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 to
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 to
zero.Evaluate the reduction in safety inventory that Dell can expect as a result of this initiative. Example 8:Impact of Correlation on Value of Aggregation A BMW dealership has four retail outlets serving the entire Chicago area(disaggregate option).Weekly demand at each outlet is normally distributed,with a mean of D =25 cars and a standard deviation of o=5D.The lead time for replenishment from the manufacturer is L=2 weeks.Each outlet covers a separate geographic area,and the correlation of demand across any pair of areas is The dealership is considering the possibility of replacing the four outlets with a single large outlet (aggregate option).Assume that the demand in the central outlet is the sum of the demand across all four areas.The dealership is targeting a CSL of 0.90.Compare the level of safety inventory needed in the two options as the correlation coefficient p varies between 0 and 1. Example 9:Trade-offs of Physical Centralization An online retailer is debating whether to serve the United States through four regional distribution centers or one national distribution center.Weekly demand in each region is normally distributed,with a mean of 1,000 and a standard deviation of 300.Demand experienced in each region is independent,and supply lead time is four weeks.The online retailer has a holding cost of 20 percent and the cost of each product is $1,000.The retailer promises its customers next-day delivery.With four regional distribution centers,the retailer can provide next-day delivery using ground transportation at a cost of $10/unit.With a single national distribution center,the retailer will have to use a more expensive mode of transport that will cost $13/unit for next-day service.Building and operating four regional DCs costs $150,000 per year more than building and operating one national distribution center.What distribution network do you recommend? Assume a desired CSL of 0.95. Example 10:Common Products Assume that Dell is to manufacture 27 PCs with three distinct components:processor,memory,and hard drive.Under the disaggregate option,Dell designs specific components for each PC,resulting in distinct components.Under the common-component option,Dell designs PCs such that three distinct processors, three distinct memory units,and three distinct hard drives can be combined to create 27 PCs.Each component is thus used in nine PCs.Monthly demand for each of the 27 PCs is independent and normally distributed,with a mean of 5,000 and a standard deviation of 3,000.The replenishment lead time for each component is one month.Dell is targeting a CSL of 95 percent for component inventory.Evaluate the safety inventory requirements with and without the use of component commonality.Also evaluate the change in safety inventory requirements as the number of finished products of which a component is a part varies from one to nine. Example 11:Postpone Consider a paint retailer who sells 100 different colors of paint.Assume that weekly demand for each color is independent and is normally distributed with a mean of 30 and a standard deviation of 10.The replenishment lead time from the paint factory is two weeks and the retailer aims for a CSL =0.95.How much safety stock will the retailer have to hold if paint is mixed at the factory and held in inventory at the retailer as individual colors?How does the safety stock requirement change if the retailer holds base paint (supplied by the paint factory)and mixes colors on demand? Example 12:Periodical Review 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,and the store manager has decided to review inventory every four weeks.Assuming a periodic-review replenishment policy,evaluate the safety inventory that the store should carry to provide a CSL of 90 percent.Evaluate the OUL for such a policy
zero. Evaluate the reduction in safety inventory that Dell can expect as a result of this initiative. Example 8: Impact of Correlation on Value of Aggregation A BMW dealership has four retail outlets serving the entire Chicago area (disaggregate option). Weekly demand at each outlet is normally distributed, with a mean of 𝐷 = 25 cars and a standard deviation of 𝜎=5𝐷. The lead time for replenishment from the manufacturer is 𝐿 = 2 weeks. Each outlet covers a separate geographic area, and the correlation of demand across any pair of areas is The dealership is considering the possibility of replacing the four outlets with a single large outlet (aggregate option). Assume that the demand in the central outlet is the sum of the demand across all four areas. The dealership is targeting a CSL of 0.90. Compare the level of safety inventory needed in the two options as the correlation coefficient 𝜌 varies between 0 and 1. Example 9: Trade-offs of Physical Centralization An online retailer is debating whether to serve the United States through four regional distribution centers or one national distribution center. Weekly demand in each region is normally distributed, with a mean of 1,000 and a standard deviation of 300. Demand experienced in each region is independent, and supply lead time is four weeks. The online retailer has a holding cost of 20 percent and the cost of each product is $1,000. The retailer promises its customers next-day delivery. With four regional distribution centers, the retailer can provide next-day delivery using ground transportation at a cost of $10/unit. With a single national distribution center, the retailer will have to use a more expensive mode of transport that will cost $13/unit for next-day service. Building and operating four regional DCs costs $150,000 per year more than building and operating one national distribution center. What distribution network do you recommend? Assume a desired CSL of 0.95. Example 10: Common Products Assume that Dell is to manufacture 27 PCs with three distinct components: processor, memory, and hard drive. Under the disaggregate option, Dell designs specific components for each PC, resulting in distinct components. Under the common-component option, Dell designs PCs such that three distinct processors, three distinct memory units, and three distinct hard drives can be combined to create 27 PCs. Each component is thus used in nine PCs. Monthly demand for each of the 27 PCs is independent and normally distributed, with a mean of 5,000 and a standard deviation of 3,000. The replenishment lead time for each component is one month. Dell is targeting a CSL of 95 percent for component inventory. Evaluate the safety inventory requirements with and without the use of component commonality. Also evaluate the change in safety inventory requirements as the number of finished products of which a component is a part varies from one to nine. Example 11: Postpone Consider a paint retailer who sells 100 different colors of paint. Assume that weekly demand for each color is independent and is normally distributed with a mean of 30 and a standard deviation of 10. The replenishment lead time from the paint factory is two weeks and the retailer aims for a CSL = 0.95. How much safety stock will the retailer have to hold if paint is mixed at the factory and held in inventory at the retailer as individual colors? How does the safety stock requirement change if the retailer holds base paint (supplied by the paint factory) and mixes colors on demand? Example 12: Periodical Review 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, and the store manager has decided to review inventory every four weeks. Assuming a periodic-review replenishment policy, evaluate the safety inventory that the store should carry to provide a CSL of 90 percent. Evaluate the OUL for such a policy