Joe henry's machine shop uses 2500 brackets

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 𝟏Chapter 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