Safety Inventory-Examples Example 1: Assume that weekly demand for phones at B&M Office Supplies is normally distributed,with a mean of 2,500 and a standard deviation of 500.The manufacturer takes two weeks to fill an order placed by the B&M manager.The store manager currently orders 10,000 phones when the inventory on hand drops to 6,000.Evaluate the safety inventory and the average inventory carried by B&M.Also evaluate the average time a phone spends at B&M. Example 2: Weekly demand for phones at B&M is normally distributed,with a mean of 2,500 and a standard deviation of 500.The replenishment lead time is two weeks. (i)Assume that the demand is independent from one week to the next.Evaluate the CSL resulting from a policy of ordering 10,000 phones when there are 6,000 phones in inventory. (ii） Assume that the demand between two consecutive periods are correlated.The correlated coefficient is 0.2.Evaluate the CSL resulting from a policy of ordering 10,000 phones when there are 6,000 phones in inventory. Example 3: From Example 2,recall that weekly demand for phones at B&M is normally distributed,with a mean of 2,500 and a standard deviation of 500.The replenishment lead time is two weeks.Assume that the demand is independent from one week to the next.Evaluate the fill rate resulting from the policy of ordering 10,000 phones when there are 6,000 phones in inventory. Example 4: Weekly demand for Legos at a Wal-Mart store is normally distributed,with a mean of 2,500 boxes and a standard deviation of 500.The replenishment lead time is two weeks.Assuming a continuousreview replenishment policy,evaluate the safety inventory that the store should carry to achieve a CSL of 90 percent. Example 5: Weekly demand for Legos at a Wal-Mart store is normally distributed,with a mean of 2,500 boxes and a standard deviation of 500.The replenishment lead time is two weeks.The store manager currently orders replenishment lots of 10,000 boxes from Lego.Assuming a continuous-review replenishment policy, evaluate the safety inventory the store should carry to achieve a fill rate of 97.5 percent. Example 6: Weekly demand for white shirts at a Target store is normally distributed,with a mean of 2,500 and a standard deviation of 800.The replenishment lead time from the current supplier is nine weeks.The store manager aims for a cycle service level of 95 percent.What savings in safety inventory can the store expect if the supplier reduces lead time to one week?What savings in safety inventory can the store expect if the demand uncertainty is reduced such that the standard deviation of demand is only 400? Example 7: Daily demand for PCs at Dell is normally distributed,with a mean of 2,500 and a standard deviation of 500. A key component in PC assembly is the hard drive.The hard drive supplier takes an average of L=7 days to replenish inventory at Dell.Dell is targeting a CSL of 90 percent(providing a fill rate close to 100 percent) for its hard drive inventory.Evaluate the safety inventory of hard drives that Dell must carry if the standard deviation of the lead time is seven days.Dell is working with the supplier to reduce the standard deviation toSafety Inventory-Examples Example 1: Assume that weekly demand for phones at B&M Office Supplies is normally distributed, with a mean of 2,500 and a standard deviation of 500. The manufacturer takes two weeks to fill an order placed by the B&M manager. The store manager currently orders 10,000 phones when the inventory on hand drops to 6,000. Evaluate the safety inventory and the average inventory carried by B&M. Also evaluate the average time a phone spends at B&M. Example 2: Weekly demand for phones at B&M is normally distributed, with a mean of 2,500 and a standard deviation of 500. The replenishment lead time is two weeks. (i) Assume that the demand is independent from one week to the next. Evaluate the CSL resulting from a policy of ordering 10,000 phones when there are 6,000 phones in inventory. (ii) Assume that the demand between two consecutive periods are correlated. The correlated coefficient is 0.2. Evaluate the CSL resulting from a policy of ordering 10,000 phones when there are 6,000 phones in inventory. Example 3: From Example 2, recall that weekly demand for phones at B&M is normally distributed, with a mean of 2,500 and a standard deviation of 500. The replenishment lead time is two weeks. Assume that the demand is independent from one week to the next. Evaluate the fill rate resulting from the policy of ordering 10,000 phones when there are 6,000 phones in inventory. Example 4: Weekly demand for Legos at a Wal-Mart store is normally distributed, with a mean of 2,500 boxes and a standard deviation of 500. The replenishment lead time is two weeks. Assuming a continuousreview replenishment policy, evaluate the safety inventory that the store should carry to achieve a CSL of 90 percent. Example 5: Weekly demand for Legos at a Wal-Mart store is normally distributed, with a mean of 2,500 boxes and a standard deviation of 500. The replenishment lead time is two weeks. The store manager currently orders replenishment lots of 10,000 boxes from Lego. Assuming a continuous-review replenishment policy, evaluate the safety inventory the store should carry to achieve a fill rate of 97.5 percent. Example 6: Weekly demand for white shirts at a Target store is normally distributed, with a mean of 2,500 and a standard deviation of 800. The replenishment lead time from the current supplier is nine weeks. The store manager aims for a cycle service level of 95 percent. What savings in safety inventory can the store expect if the supplier reduces lead time to one week? What savings in safety inventory can the store expect if the demand uncertainty is reduced such that the standard deviation of demand is only 400? Example 7: Daily demand for PCs at Dell is normally distributed, with a mean of 2,500 and a standard deviation of 500. A key component in PC assembly is the hard drive. The hard drive supplier takes an average of L=7 days to replenish inventory at Dell. Dell is targeting a CSL of 90 percent (providing a fill rate close to 100 percent) for its hard drive inventory. Evaluate the safety inventory of hard drives that Dell must carry if the standard deviation of the lead time is seven days. Dell is working with the supplier to reduce the standard deviation to