Question

XYZ is a company based in Cape Town. XYZ Imports printers from China and sells it to local corporate clients. Delivery normally takes 2 weeks. XYZ sells 5011 printers on average per year. Annual carrying costs is 21%. XYZ negotiated the purchase price per printer to be R304. Every time that XYZ places an order the fixed ordering costs per order is R1079.

1. What is the economic order quantity of printers of XYZ?

2. Assuming certainty in delivery and usage, at what inventory level should the firm reorder?

3. Assume a 230-unit safety stock is carried. What will the additional inventory cost be?

Answer 1

1. Economic order quantity EOQ = [(2*D*S) / H]

where, D - Annual Demand in units, S - Ordering cost per order, H - Annual Holding or carrying cost per unit

XYZ sells 5011 printers on average per year, so this will be the annual demand, hence D = 5011 printers

The fixed ordering costs per order is R1079, so S = R1079

Purchase price per printer for XYZ is R304 and annual carrying costs are 21%. Therefore, amount of the Annual carrying costs per unit H =  R304 x 21% = R63.84 or R64

EOQ = [(2*D*S) / H]

=  [(2 * 5011 * R1079) / R64]

= [168,965]

= 411 printers

2. Reorder Level of inventory = Average Demand x Normal Lead time for delivery

Delivery normally takes 2 weeks, so this is the Lead time.

Average sales or demand per year for XYZ is 5011 printers, so the demand per week = 5011 / 52 weeks in a year = 96 printers per week

Reorder Level = 96 printers x 2 weeks = 192 printers

3. A 230-unit safety stock is carried.

The additional inventory cost for this safety stock is the Expected Carrying Cost of the stock = Safety stock x Annual carrying cost per unit (H)

= 230 units x R64 (calculated in part 1)

= R14,720