Question

The Bellevue University bookstore purchases sweatshirts with the school name and logo from a vendor. The vendor sells the sweatshirts to the store for $38 per shirt. The cost to the bookstore for placing an order is $120 and the annual carrying cost is 25 percent of the cost of a sweatshirt. The bookstore manager estimates that 1700 sweatshirts will be sold during the year. The vendor has offered the bookstore the following volume discount schedule:

Order Size	1-200	201-599	600-799	800+
Discount	0%	3%	3.5%	5%

a) What is the bookstore's optimal order quantity given this quantity discount information? Why?

b) What will be its annual inventory cost (including the holding cost, ordering cost and cost of the sweatshirts) for this optimal order quantity?

c) What is the lowest total annual inventory cost (as defined in b) for each of the other price (equivalently discount) options?

Answer 1

Given Data,

[ Ch] Holding Cost = 25 % of the Unit cost,

[Co ]Ordering Cost = $120

So, [ Dₐ ]Annual Demand = 1700 Units,

Unit Purchase cost = USD 38

Optimal order quantity = Square Root of [( 2 X D X Co)/ Ch]

Optimal order quantity= Square Root of [( 2 X 1700 X 120)/ (0.25*(38-38*0.03))]

Optimal order quantity=210.42

a)

As optimal order quantity fall between 201 -599, hence, 3% discount is applied,

Hence, Optimal order quantity=210.42

b)

Number of order = Annual Demand/ Optimal order quantity=1700/210.42=8.08

Annual ordering cost = 8.08*120=969.60

Annual Holding cost=(210.42/2)* 0.25*(38-38*0.03)=969.51

Annual Purchase cost =1700*(38-38*0.03)=62662

Total cost or annual inventory cost at optimal order quantity = Annual ordering cost+ Annual Holding cost+ Annual Purchase cost=969.60+969.51+62662=$64601

c)

Considering discount option 3%, we can have lowest total inventory cost, as it is calculated using optimal order quantity, considering other quantities and other discount options, total Inventory cost would be increased, hence, lowest total inventory cost = $64601