Valuing lead-time and its variance in batch-ordering inventory policies

Time-based competition has attracted a lot of attention since the 1980s. Supply chain managers have tried various approaches to improve their performance by lead-time reduction: both lead-time itself and its variance. This paper explores and quantifies these benefits of such lead-time reduction for commonly used reorder-point batch-ordering inventory policies. Rather than using approximate total cost equations, we present an exact total cost equation that is built on an inherent relationship between on-hand inventory and backorder. Thus, our marginal value analysis on lead-time and its variance achieves more accurate results. Our analytical results show that the inventory cost is a strictly increasing, concave function of both lead-time and its variance. In other words, the cost savings on both lead-time and its variance reduction decrease when lead-time becomes larger. We also show that both cost savings increase linearly in the inventory holding cost rate. Our numerical examples confirm our analytical results and provide sensitivity analysis on different levels of variable demand and variable lead-time. When both demand and lead-time coefficients of variation are very small, the focus is on lead-time variance reduction. For other cases, the focus should be on lead-time reduction.