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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Valuation of Memory Effect of Fuzzy EOQ Model with Constant Demand Rate

Discontinuity, Nonlinearity, and Complexity 13(3) (2024) 437--453 | DOI:10.5890/DNC.2024.09.004

Rituparna Pakhira$^1$, Bapin Mondal$^2$, Uttam Ghosh$^2$, Vishnu Narayan Mishra$^3$

$^1$ Academy of Technology, Adisaptagram, Hooghly, West Bengal, India

$^2$ Department of Applied Mathematics, University of Calcutta, Kolkata-700009, India

$^3$ Department of Applied Mathematics Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh, India

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Abstract

It is well-known to everyone that the system is very much disturbed by the past experience effect so past experiences should be incorporated into the system. For a rapidly changing market, the cost parameters of the inventory system are highly uncertain. Due to the above reasons, in this paper, we want to develop an EOQ model with a constant demand rate for non - deteriorating items where shortages are not allowed with Caputo fractional order derivative under a fuzzy environment. Here, we have used the concept ``fractional order is an index of memory''. Two types of memory indexes have been established. Memory effect has been observed by the step of long memory, short memory, and memoryless stages. The fractional order inventory model has been defuzzified using the graded mean integration method and signed distance method. Our numerical analysis clears us that profit is maximum for the presence of both memory indexes. In the long memory effect, inventory level changes roughly but this type of change happens, in reality, i.e., once increases then decrease again increases. From the graphical presentations, it can be suggested that there is a critical value of the ordering interval where long memory affected the total average cost and short memory affected total average cost becomes equal in both defuzzification techniques graded mean integration method, signed distance method.

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