This article deals with an increasing total profit for inventory optimal ordered quantity and partial backlogging with the holding cost depending on the storage time period, and the rate of market demand is assumed to fluctuate as a function, based on level of stock and selling price. Thereafter, using the concept of a Hessian matrix, we have proved the concave nature of the profit function for the case where maximum cost is obtained. Finally, in order to validate the derived models, numerical examples and sensitivity analysis are explained. Through numerical test, we show that the proposed algorithms give quite satisfactory solutions. Hence, it can be concluded that the total profit can be increased by allowing shortage and partial backlogging.
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