pith. sign in

arxiv: 2604.23140 · v1 · submitted 2026-04-25 · 🧮 math.OC

Green Manufacturing Capacity Planning by Integrating Distributionally Robust Optimization and Generative AI

Xin Zhou , Zhengsong Lu , Bo Zeng , Na Geng This is my paper

Pith reviewed 2026-05-08 07:47 UTC · model grok-4.3

classification 🧮 math.OC
keywords green manufacturingcapacity planningdistributionally robust optimizationgenerative AIrenewable energy uncertaintydecomposition algorithmdata-driven ambiguity set
0
0 comments X

The pith

Integrating distributionally robust optimization with generative AI enables robust and computationally efficient green manufacturing capacity planning under uncertainty in demand and renewable generation.

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

The paper develops a two-stage distributionally robust optimization model to coordinate production capacity decisions and renewable energy investments across multiple factories, capacities, and products. It constructs the uncertainty set via clustering on historical data of varying quality to capture joint randomness in product demand and renewable output. A generative AI network is inserted into an exact decomposition algorithm through a custom encoding and decoding scheme that supplies structurally informative training data and converts outputs into usable formats. Experiments on real instances show the combined method delivers stronger economic results and maintained feasibility than standard approaches while cutting computation time and improving solution consistency. Firms can therefore plan green capacity expansions that better balance profitability, sustainability, and resilience to climate variability.

Core claim

We develop a comprehensive two-stage distributionally robust optimization (DRO) model for green manufacturing capacity planning in a multi-factory, multi-capacity, and multi-product setting, based on an ambiguity set constructed by a data-driven clustering technique that leverages historical data of different availabilities and qualities. To handle the computational challenges of practical instances, an effective generative AI network is integrated into an exact decomposition algorithm, through a novel encoding/decoding scheme designed to provide the AI model with structurally informative training data and to convert AI-generated outputs into algorithm-accessible formats.

What carries the argument

Two-stage distributionally robust optimization model whose ambiguity set is built by clustering historical data, with a generative AI network embedded in an exact decomposition algorithm via custom encoding and decoding.

If this is right

  • The model maintains robust feasibility against uncertain demand and renewable generation.
  • Computational efficiency and solution consistency improve markedly over standard decomposition approaches.
  • Coordinated planning of green technology adoption and capacity yields better renewable energy utilization.
  • Production decisions can be aligned with both profitability and corporate sustainability objectives.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same encoding scheme and AI integration could be tested on other multi-stage planning problems that combine production and energy uncertainties.
  • If the clustering step is replaced by more advanced distribution estimation techniques, the framework might handle higher-dimensional or non-stationary uncertainty more flexibly.
  • Policy analyses could use the model to quantify how incentives for renewable adoption affect optimal factory expansion paths.

Load-bearing premise

Clustering on historical data produces an ambiguity set that matches the true joint distributions of demand and renewable generation, and the generative AI supplies outputs accurate enough for the decomposition algorithm to recover optimal or near-optimal solutions without systematic bias.

What would settle it

On new real-world instances not used in training, the integrated method produces solutions that violate feasibility constraints more frequently or yield worse expected costs than standard robust or stochastic methods, or the AI component causes the decomposition algorithm to return inconsistent or clearly suboptimal decisions.

Figures

Figures reproduced from arXiv: 2604.23140 by Bo Zeng, Na Geng, Xin Zhou, Zhengsong Lu.

Figure 6
Figure 6. Figure 6: The efficiency improvement is measured by the relative solution time reduction when the samples view at source ↗
read the original abstract

Green manufacturing has become a strategic priority for many firms seeking to address sustainability and social responsibility, while improving production efficiency and profitability. However, integrating green technologies and renewable energy unavoidably introduces climate-related randomness that affects both product demand and renewable energy generation, underscoring the need for coordinated planning of production capacity and renewable energy development. To address this challenge, we develop a comprehensive two-stage distributionally robust optimization (DRO) model for green manufacturing capacity planning in a multi-factory, multi-capacity, and multi-product setting, based on an ambiguity set constructed by a data-driven clustering technique that leverages historical data of different availabilities and qualities. To handle the computational challenges of practical instances, an effective generative AI network is integrated into an exact decomposition algorithm, through a novel encoding/decoding scheme designed to provide the AI model with structurally informative training data and to convert AI-generated outputs into algorithm-accessible formats. Experimental results on real-world instances demonstrate that the proposed DRO approach achieves strong economic performance and robust feasibility under demand and renewable generation uncertainty, while also significantly improving computational efficiency and solution consistency relative to the standard approaches. Furthermore, our results highlight the managerial value of integrating green technology adoption with coordinated capacity planning to better utilize renewable energy and align production efficiency with sustainability and corporate social responsibility objectives.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper develops a two-stage distributionally robust optimization (DRO) model for green manufacturing capacity planning in a multi-factory, multi-capacity, multi-product setting. The ambiguity set is constructed via a data-driven clustering technique on historical data of demand and renewable generation availabilities. A generative AI network is integrated into an exact decomposition algorithm through a novel encoding/decoding scheme to improve scalability. Experiments on real-world instances are reported to demonstrate strong economic performance and robust feasibility under uncertainty, plus gains in computational efficiency and solution consistency over standard approaches, with managerial insights on coordinating green technology adoption.

Significance. If the integration and experimental claims hold, the work offers a scalable hybrid framework for applying DRO to practical sustainable manufacturing problems involving joint demand-renewable uncertainty. The clustering-based ambiguity construction and AI-assisted decomposition could provide efficiency advantages for large instances while preserving robustness, and the managerial discussion on aligning capacity planning with sustainability objectives adds applied value.

major comments (1)
  1. [Generative AI integration into the exact decomposition algorithm (via the novel encoding/decoding scheme)] The central claim of an 'exact decomposition' that recovers optimal or near-optimal recourse decisions under the clustered ambiguity set requires that generative AI outputs satisfy all structural constraints (e.g., capacity limits, renewable utilization). The manuscript provides no explicit feasibility verification, bound checks, or post-processing steps for AI-generated solutions, which is load-bearing for the 'robust feasibility' and efficiency assertions. Without this, reported gains may reflect approximation error rather than exact recovery.
minor comments (2)
  1. [Abstract] The abstract asserts 'strong economic performance' and 'significantly improving computational efficiency' but supplies no quantitative metrics, instance sizes, or baseline comparisons; adding a brief summary of key numerical results would improve clarity.
  2. [Model formulation and algorithmic sections] Notation for the ambiguity set construction and the two-stage model should be introduced with explicit definitions of the clustering hyperparameters and the generative network architecture to aid reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The feedback on the generative AI integration is particularly helpful for strengthening the presentation of our methodological contributions. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The central claim of an 'exact decomposition' that recovers optimal or near-optimal recourse decisions under the clustered ambiguity set requires that generative AI outputs satisfy all structural constraints (e.g., capacity limits, renewable utilization). The manuscript provides no explicit feasibility verification, bound checks, or post-processing steps for AI-generated solutions, which is load-bearing for the 'robust feasibility' and efficiency assertions. Without this, reported gains may reflect approximation error rather than exact recovery.

    Authors: We thank the referee for highlighting this critical point. The novel encoding/decoding scheme is specifically designed to embed the problem's structural constraints (including capacity limits and renewable utilization) directly into the training data generation and to map AI outputs back into feasible, algorithm-accessible formats that preserve the exactness of the decomposition. This construction ensures that the generated recourse decisions satisfy the constraints by design rather than through post-hoc correction. That said, we acknowledge that the current manuscript does not explicitly describe verification procedures or bound checks. In the revised version, we will add a dedicated subsection on feasibility verification, including formal bound checks, projection steps if needed, and empirical confirmation from the experiments that all AI-generated solutions satisfy the constraints. This will clarify that the reported gains in efficiency and robust feasibility arise from the exact recovery mechanism. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain; model and experiments are self-contained

full rationale

The paper formulates a standard two-stage DRO model whose ambiguity set is constructed directly from historical data via clustering, then augments an exact decomposition algorithm with a generative AI network trained on structurally encoded data. All performance claims rest on numerical experiments over real-world instances rather than any reduction of outputs to inputs by definition, fitted-parameter renaming, or load-bearing self-citation. No equation or algorithmic step is shown to be equivalent to its own premise; the framework therefore satisfies the default expectation of non-circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard DRO assumptions plus two practical modeling choices whose values are not derived from first principles.

free parameters (2)
  • clustering hyperparameters
    Number of clusters and distance metric used to build the data-driven ambiguity set from historical demand and renewable data.
  • generative AI training parameters
    Network architecture, loss weights, and training schedule that determine the quality of AI-generated solutions fed to the decomposition algorithm.
axioms (1)
  • domain assumption Uncertainty realizations lie within the ambiguity set constructed from historical data
    Core premise of the distributionally robust formulation stated in the abstract.

pith-pipeline@v0.9.0 · 5526 in / 1308 out tokens · 68231 ms · 2026-05-08T07:47:46.090747+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    Alvarez, A. M., Q. Louveaux, L. Wehenkel. 2017. A machine learning-based approximation of strong branching. INFORMS Journal on Computing\/ , 29 (1), 185-195

    work page 2017

  2. [2]

    Ahmed, S

    Basciftci, B., S. Ahmed, S. Shen. 2021. Distributionally robust facility location problem under decision-dependent stochastic demand. European Journal of Operational Research\/ , 292 (2), 548-561

    work page 2021

  3. [3]

    Nemirovski, L

    Ben-Tal, A., A. Nemirovski, L. El Ghaoui. 2009. Robust optimization\/ . Princeton University Press

    work page 2009

  4. [4]

    Cory-Wright, J

    Bertsimas, D., R. Cory-Wright, J. Vassilis Digalakis. 2023. Decarbonizing OCP . Manufacturing & Service Operations Management\/ , 27 (6), 1760-1778

    work page 2023

  5. [5]

    Aboussalah, E

    Chi, C., A. Aboussalah, E. Khalil, J. Wang, Z. Sherkat-Masoumi. 2022. A deep reinforcement learning framework for column generation. Advances in Neural Information Processing Systems\/ , 35 9633-9644

    work page 2022

  6. [6]

    Jiang, X

    Cui, F., Z. Jiang, X. Zhou, J. Zheng, N. Geng. 2025. A configuration optimization approach for reconfigurable manufacturing system based on column-generation combined with graph neural network. International Journal of Production Research\/ , 63 (3), 970-991

    work page 2025

  7. [7]

    Martin, M

    De Haas, R., R. Martin, M. Muûls, H. Schweiger. 2025. Managerial and financial barriers to the green transition. Management Science\/ , 71 (4), 2890-2921

    work page 2025

  8. [8]

    Delage, E., Y. Ye. 2010. Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research\/ , 58 (3), 595-612

    work page 2010

  9. [9]

    Drake, D. F., P. R. Kleindorfer, L. N. Van Wassenhove. 2016. Technology choice and capacity portfolios under emissions regulation. Production and Operations Management\/ , 25 (6), 1006-1025

    work page 2016

  10. [10]

    Huang, X

    Gao, Y., W. Huang, X. Liu. 2025. Adjustable robust disassembly planning and dynamic capacity expansion for reverse supply chain network. Available at SSRN 5270969

    work page 2025

  11. [11]

    Golari, M., N. Fan, T. Jin. 2017. Multistage stochastic optimization for production‐inventory planning with intermittent renewable energy. Production and Operations Management\/ , 26 (3), 409-425

    work page 2017

  12. [12]

    Ahmed, M

    Gulrajani, I., F. Ahmed, M. Arjovsky, V. Dumoulin, A. C. Courville. 2017. Improved training of wasserstein gans. Advances in Neural Information Processing Systems \/ , vol. 30

    work page 2017

  13. [13]

    Hao, Z., L. He, Z. Hu, J. Jiang. 2020. Robust vehicle pre‐allocation with uncertain covariates. Production and Operations Management\/ , 29 (4), 955-972

    work page 2020

  14. [14]

    Ozaltin, R

    Hijazi, A., O. Ozaltin, R. Uzsoy. 2024. All you need is an improving column: Enhancing column generation for parallel machine scheduling via transformers. ArXiv:2410.15601 [cs]

    work page arXiv 2024

  15. [15]

    Huang, X. N., T. Tan, L. B. Toktay. 2021. Carbon leakage: The impact of asymmetric regulation on carbon‐emitting production. Production and Operations Management\/ , 30 (6), 1886-1903

    work page 2021

  16. [16]

    Jakubovskis, A. 2017. Flexible production resources and capacity utilization rates: A robust optimization perspective. International Journal of Production Economics\/ , 189 77-85

    work page 2017

  17. [17]

    Jia, H., S. Shen. 2021. Benders cut classification via support vector machines for solving two-stage stochastic programs. INFORMS Journal on Optimization\/ , 3 (3), 278-297

    work page 2021

  18. [18]

    Seizinger, J

    Kraul, S., M. Seizinger, J. O. Brunner. 2023. Machine learning–supported prediction of dual variables for the cutting stock problem with an application in stabilized column generation. INFORMS Journal on Computing\/ , 35 (3), 692-709

    work page 2023

  19. [19]

    Laura, C., G. Tim. 2024. World energy outlook 2024. Tech. rep., International Energy Agency. .iea.org

    work page 2024

  20. [20]

    Lee, C.-Y., A. L. Johnson. 2014. Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments. European Journal of Operational Research\/ , 232 (3), 537-548

    work page 2014

  21. [21]

    Lee, H. L., C. S. Tang. 2018. Socially and environmentally responsible value chain innovations: New operations management research opportunities. Management Science\/ , 64 (3), 983-996

    work page 2018

  22. [22]

    Liang, Z., F. Xiao, X. Qian, L. Zhou, X. Jin, X. Lu, S. Karichery. 2018. A column generation-based heuristic for aircraft recovery problem with airport capacity constraints and maintenance flexibility. Transportation Research Part B: Methodological\/ , 113 70-90

    work page 2018

  23. [23]

    Lin, Y.-T., H. Sun, S. Wang. 2020. Designing sustainable products under coproduction technology. Manufacturing & Service Operations Management\/ , 22(6) (6), 1181-1198

    work page 2020

  24. [24]

    Saldanha-da Gama, S

    Liu, T., F. Saldanha-da Gama, S. Wang, Y. Mao. 2022. Robust stochastic facility location: Sensitivity analysis and exact solution. INFORMS Journal on Computing\/ , 34 (5), 2776-2803

    work page 2022

  25. [25]

    Lu, M., Z. M. Shen. 2021. A review of robust operations management under model uncertainty. Production and Operations Management\/ , 30 (6), 1927-1943

    work page 2021

  26. [26]

    Lu, Z., B. Zeng. 2024. Two-stage distributionally robust optimization: Intuitive understanding and algorithm development from the primal perspective. ArXiv:2412.20708 [math]

    work page arXiv 2024

  27. [27]

    Cheung, M

    Lyu, G., W.-C. Cheung, M. C. Chou, C.-P. Teo, Z. Zheng, Y. Zhong. 2019. Capacity allocation in flexible production networks: Theory and applications. Management Science\/ , 65 (11), 5091-5109

    work page 2019

  28. [28]

    Mas-Machuca, E

    Martínez-Costa, C., M. Mas-Machuca, E. Benedito, A. Corominas. 2014. A review of mathematical programming models for strategic capacity planning in manufacturing. International Journal of Production Economics\/ , 153 66-85

    work page 2014

  29. [29]

    Desaulniers, A

    Morabit, M., G. Desaulniers, A. Lodi. 2021. Machine-learning–based column selection for column generation. Transportation Science\/ , 55 (4), 815-831

    work page 2021

  30. [30]

    Desaulniers, A

    Morabit, M., G. Desaulniers, A. Lodi. 2023. Machine-learning–based arc selection for constrained shortest path problems in column generation. INFORMS Journal on Optimization\/ , 5 (2), 191-210

    work page 2023

  31. [31]

    Solving mixed integer programs using neural networks

    Nair, V., S. Bartunov, F. Gimeno, I. v. Glehn, P. Lichocki, I. Lobov, B. O'Donoghue, N. Sonnerat, C. Tjandraatmadja, P. Wang, R. Addanki, T. Hapuarachchi, T. Keck, J. Keeling, P. Kohli, I. Ktena, Y. Li, O. Vinyals, Y. Zwols. 2021. Solving mixed integer programs using neural networks. ArXiv:2012.13349 [math]

    work page arXiv 2021

  32. [32]

    Pham, A., T. Jin, C. Novoa, J. Qin. 2019. A multi-site production and microgrid planning model for net-zero energy operations. International Journal of Production Economics\/ , 218 260-274

    work page 2019

  33. [33]

    Davarnia

    Rajabalizadeh, A., D. Davarnia. 2024. Solving a class of cut-generating linear programs via machine learning. INFORMS Journal on Computing\/ , 36 (3), 708-722

    work page 2024

  34. [34]

    Rehman, S., M. A. Bader, S. A. Al-Moallem. 2007. Cost of solar energy generated using PV panels. Renewable and Sustainable Energy Reviews\/ , 11 (8), 1843-1857

    work page 2007

  35. [35]

    Saif, A., E. Delage. 2021. Data-driven distributionally robust capacitated facility location problem. European Journal of Operational Research\/ , 291 (3), 995-1007

    work page 2021

  36. [36]

    Shapiro, A. 2001. On duality theory of conic linear problems. Nonconvex Optimization and its Applications \/ , vol. 57. Springer US, 135-155

    work page 2001

  37. [37]

    Dentcheva, A

    Shapiro, A., D. Dentcheva, A. Ruszczynski. 2021. Chapter 1: Stochastic programming models. Lectures on Stochastic Programming : Modeling and Theory , Third Edition \/ . SIAM, 1-20

    work page 2021

  38. [38]

    Govindan, L

    Song, S., K. Govindan, L. Xu, P. Du, X. Qiao. 2017. Capacity and production planning with carbon emission constraints. Transportation Research Part E: Logistics and Transportation Review\/ , 97 132-150

    work page 2017

  39. [39]

    Zhang, M

    Wang, Y., Y. Zhang, M. Zhou, J. Tang. 2023. Feature‐driven robust surgery scheduling. Production and Operations Management\/ , 32 (6), 1921-1938

    work page 2023

  40. [40]

    Wiesemann, W., D. Kuhn, M. Sim. 2014. Distributionally robust convex optimization. Operations Research\/ , 62 (6), 1358-1376

    work page 2014

  41. [41]

    Chen, J.-F

    Wu, T., W. Chen, J.-F. Cordeau, R. Jans. 2025. Machine learning-empowered Benders decomposition for flow hub location in e-commerce. INFORMS Journal on Computing\/ , 0 (0), 0

    work page 2025

  42. [42]

    Yu, X., S. Shen. 2024. On the value of risk-averse multistage stochastic programming in capacity planning. INFORMS Journal on Computing\/ , 37 (5), 1143-1162

    work page 2024

  43. [43]

    Zeng, B., L. Zhao. 2013. Solving two-stage robust optimization problems using a column-and-constraint generation method. Operations Research Letters\/ , 41 (5), 457-461

    work page 2013

  44. [44]

    Zhang, Y., Z. M. Shen, S. Song. 2016. Distributionally robust optimization of two‐stage lot‐sizing problems. Production and Operations Management\/ , 25 (12), 2116-2131

    work page 2016

  45. [45]

    Zhou, X., B. Zeng, F. Cui, N. Geng. 2025. Towards green manufacturing: Co -optimizing capacity expansion planning of production and renewable energy generation with endogenous uncertainty. Computers & Operations Research\/ , 176 106971

    work page 2025