EOQ model for deteriorating items with fuzzy demand and finite horizon under inflation effects

Kunal Shah; Hardik Joshi

doi:10.3934/dcdss.2024160

Article Contents

2025, Volume 18, Issue 5: 1304-1315. Doi: 10.3934/dcdss.2024160

This issue Previous Article Stock patterns in a class of delayed discrete-time population models Next Article Analysis of the fractional SEIR epidemic model with Caputo derivative via resolvents operators and numerical scheme

EOQ model for deteriorating items with fuzzy demand and finite horizon under inflation effects

Kunal Shah^1, and
Hardik Joshi^2, ,

1.
Department of Mathematics, SMMPISR, Kadi Sarva Vishwavidyalaya, Gandhinagar-382016, Gujarat, India
2.
Department of Mathematics, LJ Institute of Engineering and Technology, LJ University, Ahmedabad-382210, Gujarat, India

^*Corresponding author: Hardik Joshi
^*Corresponding author: Hardik Joshi

Received: June 2024

Revised: August 2024

Early access: September 2024

Published: May 2025

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Abstract

In this research, we explore an innovative finite horizon Economic Order Quantity (EOQ) model for items that deteriorate over time, incorporating the effects of inflation and fuzzy demand characteristics. By applying the centroid method, we translate the fuzzy objective function into a precise, crisp equivalent. Our study introduces a novel approach to determining the optimal replenishment frequency using advanced calculus techniques. To validate the model, we present detailed numerical examples and conduct a sensitivity analysis to examine how variations in model parameters affect the outcomes. This study advances the field by integrating fuzzy logic with economic inventory models and provides insights into managing inventory with deteriorating items in an inflationary environment.

Keywords:

Mathematics Subject Classification: Primary: 90B05.

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Figure 1. Graphical representation of the optimal solution of example 4.1

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Figure 2. Graphical representation of the optimal solution of example 4.2

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Table 1. Optimal solutions of example 2

$ ({D_1}, {D_2}, {D_3}) $	*$ n_F^ $**	*$ M\left( {\tilde T{C_F}(n_F^)} \right) $**	*$ Q_F^ $**
(250, 300, 315)	12.8840	2239.0830	224.56
(200, 300, 375)	12.9571	2252.2537	227.16

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Table 2. Sensitivity analysis in fuzzy environment

Variation	Optimal			$ \% $ Change in parameter
parameter	values	-20	-10	0	10	20
$ D $	$ \tilde T{C_F}(n) $	1997.866	2121.826	2239.083	2350.62	2457.201
$ D $	$ n_F^* $	11.5444	12.2328	12.88401	13.50347	14.09541
$ D $	$ Q_F^* $	179.6528	202.1094	224.566	247.0226	269.4792
$ A $	$ \tilde T{C_F}(n) $	2007.062	2126.426	2239.083	2346.02	2448.003
$ A $	$ n_F^* $	14.38215	13.57053	12.88401	12.29345	11.7784
$ A $	$ Q_F^* $	224.566	224.566	224.566	224.566	224.566
$ h $	$ \tilde T{C_F}(n) $	2104.554	2172.836	2239.083	2303.466	2366.134
$ h $	$ n_F^* $	12.13688	12.5161	12.88401	13.24158	13.58963
$ h $	$ Q_F^* $	224.566	224.566	224.566	224.566	224.566
$ c $	$ \tilde T{C_F}(n) $	2138.961	2189.582	2239.083	2287.536	2335.006
$ c $	$ n_F^* $	12.32797	12.6091	12.88401	13.15311	13.41675
$ c $	$ Q_F^* $	224.566	224.566	224.566	224.566	224.566
$ \theta $	$ \tilde T{C_F}(n) $	2131.709	2185.959	2239.083	2291.153	2342.232
$ \theta $	$ n_F^* $	12.24707	12.56871	12.88401	13.19339	13.4972
$ \theta $	$ Q_F^* $	222.8692	223.7155	224.566	225.4208	226.2799
$ H $	$ \tilde T{C_F}(n) $	1791.266	2015.175	2239.083	2462.991	2686.9
$ H $	$ n_F^* $	10.30721	11.59561	12.88401	14.17241	15.46081
$ H $	$ Q_F^* $	178.2954	201.3439	224.566	247.9628	271.5359
$ r $	$ \tilde T{C_F}(n) $	2255.59	2247.32	2239.083	2230.88	2222.711
$ r $	$ n_F^* $	12.92636	12.9051	12.88401	12.86308	12.84232
$ r $	$ Q_F^* $	224.566	224.566	224.566	224.566	224.566

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