Study of Memory Effect in an Inventory Model with Linear Demand and Shortage

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Rituparna Pakhira 1,* Uttam Ghosh 1 Susmita Sarkar 1

1. Department of Applied Mathematics, University of Calcutta, Kolkata, 700009, West Bengal, India

* Corresponding author.


Received: 8 Jan. 2018 / Revised: 3 Mar. 2018 / Accepted: 13 Feb. 2019 / Published: 8 Apr. 2019

Index Terms

Fractional order derivative, Fractional laplace transform method, Fractional order inventory model or memory dependent inventory model


For real market studies of any business, inclusion of memory or past experience in inventory model has great impact. Memory means it depends on the past state of the process not only current state of the process. Indeed, the inventory system is an appropriate example as a memory affected system. Presence of long past experiences or short past experiences of any company or shop has different importance on increasing or decreasing profit. The description of the memory dependent inventory model is more appropriate process compared to the memory less inventory model. Depending on demand rate, a comparison between the minimized total average costs of different numerical example has been presented. Fractional order derivative and integration have been used to establish the model. Our considered numerical example establishes that if linear type demand rate is only time proportional, profit of the business is high compared to the linear type demand rate.

Cite This Paper

Rituparna Pakhira, Uttam Ghosh, Susmita Sarkar,"Study of Memory Effect in an Inventory Model with Linear Demand and Shortage", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.5, No.2, pp.54-70, 2019. DOI: 10.5815/ijmsc.2019.02.05


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