Problem 1
Dr. Jack is
in charge of the Blood Bank at the local hospital. Blood is collected in the regional
blood center 200 miles away and is delivered to the hospital by airplane. Dr.
Jack reviews the inventory and places order every Monday morning for delivery
the following Monday morning. If demand begins to exceed supply, surgeons
postpone non-urgent procedures, in which case blood is back ordered. The demand
for blood in every given week is normal with mean 100 pints and standard
deviation 34 pints. The demands are independent across weeks.

1a) On Monday morning Dr. Jack
reviews his reserves and observes 200 pints in on-hand inventory, no back
orders, and 73 pints in pipeline inventory. Suppose the order up-to level is
285. How many pints will he order?1b) Dr. Jack targets a 99% expected
fill rate. What order up-to level should he choose?1c) Dr. Jack targets a 99% service
level. What order up-to level should he choose?1d) Dr. Jack is planning to
implement a computer system that will allow daily ordering, seven days per
week, and that the lead time will also be reduced to one day. What will be the average
order quantity?Problem 2You are the
owner of Hotspices.com, an online retailer of hip, exotic, and hard-to-find
spices. Consider your inventory of saffron, generally worth more by weight than
gold. You order saffron from an overseas supplier with a shipping lead-time of
four weeks and that you order weekly. Your average quarterly demand is normally
distributed with a mean of 415 ounces and a standard deviation of 154 ounces.
The holding cost per ounce per week is $0.75. You estimate that your back-order
penalty cost is $50 per ounce. Assume that there are 4.33 weeks per month.
2a) If you wish to minimize
inventory holding costs while maintaining 99.25% fill rate, then what should
your order up-to level be?2b) If you wish to minimize
inventory holding costs while maintaining 99.25% in-stock probability, then
what should your order up-to level be?2c) If you wish to minimize inventory holding
and backorder penalty costs, then what should your order up-to level be?2d) If you arbitrarily decide an
order up-to level of 250, what fraction of the demand will not be met
immediately? What is the expected on-hand inventory at the beginning of a period?Problem 3Livingston
Tools, a manufacturer of battery-operated, hand-held power tools for consumer
markets, has a problem. Its two biggest customers are big box discounters.
Because the customers are fiercely price competitive, each wants exclusive
products, thereby preventing consumers from making price comparisons. For
example, Livingston will sell the exact same power drill to each retailer, but
Livingston will use packing customized to each retailer (including two
different product identification numbers). Suppose weekly demand for each
product to each retailer is normally distributed with mean 5200 and standard
deviation 3800. Livingston makes stocking decisions on a weekly basis and has a
replenishment lead-time of three weeks. Because these two retailers are quite
important to Livingston, it has set a target fill rate of 99.9 percent.
3a) Based on the order up-to model,
what is Livingstons average inventory of each of the two versions of the power
drill? Problem 4Dave Jones manages the warehouse inventory for Athletics, a distributor for sport watches. From his experience, Dave knows that PR-5 jogging watch has an annual demand of 40,000 units. The fixed cost of placing an order with the manufacturer (Casio) is $50, while the holding cost per watch is $90/year. The lead-time for replenishment is 8 days and that Dave uses real-time monitoring of inventory.4a) What are the optimal reorder point and optimal order quantity for Dave assuming that the demand is fixed? What is the safety stock?4b) Daves boss is concerned that Dave is treating the demand as fixed. She suggests looking into the demand data more closely. On further investigation, Dave found that the demand is actually random with an annual average of 40,000 units and an annual standard deviation of 8,000 units. How would this new information change Daves optimal policy calculated in part (a) when Athletics policy is to provide 99% service level? How much is the safety stock now?4c) Athletics plans to install a new information system (ERP, SCM, and e-procurement software) that will achieve better information flow throughout its supply chain. The immediate benefit of this will be that the fixed cost of placing an order will be reduced to zero. Further, better information sharing will allow the less expensive periodic review policy to work perfectly for Athletics. Assume that the lead-time for replenishment is still 8 days but Dave now reviews inventory once every 3 days. The demand is random as described in part (b) above. Calculate and characterize Daves optimal inventory policy. How much is the safety stock now?Problem 1Dr. Jack is
in charge of the Blood Bank at the local hospital. Blood is collected in the regional
blood center 200 miles away and is delivered to the hospital by airplane. Dr.
Jack reviews the inventory and places order every Monday morning for delivery
the following Monday morning. If demand begins to exceed supply, surgeons
postpone non-urgent procedures, in which case blood is back ordered. The demand
for blood in every given week is normal with mean 100 pints and standard
deviation 34 pints. The demands are independent across weeks.1a) On Monday morning Dr. Jack
reviews his reserves and observes 200 pints in on-hand inventory, no back
orders, and 73 pints in pipeline inventory. Suppose the order up-to level is
285. How many pints will he order?1b) Dr. Jack targets a 99% expected
fill rate. What order up-to level should he choose?1c) Dr. Jack targets a 99% service
level. What order up-to level should he choose?1d) Dr. Jack is planning to
implement a computer system that will allow daily ordering, seven days per
week, and that the lead time will also be reduced to one day. What will be the average
order quantity?You are the
owner of Hotspices.com, an online retailer of hip, exotic, and hard-to-find
spices. Consider your inventory of saffron, generally worth more by weight than
gold. You order saffron from an overseas supplier with a shipping lead-time of
four weeks and that you order weekly. Your average quarterly demand is normally
distributed with a mean of 415 ounces and a standard deviation of 154 ounces.
The holding cost per ounce per week is $0.75. You estimate that your back-order
penalty cost is $50 per ounce. Assume that there are 4.33 weeks per month.
2a) If you wish to minimize
inventory holding costs while maintaining 99.25% fill rate, then what should
your order up-to level be?2d) If you arbitrarily decide an
order up-to level of 250, what fraction of the demand will not be met
immediately? What is the expected on-hand inventory at the beginning of a period?Livingston
Tools, a manufacturer of battery-operated, hand-held power tools for consumer
markets, has a problem. Its two biggest customers are big box discounters.
Because the customers are fiercely price competitive, each wants exclusive
products, thereby preventing consumers from making price comparisons. For
example, Livingston will sell the exact same power drill to each retailer, but
Livingston will use packing customized to each retailer (including two
different product identification numbers). Suppose weekly demand for each
product to each retailer is normally distributed with mean 5200 and standard
deviation 3800. Livingston makes stocking decisions on a weekly basis and has a
replenishment lead-time of three weeks. Because these two retailers are quite
important to Livingston, it has set a target fill rate of 99.9 percent.
3a) Based on the order up-to model,
what is Livingstons average inventory of each of the two versions of the power
drill?