Fractional order inventory system for time-dependent demand influenced by reliability and memory effect of promotional efforts?

In this paper, an optimal replenishment strategy is developed for a sales environment influenced by the factors of reliability and promotional efforts with their pertinent impression on customers' purchase behavior. The first part of this study focuses on formulating an inventory system aiming to evaluate order quantity and corresponding replenishment time. The memory effect of promotional efforts is incorporated into the model by formulating the same through a fractional order differential equation. The subsequent part of our work focuses on studying the variational effect on optimal values of replenishment quantity and time due to dissimilation in various parameters, which represent the governing factors considered in our model formulation. Results of the study have been analyzed through a data set obtained from a retailer who is into the business through e-commerce trade. The analysis of model parameters infers some managerial insights enabling an appropriate modification in inventory replenishment decisions in a response to any changes in the state of the sales environment.