Effect of memory on an inventory model for deteriorating item: fractional calculus approach

It is incontrovertible that involvement of memory has a great impact in inventory model. For any company, long past experience as well as short past experience have similar significant importance to manage the profit. Our proposed inventory model is leaded by two important factors: constant demand and deterioration. Here, we have introduced memory effect through the feasible ideas of fractional calculus. Also, we consider the order of fractional derivative as memory index. We calculate various type of costs viz total holding cost, purchasing cost, deterioration cost, shortage cost, salvage value. Additionally, optimal ordering interval, optimal starting shortage time and minimized total average cost are computed theoretically using the fractional calculus techniques. Effect of memory is justified by choosing a suitable numerical example. Finally sensitivity analysis for the model has been presented.