EOQ_Example Problem - Solutions

Example Problem 1

Number 2 pencils at the campus bookstore are sold at a fairly steady rate of 60 per
week. The pencils cost the bookstore 2 cents each and sell for 15 cents each. It costs
the bookstore $12 to initiate an order, and holding cost is based on an annual interest
rate of 25 percent.

(1) Determine the optimal purchase quantity and the time between placement of
orders.

Annual demand (D) = 60* 52 = 3120 pencils per year assuming 52 weeks in an year

Holding cost (h) = I *c = 25%*0.02$ = 0.005 $ per pencil per year

Setup cost(K) = $12 per order

EOQ or Q*= 2 ∗12 ∗3120 = 3869.9 or approx. 3870 pencils
0.005

Time between orders (T) = = 3870 = 1.24 years
3120

Example Problem 1

Number 2 pencils at the campus bookstore are sold at a fairly steady rate of 60 per
week. The pencils cost the bookstore 2 cents each and sell for 15 cents each. It costs
the bookstore $12 to initiate an order, and holding cost is based on an annual interest
rate of 25 percent.

(2) Calculate the yearly holding and setup costs.

Annual holding cost = ℎ = 0.005 ∗ 3870 = 9.675 dollars
2
2

Annual setup cost = = 12 ∗ 3120 = 9.675 dollars

3870

Total Cost holding and setup cost = 9.675 + 9.675 = 19.35 dollars

Example Problem 1

(3) Suppose the bookstore’s supplier accepts orders only in batches of 1000. What is the
optimum order quantity?

Order either 3000 or 4000 pencils. To choose compute the annual inventory cost and choose
the order quantity which leads to a lower cost.

Annual inventory cost with order of 3000 units = Holding + Setup Cost = ℎ + =
2
0.005 ∗3000 12 ∗3120
2 + 3000 = 19.98 dollars

Annual inventory cost with order of 4000 units = 19.36 dollars

Since 19.36 < 19.98, place an order of 4000 units

(4) What is the additional cost incurred due to the batch orders?

Example Problem 1

(4) What is the additional cost incurred due to the batch orders?

The annual inventory cost (holding + setup) incurred with EOQ was 19.35 dollars
The annual inventory cost with orders of 4000 units was 19.36 dollars
The additional cost incurred 19.36 – 19.35 = 0.01 dollar per year is thus a marginal
increase.

Sensitivity to order quantity

• Note that the optimal annual holding and setup cost is

ℎ ∗
∗ + 2 =

obtained by substituting the EOQ above. The ratio of the suboptimal cost to the

optimal cost

+ℎ2 = ∗ +
∗

2 ℎ

• Calculate the error using a suboptimal order quantity in Example 1 using the

expression above. ∗

+ = + = .
∗

Example Problem 2

Harvey manages procurement at Saint-Gobain, a producer of glass
bottles and purchase soda-ash, a key component of glass manufacturing.
His supplier sells you soda ash at the spot market price which is $290
per ton (assume constant for entire year)

Annual demand of glass bottles fairly stable at 100,000 tons per year
and soda ash is about 13% by weight in glass.

Harvey calculates that it costs about $30 per year to hold one ton of the
mineral in your warehouse and a fixed setup cost of $100 each time an
order is placed.

Example Problem 2

1) Calculate the Economic Order Quantity
Holding cost = 30 dollars per year per ton of soda ash
Setup Cost = 100 dollars per order
Annual demand for soda ash = 13%* 100,000 = 13,000 tons

EOQ = 2 ∗100 ∗13,000 = 294.4 tons
30

Example Problem 2

(2) Calculate the average annual cost incurred in purchasing and storing
soda ash.

Annual cost incurred in purchasing = purchase cost + setup cost

= + = 290 ∗ 13,000 + 100 ∗ 1239,040.40= 3.77 million dollars


Annual cost incurred in storage = ℎ = 30 ∗ 294.4 = 4416 thousand
2 2
dollars

Total annual cost = approx. 3.78 million dollars