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arxiv: 2406.07184 · v4 · submitted 2024-06-11 · 🧮 math.OC

Bilevel optimization with sustainability perspective: A survey on applications

Giulia Caselli , Manuel Iori , Ivana Ljubi\'c This is my paper

Pith reviewed 2026-05-24 00:09 UTC · model grok-4.3

classification 🧮 math.OC
keywords bilevel optimizationsustainabilityapplicationstransportationsupply chainsdisaster managementoperations researchsurvey
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The pith

Bilevel optimization classifies sustainable applications by domain and links to standard operations research problems.

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

The paper surveys how bilevel optimization models hierarchical decisions with sustainability objectives spanning economic, environmental, and social goals. It introduces bilevel concepts and typical pricing problem formulations, then organizes published works by application domains such as transportation and logistics, production planning, water and agriculture management, supply chains, and disaster response, while associating each with familiar operations research problems and noting solution methods. A sympathetic reader would care because the structure maps patterns across these intersecting fields and surfaces open questions. The survey aims to make the literature on sustainable bilevel models more navigable through this domain-based classification.

Core claim

Sustainable bilevel optimization applications are reviewed and classified according to their domains and associations with well-known operations research problems, with bilevel pricing problems serving as common mathematical formulations that cover many of the collected works across transportation, manufacturing, supply chains, water and waste management, agriculture, and disaster prevention.

What carries the argument

Classification of applications by domain and their association with standard operations research problems, which structures the overview of bilevel models, sustainability objectives, and solution methodologies.

If this is right

  • Many sustainable bilevel problems across domains share bilevel pricing formulations.
  • Solution methodologies can be compared within the domain and operations research problem groupings.
  • The classification highlights areas such as disaster response where bilevel models address multi-stakeholder sustainability trade-offs.
  • Open questions identified point to extensions in integrating additional sustainability criteria into existing bilevel frameworks.

Where Pith is reading between the lines

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

  • The domain classification could support cross-domain transfer of bilevel solution techniques between similar operations research problem types.
  • Future work might test whether the pricing formulations generalize to new sustainability applications not yet surveyed.
  • The structure suggests opportunities for empirical comparisons of model performance across the five domains using shared benchmarks.

Load-bearing premise

The collected works are representative of the field and the classification by domain and associated operations research problems is a useful organizing structure.

What would settle it

A search that locates many sustainable bilevel optimization papers falling outside the listed domains or lacking clear ties to the mentioned operations research problems would undermine the classification's coverage.

Figures

Figures reproduced from arXiv: 2406.07184 by Giulia Caselli, Ivana Ljubi\'c, Manuel Iori.

Figure 1
Figure 1. Figure 1: Sustainable bilevel problems in various sectors. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Taxonomy of bilevel games and players. as two members of the same supply chain (SC) or two SCs competing in the same market (“SC1” and “SC2”). In these cases, for instance, the former optimizes customer selection and routing decisions and the latter makes production planning decisions. Many real￾world bilevel problems are modeled as SLMF games between one leader, a policy maker, and multiple followers, com… view at source ↗
Figure 3
Figure 3. Figure 3: Taxonomy of economic, environmental, and social o [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

Bilevel optimization, a well-established field for modeling hierarchical decision-making problems, has recently intersected with sustainability studies and practices, resulting in a series of works focusing on bilevel optimization problems involving multiple decision makers with diverse economic, environmental, and social objectives. This survey offers a comprehensive overview of sustainable bilevel optimization applications. First, we introduce the main concepts related to the nature of bilevel optimization problems and present some typical mathematical formulations for bilevel pricing problems that cover many of the collected applications. Then, we review the most relevant works published in sustainable bilevel optimization, giving a classification based on the application domains and their association with well-known operations research problems, while briefly discussing the proposed solution methodologies. We survey applications on transportation and logistics, production planning and manufacturing, water, waste, and agriculture management, supply chains, and disaster prevention and response. Finally, we outline a list of open questions and opportunities for future research in this domain.

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 / 0 minor

Summary. The manuscript surveys applications of bilevel optimization to sustainability problems. It introduces bilevel optimization concepts and typical mathematical formulations for bilevel pricing problems, reviews relevant works classified by application domains (transportation and logistics, production planning and manufacturing, water/waste/agriculture management, supply chains, disaster prevention and response) and their links to standard OR problems while briefly discussing solution methodologies, and concludes by outlining open questions and future research opportunities.

Significance. If the reviewed literature is representative, the domain-based classification and explicit connections to classical OR problems would provide a useful organizing framework for researchers at the intersection of bilevel optimization and sustainability applications.

major comments (1)
  1. [Abstract] Abstract and opening paragraphs: the claim of offering a 'comprehensive overview' of sustainable bilevel optimization applications rests on the representativeness of the collected works, yet no search protocol, databases, keywords, date range, or inclusion criteria are provided anywhere in the manuscript. This directly affects the validity of both the overview and the proposed classification.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and constructive feedback. We agree that explicitly documenting the literature search methodology will strengthen the manuscript's claims of providing a comprehensive overview and will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract and opening paragraphs: the claim of offering a 'comprehensive overview' of sustainable bilevel optimization applications rests on the representativeness of the collected works, yet no search protocol, databases, keywords, date range, or inclusion criteria are provided anywhere in the manuscript. This directly affects the validity of both the overview and the proposed classification.

    Authors: We acknowledge this limitation. The current manuscript does not include a dedicated description of the literature collection process. In the revised version, we will add a new subsection (likely in Section 1 or as an appendix) that specifies: the databases consulted (Scopus, Web of Science, Google Scholar), the primary keywords and Boolean combinations used, the time period covered (e.g., 2000–2024), and the inclusion/exclusion criteria applied to select the reviewed papers. This addition will clarify the scope and support the representativeness of the domain-based classification. revision: yes

Circularity Check

0 steps flagged

No circularity: survey paper with no derivations or self-referential claims

full rationale

This is a literature review surveying external published works on sustainable bilevel optimization. No mathematical derivations, predictions, fitted parameters, or ansatzes are present. The classification by domain and OR problems draws from cited external results rather than reducing to the authors' own inputs or self-citations by construction. The collection process is not a derivation step and does not trigger any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a survey paper; it introduces no mathematical models, derivations, or new entities. The content rests on the existence of the cited literature in bilevel optimization and sustainability studies.

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Reference graph

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