Question

1. Suppose that a company buys about $81,000 worth of items from a vendor each year. If ordering cost is $25 per order and holding cost rate is 20%, how many dollars worth of items should be bought in each order?(Hint: Assume one dollar = one unit).

2. The vendor in the above problem will offer you a 2% discount if you buy at least $9,000 of items in each order. Should you accept this offer? If no, what is a fair counter offer?

Answer 1

1.

1$ = 1 unit
Annual Demand = D = 81000 units /year
Ordering Cost = Co = $25
Holding Cost = Cc = 20% of $1 = $0.20
Economic Order Quantity Q* = √(2DCo/Cc) = √(2*81000*25*/0.2) = 4500

Hence, $4500 worth should be ordered each time

2. When order size = 4500,
Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*Cc = (4500/2)*0.2 = $450
Annual Order cost = Number of orders * cost/order = (D/Q*)*Co = (81000/4500)*25 = $450
Purchase Cost = Annual Demand * Product Cost = 81000*1 = $81000
Annual Cost = Annual Inventory Holding Cost + Annual Order Cost + Purchase Cost= 450 + 450 + 81000 = $81900

When order size = $9000,
Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*Cc = (9000/2)*0.2 = $900
Annual Order cost = Number of orders * cost/order = (D/Q*)*Co = (81000/9000)*25 = $225
Purchase Cost = Annual Demand * Product Cost*Discount = 81000*1*0.98 = $79380
Annual Cost = Annual Inventory Holding Cost + Annual Order Cost + Purchase Cost= 900 + 225 + 79380 = $80505

Since the total cost is less when $9000 of items are ordered, we should accept the offer