Journal of Applied Nonlinear Dynamics
Study of Memory Effect in an Inventory Model with Constant Deterioration Rate
Journal of Applied Nonlinear Dynamics 10(2) (2021) 229243  DOI:10.5890/JAND.2021.06.004
Rituparna Pakhira$^{1}$, Uttam Ghosh$^{1}$, Susmita Sarkar$^{1}$, Vishnu Narayan Mishra$^{2}$
$^{1}$ Department of Applied Mathematics, University of Calcutta, Kolkata
$^{2}$ Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak 484 887,
Anuppur, Madhya Pradesh, India
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Abstract
In any business memory effect has great importance in inventory management as memory or past history cannot be ignored from the practical life of the inventory system. Many exogenous inventory parameters and factors at a given time depends not only their current values but also on the past histories. Thus an inventory management is a non Markovian process which can be tackled with memory dependent kernel of fractional derivatives. Another important factor of inventory management is deterioration of items which is directly related with memory effect as long memory of high rate of deterioration leads to poor impact on the business. Effect of long memory on deterioration of items have been studied in this paper using memory kernel of fractional derivatives. Fractional integration has been used to derive fractional order holding cost, deterioration cost, shortage cost and opportunity cost. Our analysis shows that for gradually increasing memory effect profit gradually increases. Our model is developed as a memory dependent inventory model.
Acknowledgments
The authors would like to thank Editor and Reviewers for his valuable suggestions to improve the papers. The first author would also like to thank the Department of science and Technology, Government of India, New Delhi, for the financial assistance under AORC, Inspire fellowship Scheme towards her PhD research work.
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