**Study of memory effect in an economic order quantity model with quadratic type demand rate**

Pakhira Rituparna 1, Ghosh Uttam 2, Sarkar Susmita 3

University of Calcutta

Department of Applied Mathematics

Kolkata, 700009

West Bengal, India1 E-mail: rituparna.pakhira@gmail.com

2 E-mail: uttam_math@yahoo.co.in

3 E-mail: susmita62@yahoo.co.in

### Received:

Received: 10 February 2019; revised: 07 June 2019; accepted: 10 June 2019; published online: 24 June 2019

### DOI: 10.12921/cmst.2019.0000004

### Abstract:

The study of memory effect in an economic order quantity model has a great impact on the inventory system. Although business policy almost depends on the past experiences of the system, usually the classical inventory model does not include the past experience or memory effect, i.e. one important part of the system is ignored. Our purpose is to include memory or past experience in the inventory model. The purpose of this paper is to incorporate the existence of dynamic memory in an inventory model with shortage via fractional calculus. To derive the memory dependent inventory model associated with inventory holding cost, shortage cost has been developed. Analytical solution of the proposed inventory model has been solved via primal geometric programming method. Numerically long memory effect or short memory effect of the inventory system has been established. In this paper, an effort has also been made to compare the memory effect on the minimized total average cost and the optimal ordering interval using different numerical examples.

### Key words:

classical inventory model, differential equation with memory kernel, fractional Laplace transforms method, memory dependent Inventory model

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