Discrete-time spare ordering policy with randomized lead times and discounting

The paper considers a generalized discrete-time order-replacement model for a single unit system, which is subject to random failure when in operation. Two types of discrete randomized lead times are considered for a spare unit; one is for regular (preventive) order and another is for expedited (emergency) order. The model is formulated based on the discounted cost criterion. The underlying two-dimensional optimization problem is reduced to a simple one-dimensional one and then the optimal ordering policy for the spare unit is characterized under two extreme conditions: (i) unlimited inventory time and (ii) zero inventory time for the spare unit. A numerical example is used to determine the optimal spare-ordering policy numerically and to examine the sensitivity of the model parameters.