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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.

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Definitions
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
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
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
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 inventories1
Reasons for Inventories

  • Low cost plan operation

  • Minimum investment


Inventory costs
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
Inventory Holding Costs

Category% of Value

Housing (building) cost 6%

Material handling 3%

Labor cost 3%

Opportunity/investment 11%

Pilferage/scrap/obsolescence 3%

Total Holding Cost 26%


Inventory holding costs1
Inventory Holding Costs

  • Capital cost

  • Storage cost

  • Risk cost

    - Obsolescence

    - Damage

    - Pilferage, goods lost, strayed, stolen

    - Deterioration


Abc analysis
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
Classifying Items as ABC

% Annual $ Usage

A

B

C

% of Inventory Items


Abc classification solution
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



Order quantities
Order Quantities

  • How much should be ordered at one time ?

  • When should an order be placed ?


Order quantities1
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
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

Inventory

Level

Q*

Optimal

Order

Quantity

Decrease Due to

Constant Demand

Time


EOQ

Inventory

Level

Instantaneous

Receipt of Optimal

Order Quantity

Q*

Optimal

Order

Quantity

Time


EOQ

Inventory

Level

Q*

Reorder

Point

(ROP)

Time

Lead Time


EOQ

Inventory

Level

Q*

Average

Inventory Q/2

Reorder

Point

(ROP)

Time

Lead Time


Total costs
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


How much to order
How Much to Order?

Annual Cost

Holding Cost

= H * Q/2

Order Quantity


How much to order1
How Much to Order?

Annual Cost

Ordering Cost

=k* D/Q

Holding Cost

= H * Q/2

Order Quantity


How much to order2
How Much to Order?

Total Cost

= Holding + Ordering

Annual Cost

Order Quantity


How much to order3
How Much to Order?

Total Cost

= Holding + Ordering

Annual Cost

Optimal Q

Order Quantity


Optimal quantity
Optimal Quantity

Total Costs =


Optimal quantity1
Optimal Quantity

Total Costs =

Take derivative with respect to Q =


Optimal quantity2
Optimal Quantity

Total Costs =

Take derivative with respect to Q =

Set equal

to zero


Optimal quantity3
Optimal Quantity

Total Costs =

Take derivative with respect to Q =

Set equal

to zero

Solve for Q:


Optimal quantity4
Optimal Quantity

Total Costs =

Take derivative with respect to Q =

Set equal

to zero

Solve for Q:


A question
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
Quantity Discounts

  • How does this all change if price changes depending on order size?

  • Explicitly consider price:

v = price, r = discount price


Discount example
Discount Example

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

Price Quantity EOQ

v = 5.00 Q < 500 633

4.50 501-999 666

3.90 Q >= 1000 716


Discount pricing
Discount Pricing

Total Cost

Price 1

Price 2

Price 3

X 633

X 666

X 716

Order Size

500 1,000


Discount pricing1
Discount Pricing

Total Cost

Price 1

Price 2

Price 3

X 633

X 666

X 716

Order Size

500 1,000


Discount example1
Discount Example

Order 666 at a time:

Hold 666/2 * 4.50 * 0.2= $ 299.70

Order 10,000/666 * 20 = $ 300.00

Mat’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= $390.00

Order 10,000/1,000 * 20 = $200.00

Mat’l 10,000*3.90 = $39,000.00 39,590.00


Discount model
Discount Model

1. Compute EOQ for each price

2. 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 quantity

4. Select quantity/price with lowest total cost.


Period order quantity
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 quantity1
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

Persediaan diisi kembali

Persediaan dikosongkan

Max

Tingkat persediaan

t

2t

waktu

RO/XVI/14


R = jumlah produksi per tahun

r = jumlah produksi per hari = R/365

D = jumlah permintaan per tahun

d = jumlah permintaan per hari =

d = D / 365

Agar persediaan mencapai Q, dibutuhkan Q/r hari

Selama Q/r hari, jumlah permintaan = Q/r . d

Persediaan maksimal =

Q - Q/r . d

Rata 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 :


Model dinamis eoq
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.


Ukuran persediaan
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 persediaan1
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 persediaan2
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.


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