Inventory models with mixture of backorders involving reducible lead time and setup cost

Lead time and setup cost are controllable variables in our continuous review inventory model. In this study we assume that only the first and second moments, of the probability distribution of lead time demand, are known. Order quantity and backorder price discount are decision variables in our problem with mixture of backorders and lost sales. As a result of reducing lead-time we can have significant savings and it is made known through numerical examples.