(Solved):   Looking for a number and an explanation on how you got that answer Consolidated Distribut ...

 

Looking for a number and an explanation on how you got that answer

Consolidated Distribution Example - Each retailer faces normally distributed demand - mean \( =2 \) units/month - std. dev. \( =1.41 \) units/month - Each retailer uses on OUTL inventory policy - desired service level \( =95 \% \) - order interval of 1 week - Assume 4 weeks per month Consolidated Distribution Recall from lecture the example of direct delivery versus consolidated distribution. In the direct delivery scenario, a single supplier ships directly to 100 retail stores with an 8week lead time to each store. Each retail store faces normally distributed customer demand with a mean of 2 units/month and a standard deviation of \( 1.41 \) units/month (assume 4 weeks in a month). In the consolidated distribution scenario, the supplier ships directly to a regional distribution center (DC), which then ships directly to each retail store. The lead time between the supplier and the DC is 8 weeks. The DC and the retail stores use an order-up-to level inventory policy with a target service level of 95 percent. Question: In lecture, we demonstrated that when the lead time between the DC and each retail store is 1 week, the average inventory level in the consolidated distribution scenario is 2 less than the average inventory level in the direct delivery scenario, thus providing some motivation for consolidating distribution despite the lengthened supply chain. What lead time between the DC and each retail store equalizes this benefit, i.e., what lead time results in equal average inventory levels in each system?