Investing in lead-time variability reduction in a quality-adjusted inventory model with finite-range stochastic lead-time

We study the impact of the efforts aimed at reducing the lead-time variability in a quality-adjusted stochastic inventory model. We assume that each lot contains a random number of defective units. More specifically, a logarithmic investment function is used that allows investment to be made to reduce lead-time variability. Explicit results for the optimal values of decision variables as well as optimal value of the variance of lead-time are obtained. A series of numerical exercises is presented to demonstrate the use of the models developed in this paper. Initially the lead-time variance reduction model (LTVR) is compared to the quality-adjusted model (QA) for different values of initial lead-time over uniformly distributed lead-time intervals from one to seven weeks. In all cases where investment is warranted, investment in lead-time reduction results in reduced lot sizes, variances, and total inventory costs. Further, both the reduction in lot-size and lead-time variance increase as the lead-time interval increases. Similar results are obtained when lead-time follows a truncated normal distribution. The impact of proportion of defective items was also examined for the uniform case resulting in the finding that the total inventory related costs of investing in lead-time variance reduction decrease significantly as the proportion defective decreases. Finally, the results of sensitivity analysis relating to proportion defective, interest rate, and setup cost show the lead-time variance reduction model to be quite robust and representative of practice.