Intro to operations management (final exam today)
Chapter 12: EOQ
D = Annual demand (units) S = Cost per order ($)
P = Cost per unit ($) I = Holding cost (%)
H = Holding cost ($) = I x P
Formula
𝐓𝐨𝐭𝐚𝐥 𝐚𝐧𝐧𝐮𝐚𝐥 𝐨𝐫𝐝𝐞𝐫𝐢𝐧𝐠 𝐜𝐨𝐬𝐭 (𝐬𝐞𝐭𝐮𝐩 𝐜𝐨𝐬𝐭) = 𝐃 𝐒 𝑸
(Note: when we use Q*, Q in the equation become Q*,)
𝐓𝐨𝐭𝐚𝐥 𝐚𝐧𝐧𝐮𝐚𝐥 𝐡𝐨𝐥𝐝𝐢𝐧𝐠 𝐜𝐨𝐬𝐭 (𝐜𝐚𝐫𝐫𝐢𝐧𝐠 𝐜𝐨𝐬𝐭) = 𝐐 𝐇 𝟐
(Note: when we use Q*, Q in the equation become Q*,)
EOQ = Q* = 𝟐 𝑫 𝑺 𝑯
Note: the unit of measure for “D” and “H” have to be identical (days, weeks, months,
year, etc)
Expected Number of Orders 𝐍 = 𝐃𝐞𝐦𝐚𝐧𝐝 𝐎𝐫𝐝𝐞𝐫 𝐐𝐮𝐚𝐧𝐭𝐢𝐭𝐲
= 𝐃 𝐐∗
Expected Time between Orders 𝐓 = 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐰𝐨𝐫𝐤𝐞𝐢𝐧𝐠 𝐝𝐚𝐲𝐬 𝐩𝐞𝐫 𝐲𝐞𝐚𝐫 𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐨𝐫𝐝𝐞𝐫𝐬 (𝐍)
Total cost (TC) = Total Setup cost + Total Holding cost
TC = 𝐃 𝐒 𝑸 + 𝐐 𝐇
𝟐
(Note: when we use Q*, Q in the equation become Q*,)
Reorder Point ROP = d x L
𝐝 = 𝐃
𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒘𝒐𝒓𝒌𝒊𝒏𝒈 𝒅𝒂𝒚𝒔 𝒊𝒏 𝒂 𝒚𝒆𝒂𝒓
Note: Holding cost might be given in terms of cost/unit/year or it might be given in the
form of rate%, in that case we need to find the holding cost by:
H = I* P
Chapter 12: EOQ
Question 1. Joe Henry's machine shop uses 2500 brackets during the course of a year. The following information is known about the brackets:
Annual Demand 2500 Brackets
Holding Cost per bracket per year: $1.50
Order cost per order: $18.75
Lead Time 2 days
Working days per year 250 days
a. Given the above information, what would be the economic order quantity (EOQ)? b. What would be the annual holding cost? c. What would be the annual ordering cost? d. What is the total annual cost of managing the inventor e. How many orders would be made each year? f. What is the time between orders? g. What is the reorder point (ROP)
Solution:
a. Q* = [ \ ] ^
= [∗[_``∗ab.d_ a._
= 250 units
b. Total holding cost carring cost = rs [ = [_``∗a._
[ = $187.5
c. Total ordering cost (setup cost) = w x y
= [_``∗ab.d_
[_` = $187.5
d. TC = w x y + r s
[ = $187.5+ $187.5 = $375
e. N = w{|}~ €{ r‚}~ƒ„ƒ…
= w r∗
= [_`` [_`
= 10 orders/year
f. T = †‚|‡{ ˆ‰ Šˆ‹{„~Œ }… Ž{ …{} Ž{‘ƒ{ ~‚|‡{ ˆ‰ ˆ{ (†)
= T = [_` a`
= 250 days
g. 𝑅𝑂𝑃 = 𝑑 𝑥 𝐿𝑇
d = [_`` [_`
= 10 units/day
ROP = 10 x 2 = 20 units
Question 2. If the demand = 8,000 per month, S = $45 per order, and H = $2 per unit per year, what is the economic order quantity?
Solution:
Note that annual demand is 12 * 8,000 = 96,000.
Q* = [∗™š```∗›_
[ = 2078 units
Chapter 12: EOQ
Question 3. If EOQ = 50 units, order costs are $5 per order, and carrying costs are $2 per unit/year, what is the Annual Demand?
Q* = [ \ ] ^
=
50 = 𝟐𝒙𝑫𝑿𝟓
𝟐
(50)2 = 𝟐𝒙𝑫𝒙𝟓 𝟐
2500 = 5 D
D= 500 units
Question 4. If the unit cost is $20, and the annual holding cost is 10%. Annual demand is 400 units, and the order cost is $1 per order. What is the optimal
quantity?
H = IP = 0.1 * 20 = $2
Q* = 𝟐𝑫𝑺 𝑯
= 𝟐𝒙𝟒𝟎𝟎𝒙 𝟏
𝟐 = 20 units
Question 5. Xyz company purchases 8,000 cables each year as components in computers. The cost of carrying one cable in inventory for a year is $3 and the
ordering cost is $30 per order. What are:
a. The optimal order quantity b. Annual holding cost c. Annual set up cost d. Total annual cost e. The expected number of orders placed each year, and f. The expected time between order? Assume that xyz company operates on a 200-
day working year
Note: below are the final answers for each question, in the exam you need to show the
steps
Solution:
a. 400 units b. $600 c. $600 d. $1200
Chapter 12: EOQ
e. 20 orders f. 10 working days
Question 6. Lead time for one of your fastest- moving products is 21 days. Demand during this period averages 100 units per day. What would be an
appropriate reorder point?
Solution:
a) ROP = d x LT = 100 X 21 = 2100 units
Question 7. If the economic order quantity = 300, annual demand = 8,000 units, and order costs = $45 per order, what is the annual per unit holding cost (H)?
Solution:
Q* = [ \ ] ^
300 = [∗b``∗›_
^
(300)2 = [∗b``∗›_
^
90000 = d[`,```
^
90,000 H = 720,000
H = $8/unit/year
Chapter 12: EOQ
Question 8. Kara Chubrik uses 1,500 per year of a certain subassembly that has an annual per unit holding cost of $45 per unit. Each order placed costs Kara
$150. She operates 300 days per year, and has found that an order must be
placed with her supplier 6 working days before she can expect to receive that
order. For this subassembly, find
(a) Economic Order quantity
Q* H DS2
=
45 150*1500*2
=
100= units (b) Total annual holding cost
Annual holding cost H Q 2
=
45* 2 100
=
250,2$=
(c) Annual ordering cost
Annual ordering cost S Q D
=
150* 100 500,1
=
250,2$=
(d) Reorder point ROP = d*LT
d = 𝟏𝟓𝟎𝟎 𝟑𝟎𝟎
= 5
ROP = 5x6 = 30 units
Chapter 12: EOQ
Question 9. Xyz company stocks books with the following characteristics: Demand D = 19,500 units/year, Ordering cost = $25/order, Carrying cost =
$4/unit/year
a. Calculate the EOQ b. What are the annual holding costs? c. What are the annual ordering costs? d. The expected number of orders placed each year, and e. The expected time between orders? Assume that xyz company operates on a 300
day/year
Note: below are the final answers for each question, in the exam you need to show the
steps
Solution:
a. 493.7 workbooks b. $987 c. $987 d. 39 order/year e. 7.7 days