Explainable Optimization: A Call for Interdisciplinary Action

Altu\u{g} Yal\c{c}{\i}nta\c{s}; \c{S}. \.Ilker Birbil; \.Ilker K\"u\c{c}\"ukparlak; Nur\c{s}en Ayd{\i}n

Mathematical transparency alone does not suffice for stakeholders to trust optimization decisions

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-06-27 17:53 UTC pith:3J4IYKMV

load-bearing objection Position paper calls for 'explainable optimization' as a new field but asserts the explanatory gap without examples or evidence. the 2 major comments →

arxiv 2606.08675 v2 pith:3J4IYKMV submitted 2026-06-07 math.OC

Explainable Optimization: A Call for Interdisciplinary Action

Nur\c{s}en Ayd{\i}n , \c{S}. \.Ilker Birbil , \.Ilker K\"u\c{c}\"ukparlak , Altu\u{g} Yal\c{c}{\i}nta\c{s} This is my paper

classification math.OC

keywords explainable optimizationXOptoperations researchmanagement sciencedecision justificationstakeholder trustinterdisciplinary research

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper contends that operations research models influence real people but are judged mainly on computational performance rather than explanatory power. Access to objectives, constraints, and sensitivity reports fails to deliver the intuitive justifications needed for trust, contestation, and implementation. It therefore advocates establishing explainable optimization, known as XOpt, as a new interdisciplinary domain that draws on behavioral, cognitive, and pragmatic insights to close this gap.

Core claim

The central claim is that the field must develop explainable optimization (XOpt) as a distinct interdisciplinary area because traditional mathematical transparency does not meet stakeholder needs for understanding, trusting, contesting, and implementing decisions.

What carries the argument

explainable optimization (XOpt), an interdisciplinary approach that incorporates behavioral, cognitive, and pragmatic perspectives beyond algorithmic efficiency

Load-bearing premise

Current mathematical transparency through objectives, constraints, shadow prices, and sensitivity reports is insufficient for stakeholders to understand, trust, contest, or implement decisions.

What would settle it

Empirical evidence that providing standard optimization outputs like shadow prices enables stakeholders to fully understand and implement decisions without further explanation.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Optimization models will be evaluated not only on feasibility and optimality but also on their explanatory value.
Interdisciplinary teams will work to create justifications that bridge math outputs and stakeholder reasoning.
Decision makers in healthcare, disaster relief, and workforce management will gain actionable explanations for recommended actions.

Where Pith is reading between the lines

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

Similar explanatory deficits may exist in other quantitative decision fields like machine learning or statistics.
Developing XOpt could involve empirical studies testing which forms of explanation increase stakeholder acceptance.
XOpt might integrate with existing explainable AI methods but focus specifically on optimization structures like constraints and dual variables.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Position paper calls for 'explainable optimization' as a new field but asserts the explanatory gap without examples or evidence.

read the letter

This paper is a position statement arguing that optimization needs a new interdisciplinary area called explainable optimization because access to objectives, constraints, shadow prices, and sensitivity reports does not give stakeholders what they need to understand, trust, contest, or implement decisions.

It does a reasonable job laying out the context: optimization models affect patients, workers, and public resources, and the field has historically measured success by computational performance rather than explanatory power. That observation is straightforward and worth stating.

The soft spot is the lack of grounding for the central claim. The argument rests on the assertion that current mathematical transparency is insufficient, but the text supplies no concrete cases, stakeholder feedback, or references showing where shadow prices or sensitivity reports have actually failed in practice. It also skips any discussion of related work in explainable AI or decision support systems that already address similar issues. Without that, the case for carving out a distinct named field rather than incremental improvements inside existing optimization practice stays untested.

This is for operations research and management science readers who want to think about how their models land with non-experts. It raises a discussion point but contains no methods, data, or derivations.

I would send it for peer review as a perspective piece. The topic deserves community input even if the current version needs more substance to carry the argument.

Referee Report

2 major / 0 minor

Summary. The manuscript argues that optimization models in operations research and management science require explanations beyond traditional mathematical transparency (such as objectives, constraints, shadow prices, and sensitivity reports) to enable stakeholders to understand, trust, contest, and implement decisions. It calls for the establishment of explainable optimization (XOpt) as a new interdisciplinary field that integrates behavioral, cognitive, and pragmatic perspectives.

Significance. If the claimed explanatory deficit is real and widespread, the paper could catalyze research into more stakeholder-friendly optimization methods, potentially increasing the practical impact of OR/MS in domains like healthcare scheduling and resource allocation. The call highlights a potential gap between technical optimality and decision justification.

major comments (2)

Abstract: The central premise that 'Mathematical transparency, provided through access to objectives, constraints, shadow prices, or sensitivity reports, does not automatically offer the forms of justification that stakeholders need to understand, trust, contest, or implement optimization-based decisions' is presented as an assertion without supporting examples, case studies, references to documented failures, or stakeholder feedback showing where standard OR/MS tools have proven inadequate in practice.
The proposal to create XOpt as a distinct field rests on the unverified size of the explanatory gap; the manuscript does not address whether incremental extensions within existing optimization practice (e.g., enhanced sensitivity analysis interfaces or decision-support tools) could address the stated needs without requiring a new named area.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our position paper. We address each major comment below and indicate where revisions will be made to strengthen the argument.

read point-by-point responses

Referee: Abstract: The central premise that 'Mathematical transparency, provided through access to objectives, constraints, shadow prices, or sensitivity reports, does not automatically offer the forms of justification that stakeholders need to understand, trust, contest, or implement optimization-based decisions' is presented as an assertion without supporting examples, case studies, references to documented failures, or stakeholder feedback showing where standard OR/MS tools have proven inadequate in practice.

Authors: We agree that the abstract states the premise concisely. The full manuscript provides context through application domains (healthcare scheduling, disaster relief, workforce planning) but does not include specific case studies or references to failures. In revision we will expand the abstract and add a short section with illustrative examples and citations to existing literature on implementation barriers in OR/MS. revision: yes
Referee: The proposal to create XOpt as a distinct field rests on the unverified size of the explanatory gap; the manuscript does not address whether incremental extensions within existing optimization practice (e.g., enhanced sensitivity analysis interfaces or decision-support tools) could address the stated needs without requiring a new named area.

Authors: The call for a distinct XOpt field is based on the argument that systematic integration of behavioral, cognitive, and pragmatic perspectives requires dedicated interdisciplinary structures that incremental extensions within traditional OR/MS may not prioritize. We will revise the manuscript to explicitly compare the proposed approach with possible incremental enhancements and clarify the rationale for a named area. revision: partial

Circularity Check

0 steps flagged

No circularity: position paper with no derivations or self-referential reductions

full rationale

The paper is a call for creating an interdisciplinary field (XOpt) based on the assertion that existing mathematical transparency tools are insufficient for stakeholder needs. No equations, fitted parameters, predictions, or derivations are present. The central claim does not reduce to any self-definition, fitted input, or self-citation chain; it is an unverified premise about explanatory gaps rather than a technical result constructed from its own inputs. No load-bearing self-citations or ansatz smuggling occur. This matches the default case of a non-circular position paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a position paper with no technical content, the claim rests on the untested premise of an explanatory deficit but introduces no free parameters, mathematical axioms, or postulated entities.

pith-pipeline@v0.9.1-grok · 5723 in / 1000 out tokens · 15171 ms · 2026-06-27T17:53:57.665771+00:00 · methodology

0 comments

read the original abstract

Operations research and management science models support decisions that affect patients, workers, citizens, and public institutions. Decision-makers, such as clinicians approving surgical schedules, planners allocating disaster relief resources, or managers designing workforce rotations, increasingly require clear and actionable justifications that bridge the gap between mathematical optimization outputs and the intuitive reasoning stakeholders need to trust, contest, and implement recommended decisions. Yet the field has traditionally evaluated optimization models through computational criteria such as feasibility, optimality, scalability, and solution time, while treating explanation as a secondary concern. Mathematical transparency, provided through access to objectives, constraints, shadow prices, or sensitivity reports, does not automatically offer the forms of justification that stakeholders need to understand, trust, contest, or implement optimization-based decisions. This paper calls for the development of explainable optimization (XOpt) as a distinct interdisciplinary area that moves beyond algorithmic efficiency and incorporates behavioral, cognitive, and pragmatic perspectives to address this explanatory deficit.

Figures

Figures reproduced from arXiv: 2606.08675 by Altu\u{g} Yal\c{c}{\i}nta\c{s}, \c{S}. \.Ilker Birbil, \.Ilker K\"u\c{c}\"ukparlak, Nur\c{s}en Ayd{\i}n.

**Figure 1.** Figure 1: Illustration of the four agent roles in XOpt: model owner, oversight body, operator, and affected party. satisfies a model owner’s need for system verification will systematically alienate an affected party whose actual need is actionable recourse. Similarly, the same operator may require different explanatory structures in different situations: a high-level visual summary during routine operations, but g… view at source ↗

discussion (0)

Reference graph

Works this paper leans on

12 extracted references · 9 canonical work pages · 1 internal anchor

[1]

EXALT: EXplainable ALgo- rithmic Tools for optimization problems.arXiv preprint arXiv:2503.05789,

Zuzanna Bączek, Michał Bizoń, Adam Pawelec, and Piotr Sankowski. EXALT: EXplainable ALgo- rithmic Tools for optimization problems.arXiv preprint arXiv:2503.05789,

work page arXiv
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Operations research: Topics, impact, and trends from 1952–2019.Operations Research, 69(5):1487–1508,

Angelito Calma, William Ho, Lusheng Shao, and Huashan Li. Operations research: Topics, impact, and trends from 1952–2019.Operations Research, 69(5):1487–1508,

1952
[3]

İlker Birbil, and Ted Ralphs

Felix Engelhardt, Jannis Kurtz, Ş. İlker Birbil, and Ted Ralphs. Counterfactual explanations for integer optimization problems.arXiv preprint, arXiv:2510.17624,

work page arXiv
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Internet of Things27, 101272 (Oct 2024)

doi: 10.1016/j.cola.2024.101272. Michael Fairley, David Scheinker, and Margaret L. Brandeau. Improving the efficiency of the operating room environment with an optimization and machine learning model.Health Care Management Science, 22:756–767,

work page doi:10.1016/j.cola.2024.101272 2024
[5]

Metrics for Explainable AI: Challenges and Prospects

Robert R. Hoffman, Shane T. Mueller, Gary Klein, and Jordan Litman. Metrics for explainable AI: Challenges and prospects.arXiv preprint arXiv:1812.04608,

work page internal anchor Pith review Pith/arXiv arXiv
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Keane, Eoin M

Mark T. Keane, Eoin M. Kenny, Eoin Delaney, and Barry Smyth. If only we had better counterfac- tual explanations: Five key deficits to rectify in the evaluation of counterfactual xai techniques. arXiv preprint, arXiv:2103.01035,

work page arXiv
[7]

It was a magical box

Connor Lawless, Jakob Schoeffer, and Madeleine Udell. “It was a magical box”: Understanding practitioner workflows and needs in optimization.arXiv preprint arXiv:2509.16402,

work page arXiv
[8]

Vera Liao, Daniel Gruen, and Sarah Miller

Q. Vera Liao, Daniel Gruen, and Sarah Miller. Questioning the AI: Informing design practices for explainable AI user experiences. InProceedings of the 2020 CHI Conference on Human Factors in Computing Systems, pages 1–15,

2020
[9]

Planning and scheduling in digital health with answer set programming.arXiv preprint arXiv:2208.03099,

Marco Mochi. Planning and scheduling in digital health with answer set programming.arXiv preprint arXiv:2208.03099,

work page arXiv
[10]

İlker Birbil

Daan Otto, Jannis Kurtz, and Ş. İlker Birbil. Coherent local explanations for mathematical opti- mization.arXiv preprint arXiv:2502.04840,

work page arXiv
[11]

Decision information meets large language models: The future of explainable operations research

Yansen Zhang, Qingcan Kang, Wing Yin Yu, Xiaojin Fu, Xiongwei Han, Tao Zhong, and Chen Ma. Decision information meets large language models: The future of explainable operations research. InInternational Conference on Learning Representations, volume 2025, pages 65698–65722,

2025
[12]

Walker, and Ting Hu

Ryan Zhou, Jaume Bacardit, Alexander Brownlee, Stefano Cagnoni, Martin Fyvie, Giovanni Iacca, John McCall, Niki van Stein, David J. Walker, and Ting Hu. Evolutionary computation and ex- plainable ai: A roadmap to understandable intelligent systems.arXiv preprint arXiv:2406.07811,

work page arXiv

[1] [1]

EXALT: EXplainable ALgo- rithmic Tools for optimization problems.arXiv preprint arXiv:2503.05789,

Zuzanna Bączek, Michał Bizoń, Adam Pawelec, and Piotr Sankowski. EXALT: EXplainable ALgo- rithmic Tools for optimization problems.arXiv preprint arXiv:2503.05789,

work page arXiv

[2] [2]

Operations research: Topics, impact, and trends from 1952–2019.Operations Research, 69(5):1487–1508,

Angelito Calma, William Ho, Lusheng Shao, and Huashan Li. Operations research: Topics, impact, and trends from 1952–2019.Operations Research, 69(5):1487–1508,

1952

[3] [3]

İlker Birbil, and Ted Ralphs

Felix Engelhardt, Jannis Kurtz, Ş. İlker Birbil, and Ted Ralphs. Counterfactual explanations for integer optimization problems.arXiv preprint, arXiv:2510.17624,

work page arXiv

[4] [4]

Internet of Things27, 101272 (Oct 2024)

doi: 10.1016/j.cola.2024.101272. Michael Fairley, David Scheinker, and Margaret L. Brandeau. Improving the efficiency of the operating room environment with an optimization and machine learning model.Health Care Management Science, 22:756–767,

work page doi:10.1016/j.cola.2024.101272 2024

[5] [5]

Metrics for Explainable AI: Challenges and Prospects

Robert R. Hoffman, Shane T. Mueller, Gary Klein, and Jordan Litman. Metrics for explainable AI: Challenges and prospects.arXiv preprint arXiv:1812.04608,

work page internal anchor Pith review Pith/arXiv arXiv

[6] [6]

Keane, Eoin M

Mark T. Keane, Eoin M. Kenny, Eoin Delaney, and Barry Smyth. If only we had better counterfac- tual explanations: Five key deficits to rectify in the evaluation of counterfactual xai techniques. arXiv preprint, arXiv:2103.01035,

work page arXiv

[7] [7]

It was a magical box

Connor Lawless, Jakob Schoeffer, and Madeleine Udell. “It was a magical box”: Understanding practitioner workflows and needs in optimization.arXiv preprint arXiv:2509.16402,

work page arXiv

[8] [8]

Vera Liao, Daniel Gruen, and Sarah Miller

Q. Vera Liao, Daniel Gruen, and Sarah Miller. Questioning the AI: Informing design practices for explainable AI user experiences. InProceedings of the 2020 CHI Conference on Human Factors in Computing Systems, pages 1–15,

2020

[9] [9]

Planning and scheduling in digital health with answer set programming.arXiv preprint arXiv:2208.03099,

Marco Mochi. Planning and scheduling in digital health with answer set programming.arXiv preprint arXiv:2208.03099,

work page arXiv

[10] [10]

İlker Birbil

Daan Otto, Jannis Kurtz, and Ş. İlker Birbil. Coherent local explanations for mathematical opti- mization.arXiv preprint arXiv:2502.04840,

work page arXiv

[11] [11]

Decision information meets large language models: The future of explainable operations research

Yansen Zhang, Qingcan Kang, Wing Yin Yu, Xiaojin Fu, Xiongwei Han, Tao Zhong, and Chen Ma. Decision information meets large language models: The future of explainable operations research. InInternational Conference on Learning Representations, volume 2025, pages 65698–65722,

2025

[12] [12]

Walker, and Ting Hu

Ryan Zhou, Jaume Bacardit, Alexander Brownlee, Stefano Cagnoni, Martin Fyvie, Giovanni Iacca, John McCall, Niki van Stein, David J. Walker, and Ting Hu. Evolutionary computation and ex- plainable ai: A roadmap to understandable intelligent systems.arXiv preprint arXiv:2406.07811,

work page arXiv