Issue |
RAIRO-Oper. Res.
Volume 57, Number 4, July-August 2023
|
|
---|---|---|
Page(s) | 1767 - 1784 | |
DOI | https://doi.org/10.1051/ro/2023095 | |
Published online | 14 July 2023 |
Effect of reliability and memory on fractional inventory model incorporating promotional effort on demand
1
Maulana Abul Kalam Azad University of Technology, Kolkata 700064, India
2
Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, India
3
Department of Mathematics, Arignar Anna Government Arts and Science College, Karaikal 609605, Puducherry, India
4
Department of Mathematics, Dr. Kalaignar M. Karunanidhi Government Institute for P.G. Studies & Research, Karaikal 609605, India
* Corresponding author: akhilesh.maths@gmail.com
Received:
7
November
2022
Accepted:
12
June
2023
This paper presents a study of inventory replenishment strategy for efficiently managing sales of a deteriorating item in a retail store. The study addresses pertinent effect on sales pattern due to promotional initiatives. The memory effect generated in the consumers’ mind due to various factors like branding and the stock visibility to customers is incorporated in our model by formulating it as a Caputo–Fabrizio fractional differential equation. Even, in practice, consumers’ purchase patterns are noticed to get influenced by the reliability of product, the same is modelled through demand rate formulation. Influence of both these factors is incorporated into the proposed formulation by representing them as model parameters. The study aims at determining the optimal replenishment quantity and its reordering time for the addressed item in terms of said factors estimated as parameters. Results of the study are analyzed through the data set obtained from a retail store. The analysis of model-parameters infers some managerial insights which match the reality of sales patterns. Our study provides a decision support framework for determining replenishment quantities along with an estimate of replenishment time in connection with promotional initiatives and reliability of the product for achieving minimal total cost incurred while keeping the selling price of the product as fixed.
Mathematics Subject Classification: 90B05 / 90B25 / 90B50
Key words: Inventory model / Caputo–Fabrizio derivatives / Promotions / Reliability / Deterioration
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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