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International Journal of Creative and Open Research in Engineering and Management

A Peer-Reviewed, Open-Access International Journal Supporting Multidisciplinary Research, Digital Publishing Standards, DOI Registration, and Academic Indexing.
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ISSN: 3108-1754 (Online)
Crossref DOI: Available
ISO Certification: 9001:2015
Publication Fee: 599/- INR
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License: CC BY 4.0
Peer Review: Double Blind
Volume 02, Issue 8

Published on: August 2026

SHIFT-INVARIANT SPECTRAL ANALYSIS OF MULTI-ECHELON SUPPLY-CHAIN LEAD TIMES VIA THE FKF TRANSFORM

Akarshan Gulhane

PTC Software Inc.
DOI:https://doi.org/10.55041/ijcope.v2i8.136

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Plagiarism Passed Peer Reviewed Open Access

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Abstract

The FKF transform furnishes a joint spectral representation of temporal dynamics and positive-valued scale variables that arise naturally in multi-echelon supply chains. This paper presents a complete theoretical treatment of the shift (time-translation) property of the FKF transform. We prove that a pure lead-time delay L maps to multiplication of the spectrum by the complex exponential e^{−i s L}, rigorously establish magnitude preservation and phase-based recovery of L, and extend the result to cascaded (series) and concurrent (parallel) delay structures. The interaction of the delay factor with the Kontorovich–Lebedev scale variable q is examined, revealing how lead-time criticality can depend on shipment volume or inventory intensity. Practical estimation procedures based on phase unwrapping and linear regression are derived. The framework is linked to contemporary research on digital twins, Industry 5.0 logistics, artificial-intelligence forecasting and supply-chain resilience. Supporting tables, S-curve illustrations of cumulative delay impact, and conceptual schematics of series/parallel architectures are provided. All mathematical expressions are rendered in native professional equation format.

How to Cite this Paper

Gulhane, A. (2026). Shift-Invariant Spectral Analysis of Multi-Echelon Supply-Chain Lead Times via the FKF Transform. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-9. https://doi.org/10.55041/ijcope.v2i8.136

Gulhane, Akarshan. "Shift-Invariant Spectral Analysis of Multi-Echelon Supply-Chain Lead Times via the FKF Transform." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 8, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i8.136.

Gulhane, Akarshan. "Shift-Invariant Spectral Analysis of Multi-Echelon Supply-Chain Lead Times via the FKF Transform." International Journal of Creative and Open Research in Engineering and Management 02, no. 8 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i8.136.

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References


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  • •Review follows editorial policy.
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  • •Peer Review Type: Double-Blind Peer Review
  • •Published on: Aug 17 2026
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