A note on lead time and distributional assumptions in continuous review inventory models

There is a rapidly growing literature on modelling the effects of investment strategies to control givens such as setup time, setup cost, quality level and lead time. Recently, a continuous review inventory model with a mixture of backorders and lost sales in which both lead time and the order quantity are decision variables has been studied. The objectives of this paper are twofold. Firstly, we want to correct and improve the recently studied model by simultaneously optimizing both the order quantity and the reorder point. A significant amount of savings over the model can be achieved. We illustrate these savings by solving the same examples in the study. Secondly, we then develop a minimax distribution free procedure for the problem. Recently, there have been some studies on lead time reduction to provide more meaningful mathematical models to decision makers. Ouyang et al. study a continuous review inventory model in which lead time is a decision variable. However, their algorithm cannot find the optimal solution due to the flaws in the modeling and the solution procedure. We present a complete procedure to find the optimal solution for the model. In addition to the above contribution, we also apply the minimax distribution free approach to the model to devise a practical procedure which can be used without specific information on demand distribution.