Abstract
We derived the inventory costs in series 1 (Omorodion 2014) costs for the inventory model (M.R.T) in which the model has constant lead times, quadratic and exponential back order costs and random supply. In series 2 we considered the continuous lead times, random supply and quadratic backorder costs. In this paper series 3, we derive the inventory costs when the backorder cost is exponential and random supply and continuous lead times. The results of series 1 is made use of. The model result for this paper is derived by averaging the results of exponential backorder costs of series 1 over the states of lead time, where lead time is a gamma variate.