Effect of reliability and memory on fractional inventory model incorporating promotional effort on demand.

This paper presents a study of inventory replenishment strategy for efficiently managing sales of a deteriorating item in a retail store. The study addresses pertinent effect on sales pattern due to promotional initiatives. The memory effect generated in the consumers' mind due to various factors like branding and the stock visibility to customers is incorporated in our model by formulating it as a Caputo-Fabrizio fractional differential equation. Even, in practice, consumers' purchase patterns are noticed to get influenced by the reliability of product, the same is modelled through demand rate formulation. Influence of both these factors is incorporated into the proposed formulation by representing them as model parameters. The study aims at determining the optimal replenishment quantity and its reordering time for the addressed item in terms of said factors estimated as parameters. Results of the study are analyzed through the data set obtained from a retail store. The analysis of model-parameters infers some managerial insights which match the reality of sales patterns. Our study provides a decision support framework for determining replenishment quantities along with an estimate of replenishment time in connection with promotional initiatives and reliability of the product for achieving minimal total cost incurred while keeping the selling price of the product as fixed.