NUMERICAL HALLUCINATION IN SOLVER: INTEGRITY BREAKDOWN UNDER REGIONAL SETTINGS IN Â Â Â Â Â Â Â Â MICROSOFT EXCEL
Abstract
This study investigates a critical computational behavior in Microsoft Excel associated with the use of Solver in optimization problems. In experiments conducted using the GRG Nonlinear method, it is observed that removing the integrality constraint (INT) may produce mathematically consistent results that are nevertheless incompatible with the model’s constraints. The phenomenon, termed numerical hallucination, is characterized by the generation of magnitudes incompatible with the feasible region. The analysis is based on models with explicit bounds subjected to different regional settings. The results indicate that the inconsistency does not originate in the solution process, but in the interpretation of data during state reconstruction, being directly associated with the use of decimal separators. Scenario restoration reveals this distortion by producing results that preserve algebraic consistency but violate the model’s constraints. It is further observed that enforcing the integrality constraint (INT) acts as a containment mechanism, whereas its removal exposes the system to susceptibility to scale distortions under certain configurations. It is concluded that the observed behavior does not arise from the optimization method itself, but from limitations in data interpretation, requiring rigorous verification of regional settings and constraints in continuous models.
Â
Author Biography
Writer and University Professor in topics related to the exact sciences and Educational Technologies. Master’s degree in Natural Sciences and Mathematics from the Regional University of Blumenau – FURB (2012). Specialist in Methodology of Mathematics Teaching – IBPEX (2006). Bachelor’s degree in Accounting from the University of the Region of Joinville – UNIVILLE (2000). Holds a Pedagogical Teaching Certification from the University Center of Jaraguá do Sul – UNERJ (2006). Professor in professional and technological education, at the levels of technical secondary education, undergraduate technological education, and graduate studies. Has over 20 years of experience in accounting, administrative, and production processes in the Vale do Itapocu region – SC.
References
BAXTER, Richard; THORNE, Simon. Spreadsheet risk and data integrity in modern organizations. Information Systems Journal, v. 31, n. 4, p. 567–589, 2021.
BAZARAA, M. S.; SHERALI, H. D.; SHETTY, C. M. Nonlinear Programming: Theory and Algorithms. 3. ed. Hoboken: John Wiley & Sons, 2006.
BEASLEY, John E. Heuristic algorithms for optimization. In: Advances in Computational Optimization. Dordrecht: Springer, p. 1–23, 1996.
BORBA, Marcelo C.; VILLARREAL, Mónica E. Humans-with-Media and the Reorganization of Mathematical Thinking. New York: Springer, 2005.
CAULKINS, Jonathan P.; MORRISON, Ellen L.; WECHSLER, Harry. Spreadsheet errors and decision making: evidence and implications. Interfaces, v. 49, n. 3, p. 189–203, 2019.
GASS, Saul I. Linear Programming: Methods and Applications. New York: Dover Publications, 2003.
GONÇALVES, Rafael Alberto. Introdução à matemática financeira por meio de planilhas eletrônicas: Calc & Excel no ensino médio. Saarbrücken: Novas Edições Acadêmicas, 2014.
GONÇALVES, Rafael Alberto. Aritmética no Excel: o silêncio da Microsoft frente à educação global. ARACÊ – Revista Brasileira de Tecnologia Educacional, São José dos Pinhais, v. 7, n. 9, p. 1–20, 2025 DOI: https://doi.org/10.56238/arev7n9-086
GONÇALVES, Rafael Alberto; MARTIM, Robert F. Série ao extremo: programando o Excel com VBA – do básico até banco de dados e APIs do Windows. 1. ed. Juatuba, MG: Instituto Alpha Educação a Distância e Editora, 2018.
GROSSMAN, Thomas A. Spreadsheet engineering: a research framework. In: EUROPEAN SPREADSHEET RISKS INTEREST GROUP CONFERENCE, 2002.
HILLIER, Frederick S.; LIEBERMAN, Gerald J. Introduction to Operations Research. 10. ed. New York: McGraw-Hill, 2015.
KANKANHALLI, Atreyi; TAN, Bernard C. Y.; WEI, Kwok Kee. Spreadsheet risks and controls: a review. MIS Quarterly Executive, v. 17, n. 1, p. 1–13, 2018.
PANKO, Raymond R. What we know about spreadsheet errors. Journal of End User Computing, v. 10, n. 2, p. 15–21, 2008.
PANKO, Raymond R. What we know about spreadsheet errors. Journal of End User Computing, v. 27, n. 2, p. 1–18, 2015.
POWELL, Stephen G.; BAKER, Kenneth R.; LAWSON, Barry. Errors in operational spreadsheets. Decision Support Systems, v. 46, n. 1, p. 128–138, 2009.
RAFFENSPERGER, John F. New guidelines for spreadsheets. European Journal of Operational Research, v. 128, n. 3, p. 671–687, 2001.
SKOVSMOSE, Ole. Towards a Philosophy of Critical Mathematics Education. Dordrecht: Kluwer Academic Publishers, 2001.
WILLIAMS, H. Paul. Model Building in Mathematical Programming. 5. ed. Chichester: Wiley, 2013.
License
Copyright (c) 2026 RECIMA21 - Revista CientÃfica Multidisciplinar - ISSN 2675-6218
This work is licensed under a Creative Commons Attribution 4.0 International License.
Os direitos autorais dos artigos/resenhas/TCCs publicados pertecem à revista RECIMA21, e seguem o padrão Creative Commons (CC BY 4.0), permitindo a cópia ou reprodução, desde que cite a fonte e respeite os direitos dos autores e contenham menção aos mesmos nos créditos. Toda e qualquer obra publicada na revista, seu conteúdo é de responsabilidade dos autores, cabendo a RECIMA21 apenas ser o veÃculo de divulgação, seguindo os padrões nacionais e internacionais de publicação.Â