An inventory model for partial backlogging items with memory effect

Abstract

Abstract In this paper, an EOQ model has been considered where the demand rate is constant for both the stock period and stock out period (i.e. for the period of shortage) and during shortage i.e. stock out period, demand is partially fulfilled at a constant rate. The holding cost here is assumed as time-dependent.The effect of constant backlogging rate and variable backlogging rate are discussed depending on the previous model and present model.Inventory and related phenomena are of agreat importance in the study memory effect.To incorporate memory effect,the model can not be described by the standard ordinary differential equation,it should be developed by standard fractional order differential equation.Moreover,in order to show the relationship between fractional models and standard ordinary first order differential equations,two type of memory indices consider(i) Differential memory index,(ii) integral memory index,equationg two indices to 1,the model would be considered as memoryless model.Different type partial backlogging rate i.e. high partial backlogging rate and low partial backlogging rate has been considered and it is observed that at certain order of differential memory index i.e. at a level of memory effect,profit is equal for high partial backlogging rate and low partial backlogging rate.Atlast,some recommendation is given to develop another paper with the help of this paper.

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