An inventory model with -rational type-backlogged demand rate and quadratic backlogging cost

In this paper, we consider a single item inventory model with a mixture of backorders and lost sales, in which the demand during the stockout period is partially backlogged according to a rational type function. The parameters associated with the purchasing cost, selling price, ordering cost, goodwill cost, demand rate and holding cost per unit and unit time are constant, but the cumulative backordering cost per unit is a quadratic function of the length of time for which the backorder exists. A procedure is developed for determining the optimal policy and the minimum total inventory cost. Illustrative numerical examples, which help us to understand the theoretical results, are also presented.