Minimax distribution-free procedure for integrated inventory model with backorder price discount and controllable lead time

Abstract

The integrated vendor–buyer inventory model has been an object of study for a long time, but little is done about the effect of reducing lead time on the integrated inventory models with backorder price discount and defective items. The aim is to minimise the total related cost in the continuous review model 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 the mean and variance of lead-time demand are known. We apply the minimax distribution-free procedure to find the optimal solution. In the integrated system we discussed here, it assumes that, when the buyer places an order, the vendor produces m-times the order quantity in each production cycle, to reduce the set-up cost. In addition, the buyer offers a 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. We develop an effective iterative procedure for finding the optimal policy and give a numerical example to illustrate the solution procedure.