Question

X Company supplies ink cartridges for printers on the aftermarket. The demand for the cartridge averages 20,002 units per year, and operates 365 days per year. The holding cost of the cartridge is $5 per unit per year while the ordering cost is $100 per order. The company is currently using a periodic (P) inventory system, holding 1000 units in safety stock to cover demand uncertainty and placing orders for every 73 days. The company is investigating the possibility of implementing a continuous review (Q) inventory system holding 15 units in safety stock to cover demand uncertainty. Use this information to answer the following questions.

1-If Company X were to use a Q system with a lot size of 200 (not the EOQ), what should the reorder point be? Assume 15 units will still be held in safety stock.

2-Under the company's current P system, how much will the annual holding costs be? Assume 1000 units will still be held in safety stock.

3-Under the company's current P system, how much will the annual ordering costs be? Assume 1000 units will still be held in safety stock.

4-What should the target level be for the P system?

Answer 1

Given,

Annual Demand (D) = 20,002 units

Holding cost (H) = $5 per unit per year

Ordering cost (S) = $100 per order

Therefore,

1) Economic order quantity (EOQ) = sqrt(2DS/H)

                                                       = sqrt(2*20002*100/5)

                                                       = 894.47 units

2) Given, lot size(Q) = 200

Safety stock (ss) = 15 units

Hence, Annual holding cost = (Q/2 + ss) * H

                                            = (200/2 + 15)*$5

                                           = $575

3) Annual Ordering cost = (D/Q*) S

                                       = (20002/200)*$100

                                       = $10,001

4) Time would between orders = 365/number of orders in a year

                                                 = 365/(D/Q)

                                                 = 365/(20002/200)

                                                 = 3.649

Hence, Time between two orders = 4 days