerated, and the full policy evaluation is rerun; if the cost-savings figure or the price-value conclusion changes materially, the abstract and conclusions must be qualified.
  2. [Table 4] All policy performance indicators are reported as single averages over 100 runs and 3 repetitions, with no standard errors, confidence intervals, or statistical tests. Several policy comparisons that carry the paper's message involve very small cost differences, for example GAMLSS SH with λrisk=1 (6100.44 EUR), LEAR SH (6097.34 EUR), and GAMLSS SH (6102.17 EUR). Without a measure of dispersion, the ranking of policies and the extrapolated annual savings of 236,355.75 EUR (about 9%) cannot be distinguished from sampling noise. I request that the authors report run-level variability (e.g., standard errors or quantile ranges) for the Table 4 indicators and, where appropriate, apply tests to the cost differences between the main policies.
  3. [Section 3.3] The sensitivity-analysis conclusions, in particular that the marginal value of further improvements in electricity price forecasts appears comparatively limited and that most exploitable price information is already captured, are based on comparisons such as GAMLSS PF EPF SH versus GAMLSS SH that are reported without any uncertainty measures. As these claims are central takeaways of the paper, they should be either supported by statistical evidence (error bars, confidence intervals, or formal tests) or restated more cautiously as qualitative observations that are not yet statistically grounded.
minor comments (7)
  1. [Section 1.1, Assumptions] The assumption numbering skips Assumption 3, and Assumption 5 refers to Assumption 1.1 for the retroactive day-ahead participation; please renumber the assumptions consistently.
  2. [Section 1.1] In the paragraph on electricity procurement, 'Wile preliminary IBP estimates' should read 'While preliminary IBP estimates'.
  3. [Section 2.3] At the start of Section 2.3, 'In the proceeding we first derive' should read 'In the following we first derive'.
  4. [Section 2.3.3] The sentence 'The resulting model are denoted as DAPF GAMLSS tdist' should read 'The resulting models are denoted as DAPF GAMLSS tdist'.
  5. [Equation (31)] The notation HDI(w_WD_t-L, t) is introduced without defining w_WD_t-L, while the surrounding text refers to D_t-L; please align the notation.
  6. [Table 4] The footnote markers asterisk and double asterisk are explained in the table region, but the explanation is not integrated into the table caption; please move the notes into a proper table note so that the meaning of the starred rows is unambiguous.
  7. [Section 3.3, extrapolation] The extrapolation from the normalized costs in Table 4 to the annual savings of 236,355.75 EUR is not described; please provide the calculation formula so that the 9% headline figure can be reproduced.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: forecasts are estimated out-of-sample, policies are evaluated on realized test trajectories, and no prediction reduces to its fitted inputs.

full rationale

The derivation chain is self-contained. Probabilistic forecast models (Naive, LEAR, GAMLSS) are estimated on the 2021–2024 training period and their ensembles are generated for the 2025 test period; policy performance in Table 4 is computed from realized exogenous trajectories, not from the forecast scenarios used inside the optimization. The risk-aware storage bounds in Eq. (14) are fixed inputs obtained from the demand forecast distribution, but they are not fitted to policy outcomes, and the robustness/cost metrics are evaluated on realized data, so no claimed prediction is equivalent to its input by construction. Perfect-foresight policies (PF DET SH, PF DET FH) serve as oracle lower bounds rather than as fitted predictions. Self-citations (tsrobprep, Kley-Holsteg and Ziel 2020, Narajewski and Ziel 2020, Ziel 2021) supply software and established statistical methods that are independently re-estimated and tested here; none is invoked as a uniqueness theorem or as the sole support of the central claim. The acknowledged non-anticipativity violation for RES forecasts in Section 1.2 is a correctness/external-validity concern, not a circularity, because it does not make any result logically equivalent to its inputs. Hence no circular step is identified.

Assumptions & free parameters 17 free parameters · 8 assumptions · 0 invented entities

The central numerical results depend on a large number of operator-defined and empirically fitted parameters, especially the pump curve coefficients and head thresholds that are not reported. The most consequential ad hoc assumption is the acceptance of RES forecasts that violate non-anticipativity. No new entities are introduced.

free parameters (17)
  • lambda_risk = 0.5 (sensitivity: 0 and 1)
    Economic risk-aversion weight in the objective function (Eq. 15); user-specified, not fitted to data.
  • alpha_econ = 0.8
    Confidence level for the economic CVaR term; chosen, not fitted.
  • alpha_rel = 0.8
    Confidence level for the reliability exceedance-risk measures; chosen, not fitted.
  • alpha_lba, alpha_lbc = 0.95 each
    Confidence levels for the risk-aware lower storage bounds in Eq. 14; operator-defined.
  • b_lba, b_lbc = 1 h, 0.75 h
    Intervention horizons for the lower storage bounds; operator-defined.
  • c_cor = 30 EUR
    Penalty weight for critical-range reliability violations in Eq. 20; chosen by the authors.
  • c_psc = 10 EUR
    Pump start-up penalty in Eq. 19; chosen by the authors.
  • c_eor = not reported
    Emergency-range penalty weight, described as an estimated upper bound on joint economic and switching costs; exact value not given.
  • storage bounds v_uba, v_ubc = 41000, 44000 m3
    Operator-defined upper storage bounds used in the reliability penalties.
  • initial storage volume V0 = 27000 m3
    Initial storage level for each optimization run; assumed value.
  • pump curve coefficients beta_Q, beta_P = not reported
    Affine flow and power model coefficients per pump combination (Eqs. 11-12), fitted to historical operational data; values not published.
  • pump head thresholds h_lba, h_uba, h_lbc, h_ubc = empirical quantiles, not reported
    Operating thresholds per pump combination derived from historical head observations; exact values not reported.
  • scenario reduction size M_red = 5
    Number of reduced scenarios used in the stochastic optimization; chosen for tractability.
  • energy distance exponent p = 1
    Distance exponent in the energy distance scenario reduction (Eq. 38); chosen, with p=0.5 also tested.
  • target cardinality of preselected pump combinations = 9
    Size of the reduced pump combination set; chosen as the 80th percentile of historical 36-hour windows.
  • sub-horizon length and overlap = 12 h, 6 h overlap
    Sequential overlapping horizon decomposition parameters; chosen for computational tractability.
  • imbalance risk premium = 2 EUR/MWh
    Assumed premium used to extrapolate annual cost savings of 9%; not derived from data.
assumptions (8)
  • domain assumption Simplified hydraulic system: all pumped water passes through storage, no friction losses, negligible ramping, and affine pump curves.
    Assumption 1 in Section 1.1 reduces hydraulic detail to a mass balance and affine approximations, which shapes all transition dynamics.
  • domain assumption Electricity is procured only through the day-ahead auction, imbalance settlement is symmetric, and no hedging or other short-term markets are considered.
    Assumption 2 restricts the economic environment to day-ahead and imbalance markets, which is central to the cost model.
  • domain assumption Uncertainty enters only through water demand, day-ahead price, and imbalance price; all other system components are deterministic.
    Assumption 4 excludes model misspecification and other uncertainties, simplifying the stochastic process to three exogenous series.
  • domain assumption Independent optimization runs with retroactive day-ahead participation for early hours and finite horizon end effects.
    Assumption 5 defines the study design, enabling tractable evaluation but deviating from classical MPC with re-optimization.
  • ad hoc to paper RES forecasts are used in price models even though published after day-ahead gate closure, violating non-anticipativity.
    Section 1.2 explicitly acknowledges the violation and accepts it because RES forecasts are widely used in practice; this can bias the price forecasts and derived cost savings.
  • domain assumption Water demand is independent of electricity price processes; joint trajectories are formed by index-wise pairing.
    Section 2.3.6 adopts independence after finding low residual correlations, which affects the joint scenario distribution.
  • domain assumption Risk-aware storage bounds are computed from CVaR of forecast demand under zero inflow.
    Equation 14 defines lower storage bounds from forecast demand quantiles, coupling the reliability penalties to the demand forecast model.
  • domain assumption Market neutrality: deviations between realized and procured electricity have zero mean under the policy.
    Equation 7 assumes no systematic arbitrage, but no constraint enforcing this assumption is present in the MILP formulation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Risk-Aware Pump Control in Water Supply Systems Using Probabilistic Water Demand and Electricity Price Forecasts." pith.science (2026). https://pith.science/paper/SF24WOD4

@misc{pith2026260808790,
  author       = {Pith},
  title        = {Pith review of: Risk-Aware Pump Control in Water Supply Systems Using Probabilistic Water Demand and Electricity Price Forecasts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SF24WOD4}},
  note         = {Machine review of arXiv:2608.08790}
}
abstract

Drinking water utilities face uncertain water demand and electricity prices, as well as requirements for reliable and cost-efficient operation. This paper investigates a sequential multi-stage pump scheduling problem under uncertainty for a drinking water supplier participating in the day-ahead auction with subsequent imbalance market settlement. We integrate probabilistic forecasts of water demand and electricity prices into a risk-aware stochastic optimization framework. Reliability and economic risk preferences are represented through a lexicographic objective incorporating Conditional Value-at-Risk and Exceedance Risk measures, where the framework allows to explicitly account for the imbalance market settlement. A numerical study demonstrates that improvements in forecasting performance generally translate into improved policy performance. Furthermore, we found that the primary benefit of stochastic optimization lies in improved operational robustness rather than lower expected costs. The water demand is found to be a dominant driver of policy quality, the marginal value of further improvements in electricity price forecasts appears comparatively limited, indicating that the economically exploitable component of the price information is already captured to a large extent. Compared with a price-invariant benchmark, the best stochastic policy achieves cost savings of up to $9\%$, indicating that substantial economic benefits can be realized by accepting a carefully controlled increase in imbalance exposure and operational risk.

Figures

Figures reproduced from arXiv: 2608.08790 by the authors.

Figure 1
Figure 1. Operating ranges for storage and pump control with their correspond [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Preprocessed WD, DAP, IBP, and estimate of IBP time series for the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Receding-horizon structure of consecutive optimization runs and their [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Illustration of the central and tail dependence structure [PITH_FULL_IMAGE:figures/full_fig_p031_4.png]
Figure 5
Figure 5. Figure 5: Illustration of full ensemble with mean as well as reduced sce [PITH_FULL_IMAGE:figures/full_fig_p032_5.png]
Figure 6
Figure 6. Figure 6: Scenario tree representation based on WD process and the corre [PITH_FULL_IMAGE:figures/full_fig_p033_6.png]
Figure 7
Figure 7. Figure 7: DM test results for reduced scenario sets derived from the forecasting [PITH_FULL_IMAGE:figures/full_fig_p034_7.png]
Figure 8
Figure 8. Figure 8: Comparison of scenario reduction methods for the GAMLSS based [PITH_FULL_IMAGE:figures/full_fig_p035_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

87 extracted references · 58 canonical work pages

  1. [1]

    The Annals of Statistics , year =

    Efron, Bradley and Hastie, Trevor and Johnstone, Iain and Tibshirani, Robert , title =. The Annals of Statistics , year =. doi:10.1214/009053604000000067 , url =

    doi:10.1214/009053604000000067

  2. [2]

    and Kekatos, Vassilis , journal=

    Singh, Manish K. and Kekatos, Vassilis , journal=. Optimal Scheduling of Water Distribution Systems , year=

  3. [3]

    and Varoquaux, G

    Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V. and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P. and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E. , journal=. Scikit-learn: Machine Learning in

  4. [4]

    2022 , eprint=

    The Parametric Cost Function Approximation: A new approach for multistage stochastic programming , author=. 2022 , eprint=

    2022

  5. [5]

    Powell , keywords =

    Saeed Ghadimi and Warren B. Powell , keywords =. Stochastic search for a parametric cost function approximation: Energy storage with rolling forecasts , journal =. 2024 , issn =. doi:https://doi.org/10.1016/j.ejor.2023.08.003 , url =

    doi:10.1016/j.ejor.2023.08.003 2024

  6. [6]

    Journal of the American Statistical Association , volume =

    Tilmann Gneiting and Adrian E Raftery , title =. Journal of the American Statistical Association , volume =. 2007 , publisher =. doi:10.1198/016214506000001437 , URL =. https://doi.org/10.1198/016214506000001437 , abstract =

    doi:10.1198/016214506000001437 2007

  7. [7]

    2021 , eprint=

    Problem-Driven Scenario Clustering in Stochastic Optimization , author=. 2021 , eprint=

    2021

  8. [8]

    Scenario Reduction for Stochastic Programs with Conditional Value-at-Risk , journal =

    Arp. Scenario Reduction for Stochastic Programs with Conditional Value-at-Risk , journal =. 2018 , volume =. doi:10.1007/s10107-018-1298-9 , url =

    work page doi:10.1007/s10107-018-1298-9 2018

Show all 87 references
  1. [9]

    The Value of Coordination in Multimarket Bidding of Grid Energy Storage , journal =

    L\". The Value of Coordination in Multimarket Bidding of Grid Energy Storage , journal =. 2023 , doi =. https://doi.org/10.1287/opre.2021.2247 , abstract =

    2023

  2. [10]

    Mathematical Programming , year =

    Rujeerapaiboon, Napat and Schindler, Kilian and Kuhn, Daniel and Wiesemann, Wolfram , title =. Mathematical Programming , year =. doi:10.1007/s10107-018-1269-1 , url =

    doi

  3. [11]

    Scenario reduction in stochastic programming , journal =

    Dupa. Scenario reduction in stochastic programming , journal =. 2003 , volume =. doi:10.1007/s10107-002-0331-0 , url =

    2003 doi

  4. [12]

    Journal of Water Resources Planning and Management , volume =

    Gergely Hajgató and György Paál and Bálint Gyires-Tóth , title =. Journal of Water Resources Planning and Management , volume =. 2020 , doi =. https://ascelibrary.org/doi/pdf/10.1061/ , abstract =

    2020

  5. [13]

    Archives of Computational Methods in Engineering , year =

    Sabah Parvaze and Rohitashw Kumar and Junaid Nazir Khan and Nadhir Al-Ansari and Saqib Parvaze and Dinesh Kumar Vishwakarma and Ahmed Elbeltagi and Alban Kuriqi , title =. Archives of Computational Methods in Engineering , year =. doi:10.1007/s11831-023-09944-7 , url =

    doi

  6. [14]

    Electricity price forecasting: A review of the state-of-the-art with a look into the future , journal =

    Rafał Weron , keywords =. Electricity price forecasting: A review of the state-of-the-art with a look into the future , journal =. 2014 , issn =. doi:https://doi.org/10.1016/j.ijforecast.2014.08.008 , url =

    2014 doi

  7. [15]

    Water , VOLUME =

    Kidanu, Rahel Amare and Cunha, Maria and Salomons, Elad and Ostfeld, Avi , TITLE =. Water , VOLUME =. 2023 , NUMBER =

    2023

  8. [16]

    IEEE Proceedings , keywords =

    Chance-Constrained Water Pumping to Manage Water and Power Demand Uncertainty in Distribution Networks. IEEE Proceedings , keywords =. doi:10.1109/JPROC.2020.2997520 , adsurl =

    2020

  9. [17]

    Cassiolato, Gustavo H. B. and Ruiz-Femenia, Jose Ruben and Salcedo-Diaz, Raquel and Ravagnani, Mauro A. S. S. , title =. Water Resources Management , year =. doi:10.1007/s11269-024-03733-y , url =

    doi

  10. [18]

    and Summers, Tyler Holt , journal=

    Guo, Yi and Wang, Shen and Taha, Ahmad F. and Summers, Tyler Holt , journal=. Optimal Pump Control for Water Distribution Networks via Data-Based Distributional Robustness , year=

  11. [19]

    Vieira and S

    Bruno S. Vieira and S. Optimizing drinking water distribution system operations , journal =. 2020 , issn =. doi:https://doi.org/10.1016/j.ejor.2019.07.060 , url =

    2020 doi

  12. [20]

    International conference on learning and intelligent optimization , pages=

    Intelligent pump scheduling optimization in water distribution networks , author=. International conference on learning and intelligent optimization , pages=. 2018 , organization=

    2018

  13. [21]

    Water Resources Research , volume =

    Perelman, Gal and Ostfeld, Avi , title =. Water Resources Research , volume =. doi:https://doi.org/10.1029/2023WR035508 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2023WR035508 , note =

    doi

  14. [22]

    2022 , number =

    Beschluss BK6-21-192 zur Genehmigung des Vorschlags der deutschen Übertragungsnetzbetreiber für eine Änderung des Ausgleichsenergiepreissystems , institution =. 2022 , number =

    2022

  15. [23]

    2024 , url =

    Francesco Zanetta and Sam Allen , title =. 2024 , url =

    2024

  16. [24]

    and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and

    Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and. Nature Methods , year =

  17. [25]

    Donkor and Thomas A

    Emmanuel A. Donkor and Thomas A. Mazzuchi and Refik Soyer and J. Alan Roberson , title =. Journal of Water Resources Planning and Management , volume =. 2014 , doi =. https://ascelibrary.org/doi/pdf/10.1061/ , abstract =

    2014

  18. [26]

    Recent advances in electricity price forecasting: A review of probabilistic forecasting , journal =

    Jakub Nowotarski and Rafał Weron , keywords =. Recent advances in electricity price forecasting: A review of probabilistic forecasting , journal =. 2018 , issn =. doi:https://doi.org/10.1016/j.rser.2017.05.234 , url =

    2018 doi

  19. [27]

    Journal of Business & Economic Statistics , volume =

    Francis X Diebold and Robert S Mariano , title =. Journal of Business & Economic Statistics , volume =. 2002 , publisher =. doi:10.1198/073500102753410444 , URL =. https://doi.org/10.1198/073500102753410444 , abstract =

    2002 doi

  20. [28]

    Diebold and Roberto S

    Francis X. Diebold and Roberto S. Mariano , journal =. Comparing Predictive Accuracy , urldate =

  21. [29]

    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences , volume =

    Ziel, Florian , title =. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences , volume =. 2021 , month =. doi:10.1098/rsta.2019.0431 , url =

    2021

  22. [30]

    Water Resources Research , volume =

    Thomas, Meghna and Sela, Lina , title =. Water Resources Research , volume =. doi:https://doi.org/10.1029/2023WR034526 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2023WR034526 , note =

    doi

  23. [31]

    Journal of risk , volume=

    Portfolio optimization with conditional value-at-risk objective and constraints , author=. Journal of risk , volume=

  24. [32]

    Water Resources Research , volume =

    van der Heijden, Ties and Mendoza-Lugo, Miguel Angel and Palensky, Peter and van de Giesen, Nick and Abraham, Edo , title =. Water Resources Research , volume =. doi:https://doi.org/10.1029/2024WR037115 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2024WR037...

    doi

  25. [33]

    Scenario tree modeling for multistage stochastic programs , journal =

    Heitsch, Holger and R. Scenario tree modeling for multistage stochastic programs , journal =. 2009 , volume =. doi:10.1007/s10107-007-0197-2 , url =

    2009 doi

  26. [34]

    The Schaake Shuffle: A Method for Reconstructing Space–Time Variability in Forecasted Precipitation and Temperature Fields

    Martyn Clark and Subhrendu Gangopadhyay and Lauren Hay and Balaji Rajagopalan and Robert Wilby. The Schaake Shuffle: A Method for Reconstructing Space–Time Variability in Forecasted Precipitation and Temperature Fields. Journal of Hydrometeorology. 2004. doi:10.1175/1525-7541(...

    2004 doi

  27. [35]

    M5 competition uncertainty: Overdispersion, distributional forecasting, GAMLSS, and beyond , journal =

    Florian Ziel , keywords =. M5 competition uncertainty: Overdispersion, distributional forecasting, GAMLSS, and beyond , journal =. 2022 , note =. doi:https://doi.org/10.1016/j.ijforecast.2021.09.008 , url =

    2022 doi

  28. [36]

    LASSO-type penalization in the framework of generalized additive models for location, scale and shape , journal =

    Andreas Groll and Julien Hambuckers and Thomas Kneib and Nikolaus Umlauf , keywords =. LASSO-type penalization in the framework of generalized additive models for location, scale and shape , journal =. 2019 , issn =. doi:https://doi.org/10.1016/j.csda.2019.06.005 , url =

    2019 doi

  29. [37]

    arXiv preprint arXiv:2407.08750 , year=

    Online distributional regression , author=. arXiv preprint arXiv:2407.08750 , year=

    arXiv

  30. [38]

    arXiv preprint arXiv:2504.02518 , year=

    Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting , author=. arXiv preprint arXiv:2504.02518 , year=

    arXiv

  31. [39]

    R. A. Rigby and D. M. Stasinopoulos , journal =. Generalized Additive Models for Location, Scale and Shape , urldate =

  32. [40]

    Energies , VOLUME =

    Browell, Jethro and Gilbert, Ciaran , TITLE =. Energies , VOLUME =. 2022 , NUMBER =

    2022

  33. [41]

    Econometric modelling and forecasting of intraday electricity prices , volume=

    Narajewski, Michał and Ziel, Florian , year=. Econometric modelling and forecasting of intraday electricity prices , volume=. doi:10.1016/j.jcomm.2019.100107 , journal=

    2019

  34. [42]

    Engineering Proceedings , VOLUME =

    Kley-Holsteg, Jens and Sonnenschein, Björn and Johnen, Gregor and Ziel, Florian , TITLE =. Engineering Proceedings , VOLUME =. 2024 , NUMBER =

    2024

  35. [43]

    Journal of Modern Power Systems and Clean Energy , volume =

    Ziel, Florian , title =. Journal of Modern Power Systems and Clean Energy , volume =. 2018 , month =

    2018

  36. [44]

    Journal of Water Resources Planning and Management , volume =

    Jens Kley-Holsteg and Florian Ziel , title =. Journal of Water Resources Planning and Management , volume =. 2020 , doi =. https://ascelibrary.org/doi/pdf/10.1061/ abstract =

    2020

  37. [45]

    Journal of the Royal Statistical Society: Series B (Methodological) , volume =

    Tibshirani, Robert , title =. Journal of the Royal Statistical Society: Series B (Methodological) , volume =. 1996 , month =. doi:10.1111/j.2517-6161.1996.tb02080.x , url =

    1996

  38. [46]

    Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark , volume=

    Lago, Jesus and Marcjasz, Grzegorz and De Schutter, Bart and Weron, Rafał , year=. Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark , volume=. doi:10.1016/j.apenergy.2021.116983 , journal=

  39. [47]

    Water , VOLUME =

    Gagliardi, Francesca and Alvisi, Stefano and Kapelan, Zoran and Franchini, Marco , TITLE =. Water , VOLUME =. 2017 , NUMBER =

    2017

  40. [48]

    Energy Economics , doi =

    Marcjasz, Grzegorz and Narajewski, Michał and Weron, Rafał and Ziel, Florian , title =. Energy Economics , doi =. 2023 , month =

    2023

  41. [49]

    International Journal of Forecasting , volume =

    Grzegorz Marcjasz and Bartosz Uniejewski and Rafał Weron , title =. International Journal of Forecasting , volume =. 2020 , doi =

    2020

  42. [50]

    Tyrrell and Uryasev, Stanislav , title =

    Rockafellar, R. Tyrrell and Uryasev, Stanislav , title =. Journal of Risk , volume =. 2000 , url =

    2000

  43. [51]

    Zeitschrift für Energiewirtschaft , year =

    Johannes Viehmann , title =. Zeitschrift für Energiewirtschaft , year =. doi:10.1007/s12398-017-0196-9 , url =

    doi

  44. [52]

    Model Predictive Control of water resources systems: A review and research agenda , journal =

    Andrea Castelletti and Andrea Ficchì and Andrea Cominola and Pablo Segovia and Matteo Giuliani and Wenyan Wu and Sergio Lucia and Carlos Ocampo-Martinez and Bart. Model Predictive Control of water resources systems: A review and research agenda , journal =. 2023 , issn =. doi:...

    2023 doi

  45. [53]

    Powell , keywords =

    Warren B. Powell , keywords =. A unified framework for stochastic optimization , journal =. 2019 , issn =. doi:https://doi.org/10.1016/j.ejor.2018.07.014 , url =

    2019 doi

  46. [54]

    and Kapelan, Zoran and Vamvakeridou-Lyroudia, Lydia and Savic, Dragan , year =

    Hutton, C. and Kapelan, Zoran and Vamvakeridou-Lyroudia, Lydia and Savic, Dragan , year =. Dealing with Uncertainty in Water Distribution System Models: A Framework for Real-Time Modeling and Data Assimilation , volume =. Journal of Water Resources Planning and Management , doi =

  47. [55]

    Alvisi and M

    S. Alvisi and M. Franchini , title =. Urban Water Journal , volume =. 2017 , publisher =. doi:10.1080/1573062X.2015.1057182 , URL =

    2017

  48. [56]

    European Journal of Operations Research , volume =

    Finnah, Benedikt and Gönsch, Jochen and Ziel, Florian , title =. European Journal of Operations Research , volume =. 2022 , month =

    2022

  49. [57]

    Fosso and Ayse Selin Kocaman , keywords =

    Parinaz Toufani and Ece Cigdem Karakoyun and Emre Nadar and Olav B. Fosso and Ayse Selin Kocaman , keywords =. Optimization of pumped hydro energy storage systems under uncertainty: A review , journal =. 2023 , issn =. doi:https://doi.org/10.1016/j.est.2023.109306 , url =

    2023

  50. [58]

    Open-Meteo.com Weather API , year =

    Zippenfenig, Patrick , doi =. Open-Meteo.com Weather API , year =

  51. [59]

    , title =

    Hersbach, H., Bell, B., Berrisford, P., Biavati, G., Horányi, A., Muñoz Sabater, J., Nicolas, J., Peubey, C., Radu, R., Rozum, I., Schepers, D., Simmons, A., Soci, C., Dee, D., Thépaut, J-N. , title =. doi:10.24381/cds.adbb2d47 , url =

    doi

  52. [60]

    , title =

    Muñoz Sabater, J. , title =. doi:10.24381/CDS.E2161BAC , url =

    doi

  53. [61]

    , title =

    Schimanke S., Ridal M., Le Moigne P., Berggren L., Undén P., Randriamampianina R., Andrea U., Bazile E., Bertelsen A., Brousseau P., Dahlgren P., Edvinsson L., El Said A., Glinton M., Hopsch S., Isaksson L., Mladek R., Olsson E., Verrelle A., Wang Z.Q. , title =. doi:10.24381/...

    doi

  54. [62]

    ENTSO-E Transparency Platform , year =

  55. [63]

    2025 , note =

    Gurobi Optimizer Reference Manual , author =. 2025 , note =

    2025

  56. [64]

    2021 , author =

    tsrobprep — an R package for robust preprocessing of time series data , journal =. 2021 , author =

    2021

  57. [65]

    Journal of Hydroinformatics , volume =

    van der Heijden, Ties and Lugt, Dorien and van Nooijen, Ronald and Palensky, Peter and Abraham, Edo , title =. Journal of Hydroinformatics , volume =. 2022 , month =. doi:10.2166/hydro.2022.018 , url =

    2022 doi

  58. [66]

    Water Resources Management , year =

    Menke, Ruben and Abraham, Edo and Parpas, Panos and Stoianov, Ivan , title =. Water Resources Management , year =. doi:10.1007/s11269-016-1490-8 , url =

    doi

  59. [67]

    Approximation of System Components for Pump Scheduling Optimisation , journal =

    Ruben Menke and Edo Abraham and Panos Parpas and Ivan Stoianov , keywords =. Approximation of System Components for Pump Scheduling Optimisation , journal =. 2015 , note =. doi:https://doi.org/10.1016/j.proeng.2015.08.935 , url =

    2015 doi

  60. [68]

    2017 , MONTH = Jan, DOI =

    Bonvin, Gratien and Demassey, Sophie and Le Pape, Claude and Ma. 2017 , MONTH = Jan, DOI =

    2017

  61. [69]

    Model for Optimal Operation of Water Distribution Pumps with Uncertain Demand Patterns , volume =

    Khatavkar, Puneet and Mays, Larry , year =. Model for Optimal Operation of Water Distribution Pumps with Uncertain Demand Patterns , volume =. Water Resources Management , doi =

  62. [70]

    2021 , DOI =

    Bonvin, Gratien and Demassey, Sophie and Lodi, Andrea , URL =. 2021 , DOI =

    2021

  63. [71]

    Zeraebruk and Medhanie Teklemariam and Solomon Tesfamariam , title =

    Ngandu Balekelayi and Kahsay N. Zeraebruk and Medhanie Teklemariam and Solomon Tesfamariam , title =. Journal of Pipeline Systems Engineering and Practice , volume =. 2021 , doi =. https://ascelibrary.org/doi/pdf/10.1061/\ abstract =

    2021

  64. [72]

    Lost in optimisation of water distribution systems? A literature review of system operation , journal =

    Helena Mala-Jetmarova and Nargiz Sultanova and Dragan Savic , keywords =. Lost in optimisation of water distribution systems? A literature review of system operation , journal =. 2017 , issn =. doi:https://doi.org/10.1016/j.envsoft.2017.02.009 , url =

    2017 doi

  65. [73]

    Optimal bidding of a virtual power plant on the Spanish day-ahead and intraday market for electricity , journal =

    David Wozabal and Gunther Rameseder , keywords =. Optimal bidding of a virtual power plant on the Spanish day-ahead and intraday market for electricity , journal =. 2020 , issn =. doi:https://doi.org/10.1016/j.ejor.2019.07.022 , url =

    2020 doi

  66. [74]

    Reis and Marta A.R

    Ana L. Reis and Marta A.R. Lopes and A. Andrade-Campos and Carlos. A review of operational control strategies in water supply systems for energy and cost efficiency , journal =. 2023 , issn =. doi:https://doi.org/10.1016/j.rser.2022.113140 , url =

    2023

  67. [75]

    Minimization of water pumps' electricity usage: A hybrid approach of regression models with optimization , journal =

    Saeed Asadi Bagloee and Mohsen Asadi and Michael Patriksson , keywords =. Minimization of water pumps' electricity usage: A hybrid approach of regression models with optimization , journal =. 2018 , issn =. doi:https://doi.org/10.1016/j.eswa.2018.04.027 , url =

    2018 doi

  68. [76]

    Savić , keywords =

    João Marques and Maria Cunha and Dragan A. Savić , keywords =. Multi-objective optimization of water distribution systems based on a real options approach , journal =. 2015 , issn =. doi:https://doi.org/10.1016/j.envsoft.2014.09.014 , url =

    2015 doi

  69. [77]

    Water Resources Research , volume =

    Zhou, Xinhong and Chu, Shipeng and Zhang, Tuqiao and Yu, Tingchao and Shao, Yu , title =. Water Resources Research , volume =. doi:https://doi.org/10.1029/2023WR035630 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2023WR035630 , note =

    doi

  70. [78]

    Pump scheduling optimization in water distribution system based on mixed integer linear programming , journal =

    Yu Shao and Xinhong Zhou and Tingchao Yu and Tuqiao Zhang and Shipeng Chu , keywords =. Pump scheduling optimization in water distribution system based on mixed integer linear programming , journal =. 2024 , issn =. doi:10.1016/j.ejor.2023.08.055 , url =

    2024 doi

  71. [79]

    and Mauter, M

    Musabandesu, E. and Mauter, M. S. , title =. Water Resources Research , volume =. doi:https://doi.org/10.1029/2024WR039830 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2024WR039830 , note =

    doi

  72. [80]

    Mathematical programming techniques in water network optimization , journal =

    Claudia D’Ambrosio and Andrea Lodi and Sven Wiese and Cristiana Bragalli , keywords =. Mathematical programming techniques in water network optimization , journal =. 2015 , issn =. doi:https://doi.org/10.1016/j.ejor.2014.12.039 , url =

    2015 doi

  73. [81]

    Optimal scheduling method integrating priori expert knowledge for water distribution systems based on historical operational information tensor: A new perspective , journal =

    Yifan Xie and Yipeng Wu and Yujun Huang and Ye Jin and Yuxian Li and Linfeng Li and Chengyu He and Bei Zhao and Xiangyi Li and Shuming Liu , keywords =. Optimal scheduling method integrating priori expert knowledge for water distribution systems based on historical operational...

    2025

  74. [82]

    , journal=

    Stuhlmacher, Anna and Guikema, Seth and Mathieu, Johanna L. , journal=. Assessing Power and Water Network Resilience When Water Pumps Provide Frequency Regulation , year=

  75. [83]

    Pfetsch and Andreas Schmitt , title =

    Marc E. Pfetsch and Andreas Schmitt , title =. Optimization Methods and Software , volume =. 2023 , publisher =. doi:10.1080/10556788.2022.2142581 , URL =

    2023

  76. [84]

    Summers , keywords =

    Yi Guo and Tyler H. Summers , keywords =. Distributionally Robust Stochastic Optimal Water Flow and Risk Management⁎⁎This material is based on work supported by the National Science Foundation under grant CMMI-1728605. , journal =. 2020 , note =. doi:https://doi.org/10.1016/j....

    2020 doi

  77. [85]

    Fayzul K

    Pasha, M. Fayzul K. and Lansey, Kevin , title =. Water Resources Management , year =. doi:10.1007/s11269-014-0721-0 , url =

    doi

  78. [86]

    Robust Optimization of Demand Response Power Bids for Drinking Water Systems , journal =

    Chouaïb Mkireb and Abel Dembélé and Antoine Jouglet and Thierry Denoeux , keywords =. Robust Optimization of Demand Response Power Bids for Drinking Water Systems , journal =. 2019 , issn =. doi:https://doi.org/10.1016/j.apenergy.2019.01.124 , url =

    2019 doi

  79. [87]

    Alvisi and M

    S. Alvisi and M. Franchini and V. Marsili and F. Mazzoni and E. Salomons and M. Housh and A. Abokifa and K. Arsova and F. Ayyash and H. Bae and R. Barreira and L. Basto and S. Bayer and E. Z. Berglund and D. Biondi and F. Boloukasli Ahmadgourabi and B. Brentan and J. Caetano a...

    2025

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.