A Memory Dependent Partial Backlogging Inventory Model for Non Instantaneous Deteriorating Item with Stock Dependent Demand

In this paper we introduce a more generalized inventory model for deteriorating item where the memory effect is taken into consideration to analyze for generalization of our concept. Memory effect in inventory system is introduced here through the viable ideas of fractional calculus approach. Fractional Calculus has a proficiency through which we can signify the memory effect. Here a memory dependent inventory model for non instantaneous deterioration with stock dependent demand and partial backlogging is considered. Fractional order derivative and fractional order integration has been used to calculate holding cost, deterioration cost, backlogging cost, lost sale cost. Here the fractional order differentiation is introduced in terms of Caputo sense. The idea of memory kernel is considered to establish the memory dependent inventory model. Here the different type of costs, optimal ordering interval, minimized total average cost are calculated through both theoretical and numerical way. The memory effect is clearly justified by considering a numerical example. The order of the fractional derivative and integration is considered here as the memory index. Sensitivity analysis has also been presented to recognise the essential model parameter for various memory effected problem in different situation. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.