Micro-Apple is a manufacturer of personal computers. It currently manufactures a single model-the MacinDOS-on an assembly line at a steady rate of 500 per week. MicroApple orders the floppy disk drives for the MacinDOS (1 per computer) from an outside supplier at a cost of $30 each. Additional administrative costs for placing an order total $30. The annual holding cost is $6 per drive. If MicroApple stocks out of floppy disk drives, production is halted, costing $100 per drive short. Because of the seriousness of stockouts, management wants to keep enough safety stock to prevent a shortage before the delivery arrives during 99 percent of the order cycles. The supplier now is offering two shipping options. With option 1, the lead time would have a normal distribution with a mean of 0.5 week and a standard deviation of 0.1 week. For each order, the shipping cost charged to MicroApple would be $100 plus $3 per drive. With option 2, the lead time would have a uniform distribution from 1.0 week to 2.0 weeks. For each order, the shipping cost charged to MicroApple would be $20 plus $2 per drive.
(a) Use the stochastic continuous-review model presented in Sec. 19.5 to obtain an (R, Q) policy under each of these two shipping options.
(b) Show how the reorder point is calculated for each of these two policies.
(c) Determine and compare the amount of safety stock provided by these two policies.
(d) Determine and compare the average annual holding cost under these two policies.
(e) Determine and compare the average annual acquisition cost (combining purchase price and shipping cost) under these two policies.
(f) Since shortages are very infrequent (and very small when they do occur), the only important costs for comparing the two shipping options are those obtained in parts (d) and (e). Add these costs for each option. Which option should be selected?