Summary
This report evaluates a 2010 European Journal of Operational Research paper by Canbolat and Wesolowsky (DOI: 10.1016/j.ejor.2009.04.023) for potential academic fraud. Verdict: SUSPICIOUS (low-severity). The investigation flagged a clear copy-paste citation error in the references section: the entry for Batta, Ghose & Palekar (1989) was assigned the same volume (28), issue (1), and page range (70–76) as Aneja & Parlar (1994), contradicting the actual Transportation Science 23(1), 26–36 citation. No evidence of fabricated mathematical content was found. Independent verification of Theorem 2's convexity proof and Table 2/Table 4 numerical examples showed internally consistent, mathematically plausible results with smooth piecewise-convex behavior. Figures could not be pixel-analyzed but appear programmatically generated. Overall, the citation error is most likely a careless formatting mistake rather than intentional misconduct, but it warrants correction.
Verdict
🟡 SUSPICIOUS — A copy-paste citation error was identified, but the core mathematical content and numerical results appear authentic. Low confidence that this constitutes deliberate fraud; high confidence that an erratum is needed.
Key findings
- Citation metadata error (medium severity): Two distinct references in the bibliography share identical volume (28), issue (1), and page numbers (70–76). The Aneja & Parlar (1994) citation is correctly assigned to *Transportation Science* 28(1), 70–76, but the Batta, Ghose & Palekar (1989) entry — which should be *Transportation Science* 23(1), 26–36 — was erroneously duplicated from the adjacent citation, indicating copy-paste without final proofreading.
- Mathematical content verified (positive): Independent reconstruction of the expected distance expansion
$E[l_1^B] = \frac{(x-x_i)^2}{2r} + \left(1 - \frac{l}{r}\right)|x-x_i| + \frac{l^2}{2r}$
matches the convex form stated in the Theorem 2 proof.
- Numerical examples consistent (positive): Table 4 objective values (51.43, 48.78, 46.46, 46.25, 48.21 …) trace a smooth piecewise-convex trajectory with a minimum of 46.25 at x = 7, consistent with Table 2. The pattern is non-random and aligns with convex optimization theory.
- Figure analysis not feasible: No high-resolution images were available for pixel-level inspection. Given the mathematical self-consistency of the surrounding text, image fabrication is considered unlikely.
Evidence highlights
- Reference duplication: *Transportation Science* 28(1), 70–76 cited for both Aneja & Parlar (1994) and Batta, Ghose & Palekar (1989); correct Batta citation is 23(1), 26–36.
- DOI: 10.1016/j.ejor.2009.04.023
- Theorem 2 algebraic identity verified against paper's stated convex form.
- Table 4 minimum value 46.25 at x = 7 matches Table 2 optimum, demonstrating internal coherence.
Notes
- The citation anomaly is symptomatic of careless reference management rather than fabricated scholarship, but it should be corrected in an erratum.
- No grounds for a PubPeer misconduct allegation based on current evidence.
- Pixel-level image forensics were not possible due to lack of source figures.
- Report generated with AI assistance; final determination of misconduct requires institutional investigation.
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