Continuous-review (<i>s, S</i>) inventory system with lost sales and variable lead times

In this paper, we present a continuous review lost sales inventory system in which both the items stocked and the size of demands may not take integer values, indicating that the stock type is fluid, such as oil, flour etc. We assume that the arrival times of demands form a Poisson process and that the demand sizes have i.i.d . exponential distribution. We assume an ( s, S ) ordering policy to replenish the inventory with random lead times. Using system point method of level crossing, we derive the stationary distribution of the on-hand inventory level in a continuous review inventory system with exponential and Erlang distributed lead times. After deriving some system performance measures, we computed the total expected cost rate. For the exponential lead time model, we provide some analytical properties of the cost function. Using numerical results, an optimal cost analysis is performed and some remarks are made as to the optimality of cost function with respect to each of decision variables.