Question

A local family sports store sells basketball. The store orders the balls from a

manufacturer at a cost of $250 per order. The annual holding cost is $6 per unit per year. The purchase price

of a basketball is $40 per unit per year. The store has a demand for

48,000 balls

per year.

The s

tock

is

received 5 working days after an order has been placed. No backorders are allowed. Assume 300 working

days a year.

a.

What is

the economic ordering quantity

? What is the optimum number of orders per year? What is the

optimal interval (in working days) between orders?

b.

What are the total annual holding costs? What are the total annual ordering costs? Using an appropriately

labelled diagram, graph setup cost, hol

ding cost, and total inventory cost, and show the economic order

quantity (EOQ) and the minimum total inventory cost.

c.

What is demand during the lead time? What is the inventory position immediately after an order has been

placed (i.e., inventory on-

hand pl

us inventory in-transit)?

d.

Suppose the store currently uses an order quantity of 1,500 balls

. Calculate the decrease in

the annual

holding cost and

the increase in the annual

ordering cost for

this policy? What would be the annual cost

saved by shifting fro

m the current 1,500 balls

order size to the EOQ order size?

e.

The store received an offer of a 5% discount from the manufacturer on orders of 3,000 or more

balls

.

Calculate the annual number of orders under the discount order quantity (DOQ). Calculate the average

inventory under the DOQ. Calculate the cost savings from the reduction in the price. Calculate the cost

savings from the reduc

ed number of orders. Calcul

ate the increase in holding costs. Calculate the net

savings from the discount? Would you recommend the store

to take the discount?

Why?

Answer 1

a)
EOQ = sqrt((2DS)/h) where D =48000,S = 250,h = 6

So, EOQ = sqrt((2*48000*250)/6) = 2000

What is the optimum number of orders per year?

optimum number of orders per year = Annual demand/EOQ = 48000/2000 = 24

What is the optimal interval (in working days) between orders?

optimal interval (in working days) between orders = number of working days/optimum number of orders = 300/24 = 12.5 days

b)

Total annual holding cost = (EOQ/2)*h = (2000/2)*6 = 6000

total annual ordering costs = (D/EOQ)*S = (48000/2000)*250 = 6000

EOQ 35000 30000 25000 20000 15000 10000 5000 0 400 800 1200 1600 2000 2400 2800 Annual holding cost - Annual ordering cost

EOQ is the intersection of annual ordering cost and annual holding cost

Graph data

Quantity	Annual holding cost	Annual ordering cost	`
400	1200	30000	31200
800	2400	15000	17400
1200	3600	10000	13600
1600	4800	7500	12300
2000	6000	6000	12000
2400	7200	5000	12200
2800	8400	4285.714286	12685.71429

c) Demand during lead time = daily demand * lead time in days = (48000/300)*5 = 800

Inventory position IP = ROP+EOQ = 800+2000 = 2800

d)

With ordreing quantity 1500, decrease in holding cost = (2000/2)*6 - (1500/2)*6 = 1500
With ordreing quantity 1500, increase in ordering cost = (48000/1500)*250-(48000/2000)*250 = 2000

So annual cost saved with EOQ = 2000-1500 = 1500

e)

Annual number of orders with DOQ = 48000/3000 = 16

Average inventory under DOQ = 3000/2 = 1500

Cost saving due to reduction in price = 48000*40-48000*40*0.95 = 96000

Reduction in ordering cost = (48000/2000)*250-(48000/3000)*250 = 2000

increase in holding cost = (3000/2)*6-(2000/2)*6 = 3000

Hence due to discount, net reduction is 96000+2000-3000 = 95000

Yes, the discount should be taken as total cost(purchase+ordering+holding cost) is reduced