Integrated Inventory Model with Defective Units Involving Controllable Lead-Time and Backorder Price Discount

We consider the integrated inventory model with defective units. The total related cost in the continuous review model is minimized by considering the order quantity, reorder point, lead-time and backorder price discount as decision variables. Moreover, we assume that the lead-time demand distribution is unknown but has known mean and variance of lead-time demand. The minimax distribution free procedure is applied to find the optimal solution considering that the buyer places an order, then the vendor produces m-times order quantity in each production cycles, to reduce setup cost. In addition, the buyer offers backorder price discount to the customers to motivate them for backorders. The arrival lot may contain some defective items, so its treatment is also incorporated in this paper. The effective iterative procedure for finding the optimal policy is developed.