Controllable lead time, service level constraint, and transportation discounts in a continuous review inventory model

This paper studies two models based on the distribution of lead time demand. The first model assumes a normally distributed lead time demand and the second assumes that there is no specific distribution for lead time demand, but it is with known mean and standard deviation. The continuous-review inventory model is used for both cases. Transportation cost is dependent on the ordered quantity i.e., how much quantity buyer orders for delivery, based on that, a transportation discount is used to reduce the total cost. Service level constraint is included in this model to avoid backorder cost. Two efficient lemmas are established to obtain the optimum solution of the model. The expected value of additional information (EVAI) is calculated to show the excess amount needed for the distribution free case. Some numerical examples and sensitivity analysis are given to illustrate the model