Inventory Management I

Definitions Inventory-A physical resource that a firm

holds in stock with the intent of selling it or transforming it into a more valuable state.

Inventory System- A set of policies and controls that monitors levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be

Inventory management Responsible for planning and

controlling inventory from the raw material stage to the customer and for production support.

Usually represent from 20% to 60% of total assets.

Inventory

Def. - A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state.

Raw Materials Works-in-Process Finished Goods Maintenance, Repair and Operating

(MRO)

Reasons for Inventories Improve customer service Economies of purchasing Economies of production Transportation savings Hedge against future Unplanned shocks (labor strikes, natural

disasters, surges in demand, etc.) To maintain independence of supply chain

Reasons for Inventories Low cost plan operation Minimum investment

Inventory Costs

Costs associated with inventory: Item cost / purchasing cost = c Carrying cost / Holding cost = h Ordering cost / Set up cost = k Cost of having too much / disposal Cost of not having enough

(shortage)

Inventory Holding Costs

Category % of ValueHousing (building) cost 6%Material handling 3%Labor cost 3%Opportunity/investment 11%Pilferage/scrap/obsolescence 3%

Total Holding Cost 26%

Inventory Holding Costs• Capital cost• Storage cost• Risk cost - Obsolescence - Damage - Pilferage, goods lost, strayed, stolen - Deterioration

ABC Analysis Divides on-hand inventory into 3 classes

A class, B class, C class Basis is usually annual $ volume

$ volume = Annual demand x Unit cost Policies based on ABC analysis

Develop class A suppliers more Give tighter physical control of A items Forecast A items more carefully

Classifying Items as ABC

0

20

40

60

80

100

0 50 100 150

0

20

40

60

80

100

0 50 100 150

% of Inventory Items% of Inventory Items

% Annual $ Usage% Annual $ Usage

AA

BB CC

ABC Classification Solution

Stock # Vol. Cost $ Vol. % ABC

206 26,000 $ 36 $936,000

105 200 600 120,000

019 2,000 55 110,000

144 20,000 4 80,000

207 7,000 10 70,000

Total 1,316,000

ABC Classification Solution

Stock # Vol. Cost $ Vol. % ABC

206 26,000 $ 36 $936,000 71.1 A

105 200 600 120,000 9.1 A

019 2,000 55 110,000 8.4 B

144 20,000 4 80,000 6.1 B

207 7,000 10 70,000 5.3 C

Total 1,316,000 100.0

Order Quantities How much should be ordered at

one time ? When should an order be placed ?

Order Quantities Static : - EOQ ( Economic Order Quantity ) - POQ ( Period- Order Quantity ) - EPQ ( Economic Production Quantity ) Dynamic : - EOQ - Warner – Within ( dynamic prog.) - Silver- meal

Economic Order Quantity

Assumptions Demand rate is known and constant No order lead time Shortages are not allowed Costs:

k - setup cost per order h - holding cost per unit time

EOQ

Time

Inventory Level

Q*OptimalOrderQuantity

Decrease Due toConstant Demand

EOQ

Time

Inventory Level

Q*OptimalOrderQuantity

InstantaneousReceipt of OptimalOrder Quantity

EOQ

Time

Inventory Level

Q*

Lead Time

ReorderPoint(ROP)

EOQ

Time

Inventory Level

Q*

Lead Time

ReorderPoint(ROP)

Average Inventory Q/2

Total Costs Average Inventory = Q/2 Annual Holding costs = H * Q/2 # Orders per year = D / Q Annual Ordering Costs = k * D/Q Annual Total Costs = Holding +

Ordering

Q

Dk

QHQTC *

2*)(

How Much to Order?Annual Cost

Order Quantity

Holding Cost= H * Q/2

How Much to Order?Annual Cost

Order Quantity

Holding Cost= H * Q/2

Ordering Cost=k* D/Q

How Much to Order?Annual Cost

Order Quantity

Total Cost= Holding + Ordering

How Much to Order?Annual Cost

Order Quantity

Total Cost= Holding + Ordering

Optimal Q

Optimal Quantity

Q

Dk

QH *

2*

Total Costs =

Optimal Quantity

Q

Dk

QH *

2* Total Costs =

2*

2 Q

Dk

H

Take derivative with respect to Q =

Optimal Quantity

Q

Dk

QH *

2* Total Costs =

2*

2 Q

Dk

H

Take derivative with respect to Q =

Set equal to zero0

Optimal Quantity

Q

Dk

QH *

2* Total Costs =

2*

2 Q

Dk

H

Take derivative with respect to Q =

Solve for Q:

22 Q

DkH

Set equal to zero0

Optimal Quantity

Q

Dk

QH *

2* Total Costs =

2*

2 Q

Dk

H

Take derivative with respect to Q =

Solve for Q:

22 Q

DkH

Set equal to zero0

H

kDQ

22 H

kDQ

2

A Question: If the EOQ is based on so many

horrible assumptions that are never really true, why is it the most commonly used ordering policy?

Benefits of EOQ Benefits of EOQ Profit function is very shallow Even if conditions don’t hold

perfectly, profits are close to optimal

Estimated parameters will not throw you off very far

Quantity Discounts How does this all change if price

changes depending on order size? Explicitly consider price:

vr

kDQ

2

v = price, r = discount price

Discount Example

D = 10,000 k= $20 r = 20%

Price Quantity EOQv = 5.00 Q < 500 633

4.50 501-999 6663.90 Q >= 1000 716

Discount PricingTotal Cost

Order Size500 1,000

Price 1 Price 2 Price 3

X 633

X 666

X 716

Discount PricingTotal Cost

Order Size500 1,000

Price 1 Price 2 Price 3

X 633

X 666

X 716

Discount ExampleOrder 666 at a time:Hold 666/2 * 4.50 * 0.2=$ 299.70Order 10,000/666 * 20 =$ 300.00Mat’l 10,000*4.50 =$45,000.00

45,599.70 =$45.599.00

Order 1,000 at a time:Hold 1,000/2 * 3.90 * 0.2=$390.00Order 10,000/1,000 * 20 =$200.00Mat’l 10,000*3.90 =$39,000.0039,590.00

Discount Model

1. Compute EOQ for each price2. Is EOQ ‘realizeable’? (is Q in

range?)If EOQ is too large, use lowest possible value. If too small, ignore.

3. Compute total cost for this quantity4. Select quantity/price with lowest

total cost.

Period-Order Quantity Minimize the total cost of ordering

and carrying inventory and is based on assumption that demand is uniform.

POQ = EOQ / average weekly usage

Period-Order Quantity

Example : EOQ = 2800 units, and the annual usage is 52,000 units. What is POQ ?

Average weekly usage = 52000 / 52 = 1000 per

week POQ = 2800/ 1000 = 2.8 weeks - = 3 weeks.

EPQ

Persediaan diterima secara bertahap sepanjang suatu perioda waktu

t 2t

Tin

gkat

per

sedi

aan

Max

Persediaan diisi kembali

Persediaan dikosongkan

waktu

RO/XVI/14

R = jumlah produksi per tahunr = jumlah produksi per hari = R/365D = jumlah permintaan per tahund = jumlah permintaan per hari = d = D / 365Agar persediaan mencapai Q, dibutuhkan Q/r hariSelama Q/r hari, jumlah permintaan = Q/r . dPersediaan maksimal = Q - Q/r . dRata rata persediaan maksimal =

½ ( Q – Q/ r d )=Q/2 ( 1 – d/r )

Total biaya pemeliharaan = Cc. Q/2 ( 1 – d/r )Total biaya persediaan tahunan = Tc= Co D/Q + Cc Q/2 ( 1- d/r ) Q optimal :

Total biaya persediaan tahunan :

)d/r - 1 ( Cc

D Co 2 * Q

)r

d1(

2

*QCc

*Q

D Co Tc

Model Dinamis EOQ Model EOQ statis didasarkan pada

asumsi tingkat permintaan diketahui dan relatif konstan.

Jika permintaan tidak konstan (bervariasi) maka bisa dengan pendekatan EOQ, Wagner-Within, atau Silver-Meal.

Pendekatan EOQ

Bulan 1 2 3 4 5 6 7 8 9 Jumlah

Permintaan 31 14 7 0 87 44 10 51 8 252

Pers Awal 0 0 0 0 0 0 0 51 0  

Pembelian 31 21 0 0 87 44 61 0 8 252

Pers Akhir 0 7 0 0 0 0 51 0 0  

Biaya Pesan 100 100 0 0 100 100 100 0 100 600

Biaya Simpan 0 0 0 0 0 0 204 0 0 232

           Biaya total persediaan 832

Pendekatan Wagner-Within

Bulan 1 2 3 4 5 6 7 8 9 Jumlah

Permintaan 31 14 7 0 87 44 10 51 8 252

Pers Awal 0 21 7 0 0 0 10 0 8  

Pembelian 53 0 0 0 87 54 0 59 0 252

Pers Akhir 21 7 0 0 0 10 0 8 0  

Biaya Pesan 100 0 0 0 100 100 100 0 100 400

Biaya Simpan 0 28 0 0 100 100 0 32 0 184

           Biaya total persediaan 584

Ukuran Persediaan Inventory turnover rate, seberapa cepat

produk mengalir relatif terhadap jumlah yang tersimpan sebagai persediaan

Misal perusahaan menjual 150 jenis produk, nilai persediaan rata-rata Rp. 3 milyar. Penjualan setahun Rp. 40 milyar dengan margin 25%. Berarti persediaan yang terjual dalam setahun Rp. 30 milyar, sehingga tingkat perputaran adalah 10 kali dalam setahun.

Ukuran Persediaan Inventory days of supply, rata-rata jumlah

hari suatu perusahaan bisa beroperasi dengan jumlah persediaan yang dimiliki.

Misal perusahaan beroperasi 300 hari dalam setahun, maka nilai persediaan yang terjual perhari = 30 milyar / 300 hari = 0.1 milyar. Jadi persediaan senilai Rp. 3 milyar dapat digunakan selama 3/0.1 = 30 hari kerja.

Ukuran Persediaan Fill rate, persentase jumlah item

yang tersedia saat diminta pelanggan.

Fill rate 97% berarti kemungkinan 3% dari item yang diminta oleh pelanggan tidak tersedia.