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Joe henry's machine shop uses 2500 brackets

26/11/2021 Client: muhammad11 Deadline: 2 Day

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

๐“๐จ๐ญ๐š๐ฅ ๐š๐ง๐ง๐ฎ๐š๐ฅ ๐จ๐ซ๐๐ž๐ซ๐ข๐ง๐  ๐œ๐จ๐ฌ๐ญ (๐ฌ๐ž๐ญ๐ฎ๐ฉ ๐œ๐จ๐ฌ๐ญ) = ๐ƒ ๐’ ๐‘ธ

(Note: when we use Q*, Q in the equation become Q*,)

๐“๐จ๐ญ๐š๐ฅ ๐š๐ง๐ง๐ฎ๐š๐ฅ ๐ก๐จ๐ฅ๐๐ข๐ง๐  ๐œ๐จ๐ฌ๐ญ (๐œ๐š๐ซ๐ซ๐ข๐ง๐  ๐œ๐จ๐ฌ๐ญ) = ๐ ๐‡ ๐Ÿ

(Note: when we use Q*, Q in the equation become Q*,)

EOQ = Q* = ๐Ÿ ๐‘ซ ๐‘บ ๐‘ฏ

Note: the unit of measure for โ€œDโ€ and โ€œHโ€ have to be identical (days, weeks, months,

year, etc)

Expected Number of Orders ๐ = ๐ƒ๐ž๐ฆ๐š๐ง๐ ๐Ž๐ซ๐๐ž๐ซ ๐๐ฎ๐š๐ง๐ญ๐ข๐ญ๐ฒ

= ๐ƒ ๐โˆ—

Expected Time between Orders ๐“ = ๐๐ฎ๐ฆ๐›๐ž๐ซ ๐จ๐Ÿ ๐ฐ๐จ๐ซ๐ค๐ž๐ข๐ง๐  ๐๐š๐ฒ๐ฌ ๐ฉ๐ž๐ซ ๐ฒ๐ž๐š๐ซ ๐„๐ฑ๐ฉ๐ž๐œ๐ญ๐ž๐ ๐ง๐ฎ๐ฆ๐›๐ž๐ซ ๐จ๐Ÿ ๐จ๐ซ๐๐ž๐ซ๐ฌ (๐)

Total cost (TC) = Total Setup cost + Total Holding cost

TC = ๐ƒ ๐’ ๐‘ธ + ๐ ๐‡

๐Ÿ

(Note: when we use Q*, Q in the equation become Q*,)

Reorder Point ROP = d x L

๐ = ๐ƒ

๐‘ต๐’–๐’Ž๐’ƒ๐’†๐’“ ๐’๐’‡ ๐’˜๐’๐’“๐’Œ๐’Š๐’๐’ˆ ๐’…๐’‚๐’š๐’” ๐’Š๐’ ๐’‚ ๐’š๐’†๐’‚๐’“

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* = [ \ ] ^

= [โˆ—[_``โˆ—ab.d_ a._

= 250 units

b. Total holding cost carring cost = rs [ = [_``โˆ—a._

[ = $187.5

c. Total ordering cost (setup cost) = w x y

= [_``โˆ—ab.d_

[_` = $187.5

d. TC = w x y + r s

[ = $187.5+ $187.5 = $375

e. N = w{|}~ โ‚ฌย{ย rโ€š}~ฦ’โ€žฦ’โ€ฆ

= w rโˆ—

= [_`` [_`

= 10 orders/year

f. T = โ€ โ€š|โ€ก{ย ห†โ€ฐ ล ห†ยโ€น{โ€ž~ล’ }โ€ฆย ลฝ{ย โ€ฆ{}ย ยยลฝ{โ€˜ฦ’{ ~โ€š|โ€ก{ย ห†โ€ฐ ห†ย{ยย (โ€ )

= T = [_` a`

= 250 days

g. ๐‘…๐‘‚๐‘ƒ = ๐‘‘ ๐‘ฅ ๐ฟ๐‘‡

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* = [โˆ—โ„ขลก```โˆ—โ€บ_

[ = 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 = ๐Ÿ๐’™๐‘ซ๐‘ฟ๐Ÿ“

๐Ÿ

(50)2 = ๐Ÿ๐’™๐‘ซ๐’™๐Ÿ“ ๐Ÿ

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* = ๐Ÿ๐‘ซ๐‘บ ๐‘ฏ

= ๐Ÿ๐’™๐Ÿ’๐ŸŽ๐ŸŽ๐’™ ๐Ÿ

๐Ÿ = 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 = [โˆ—b``โˆ—โ€บ_

^

(300)2 = [โˆ—b``โˆ—โ€บ_

^

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 = ๐Ÿ๐Ÿ“๐ŸŽ๐ŸŽ ๐Ÿ‘๐ŸŽ๐ŸŽ

= 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

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