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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 Value

Housing (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

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

- 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

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

Optimal Quantity

Total Costs =

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

- 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:

v = price, r = discount price

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 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

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

- 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

Persediaan diisi kembali

Persediaan dikosongkan

Max

Tingkat persediaan

t

2t

waktu

RO/XVI/14

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 )

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 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

- 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.

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