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VOL. 11, ISSUE 2 (2026)
An integrated multi-echelon inventory model with exponential demand decay, time-dependent costs, and partial deterioration
Authors
Ashish Kumar Routray, Swagatika Dehury, Sudhir Kumar Sahu
Abstract
This paper presents a comprehensive three-echelon inventory model for
deteriorating items under exponentially decaying demand. The system encompasses
an Own Warehouse (OW) supplying two Retail Warehouses (RW1 and RW2), each
exhibiting distinct deterioration rates governed by separate decay parameters
and linear time-varying holding costs. Employing the integrating factor method,
we derive closed-form analytical solutions for inventory dynamics across all
stages and echelons. The model incorporates partial backlogging with
exponential decay, time-dependent holding costs, and multi-stage deterioration
costs. The complete total cost function (TC) is formulated and its structural
convexity established, guaranteeing a global minimum. Numerical experiments
with a representative parameter set yield a base-case TC ≈ 8,981 monetary
units. Comprehensive sensitivity analysis via a tornado chart,
three-dimensional cost surfaces, and contour maps reveals that the RW2
deterioration rate r and demand scale parameter a exert the strongest influence
on TC (affecting cost by up to 20.8% and 25.7%, respectively). Strategic
managerial insights, including echelon positioning, dynamic pricing
recommendations, and a phased implementation roadmap, are provided to support
real-world deployment.
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Pages:67-77
How to cite this article:
Ashish Kumar Routray, Swagatika Dehury, Sudhir Kumar Sahu "An integrated multi-echelon inventory model with exponential demand decay, time-dependent costs, and partial deterioration". International Journal of Advanced Scientific Research, Vol 11, Issue 2, 2026, Pages 67-77
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