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 2

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?
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 3

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 Livingston’s average inventory of each of the two versions of the power drill?
Problem 4
Dave 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) Dave’s 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 Dave’s 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 Dave’s optimal inventory policy. How much is the safety stock now?