Inventory Model (M, R, T) Constant Lead Times, Quadratic, Exponential And Backorder Costs.

The paper considers the inventory model in which at a review time, when the inventory position is less than or equal to R, some quantity is ordered which is sufficient to bring it to inventory position to M. The paper follows the method of Hadley and Whitin which however does not specify the costs terms. We develop the equations for linear backorder cost. From which the quadratic and exponential backorder costs are derived. The expected on hand inventory is determined firstly and the probability that there is a stockout is determined. We assume that demand follows a normal distribution and the demand for x units in n periods follows the n-flow convolution. The expected costs per cycle is obtained and also the expected length of a circle. The inventory costs for quadratic and exponential are obtained replacing the linear backorder costs with quadratic and exponential costs respectively.