W13 service inventory (continued)

(1)

1

(2)

Inventory Models

• Economic Order Quantity (EOQ)

• Special Inventory Models

With Quantity Discounts

Planned Shortages

• Demand Uncertainty - Safety Stocks

• Inventory Control Systems

Continuous-Review (Q,r)

Periodic-Review (order-up-to)

(3)

3 Ketidakpastian

Ketidakpastian dalam inventori

● Demand :

1. unused stock

2. stockout/ shortage

● Cost

● Lead time:

1. unused stock

2. stockout/ shortage

(4)

Reorder Point

dengan

Safety Stock

Reorder point

0 In

ven

tor

y

le

vel

Time

Safety stock

(5)

5 Model Persediaan dengan Demand

Probabilistik dan LT ≠ 0 dan tetap

● Adanya

LT

membuat perlunya ditentukan

REORDER POINT: titik dimana pemesanan

harus dilakukan

● Demand probabilistik (Distribusi Normal)

membuat terdapat kemungkinan persediaan

habis sedangkan pesanan belum datang

(6)

● Reorder Point besarnya sama dengan demand

selama lead time:

ROP

=

D

×

LT

● Contoh: jika demand per tahun 10.000 unit; lead

time pemesanan selama 1 minggu; maka:



ROP

= demand selama 1 minggu



ROP

= 1/52 x 10.000 = 192,3 ~ 193



Artinya jika persediaan mencapai 193 unit

maka pemesanan harus dilakukan

● Reorder point tersebut belum memperhitungkan

besarnya Safety Stock

(7)

7 Demand selama Lead Time

Z=

2 all demand met

shortages

(8)

Demand Probabilistik

● Safety stock dibuat untuk mengurangi

kemungkinan out of stock (shortage)

● Dipengaruhi oleh lead time dan variansi demand

● Jika D adalah demand per unit waktu dan



adalah standard deviasi, maka demand selama

lead time adalah LT

×

D, variansi demand selama

lead time adalah



2 ×

_{LT dengan standard deviasi}

adalah (



2 ×

_LT)

1/2

● Safety stock ditentukan dengan perhitungan:

SS = Z

×

Standard deviasi demand selama

LT

Z

(9)

9 Demand Probabilistik

(Uncertainty in Demand)

Keputusan persediaan yang harus dibuat adalah:

● Lot (jumlah) pesanan:

● Saat pemesanan kembali:

HC

RC

D

Q

₀



2 



D

LT





Z

LT



(10)

(11)

11 Penentuan Nilai Z

Service level Stock Out

Z

value

Probability

0.90

0.10

1.28

0.95

0.05

1.65

0.98

0.02

2.05

0.99

0.01

2.33

(12)

Contoh

Permintaan sebuah item berdistribusi normal dengan

rata-rata 1000 unit per minggu dan standard deviasi

200 unit. Harga item $10 per unit dan ongkos pesan

$100. Ongkos simpan ditetapkan sebesar 30% dari

nilai inventori per tahun dan lead time tetap selama 3

minggu. Tentukan kebijakan inventori jika diinginkan

service level 95%, dan berapakah ongkos untuk safety

stock-nya

D

= 1000 per minggu (



=200)

UC

= $10 per unit

RC

= $ 100 per pesan

HC

= 0.3 x $10 = $3 per unit per tahun

(13)

13 (Lihat Tabel Distribusi Normal)

Ongkos ekspektasi safety stock:

(14)

Lead Time Probabilistik

(Uncertainty in Lead Time)

● LT lebih pendek maka akan muncul unused

stock, namun jika LT lebih panjang maka muncul

shortage

● Probabilitas shortage adalah probabilitas bahwa

demand selama lead time lebih besar daripada

reorder level, sehingga,

(15)

15 Contoh

(16)

D & LT Probabilistik

Jika

demand mempunyai rata-rata

D

dan standard

deviasi



_D

dan,

lead time mempunyai rata-rata

LT

dan standard

deviasi

LT

_D

maka,

demand selama lead time

LT

×

D

dan standard

deviasi



2  

2

2 

LT

D

(17)

17 Contoh (Uncertain in both LT dan D)

Permintaan sebuah produk berdistribusi normal

dengan rata-rata 400 unit per bulan dan standar

deviasi 30 unit per bulan. Lead time juga berdistribusi

normal dengan rata-rata 2 bulan dan standar deviasi

0.5 bulan. Berapakah ROP yang memberikan service

level 95%? Berapakah jumlah pemesanan kembali jika

ongkos pesan $400 dan ongkos simpan $10 per unit

per bulan?

D

= 400 unit per bulan



_D

= 30 unit

LT

= 2 bulan

(18)

Contoh (Uncertain in both LT dan D)

Demand selama LT = LT x D = 800 unit

Standard deviasi demand selama lead time:

Untuk service level 95%,

(19)

19 Contoh (Uncertain in both LT dan D)

Ukuran pemesanan optimal (ekonomis):

unit

179

10

400

2

2 *











(20)

Klasifikasi Inventori: ABC

• Manajemen persediaan sering kali harus dibedakan

menurut karakteristik masing-masing item

• Salah satu klasifikasi yang umum digunakan pada

manajemen persediaan adalah sistem ABC dimana

item-item dikelompokkan menjadi tiga kelas

• Pembagian kelas ini didasarkan atas tingkat kepentingan

masing-masing item

Karakteristik

A

B

C

(21)

21 Cara Melakukan Klasifikasi

1. Tabulasikan nama, harga per unit, dan jumlah unit yang

dikonsumsi per tahun.

2. Kalikan harga per unit dengan jumlah unit yang dipakai

selama setahun untuk mendapatkan nilai rupiah konsumsi

setahun dari masing-masing item.

3. Jumlahkan nilai rupiah tahunan untuk keseluruhan item dan

hitung persentase pemakaian tahunan untuk tiap-tiap item.

4. Sorting (urutkan) item-item mulai dari yang konsumsi rupiah

tahunannya besar.

(22)

Contoh Klasifikasi ABC

Nama

Rp/unit

kons/th

Rp/th

%Rp/th

A

100,000

300 30,000,000

10.08 B

1,000,000

200 200,000,000

67.23 C

50,000

30 1,500,000

0.50 D

20,000

80 1,600,000

0.54 E

10,000

700 7,000,000

2.35 F

150,000

350 52,500,000

17.65 G

90,000

20 1,800,000

0.61 H

25,000

80 2,000,000

0.67 I

5,000

100 500,000

0.17 J

2,000

300 600,000

0.20

(23)

23 Contoh Klasifikasi ABC

Tabel Perhitungan untuk klasifikasi ABC

Nama

Rp/unit

kons/th

Rp/th

%Rp/th

Kumul.%Rp/th

B

1,000,000

200 200,000,000

67.23 67.23 (A)

F

150,000

350 52,500,000

17.65 84.87 (A)

A

100,000

300 30,000,000

10.08 94.96 (B)

E

10,000

700 7,000,000

2.35 97.31 (B)

H

25,000

80 2,000,000

0.67 97.98 (B)

G

90,000

20 1,800,000

0.61 98.59 (C)

D

20,000

80 1,600,000

0.54 99.13 (C)

C

50,000

30 1,500,000

0.50 99.63 (C)

J

2,000

300 600,000

0.20 99.83 (C)

I

5,000

100 500,000

0.17 100.00 (C)

(24)

Betting on Uncertain Demand:

Newsvendor Model

(25)

The Newsboy Model: an Example

Mr. Tan, a retiree, sells the local newspaper at a

Bus terminal. At 6:00 am, he meets the news

truck and buys # of the paper at $4.0 and then

sells at $8.0. At noon he throws the unsold and

goes home for a nap.

If average daily demand is 50 and he buys just

50 copies daily, then is the average daily profit

=50*4 =$200?

(26)

Betting on Uncertain Demand

• You must take a firm bet (how much stock to

order) before some random event occurs

(demand) and then you learn that you either

bet too much or too little

• More examples: Products for the Christmas

season; Nokia’s new set, winter coats, New

(27)

Bossini -- Winter Clothes

• Season: Dec.

–

Jan./Feb.

• Purchase of key materials (fabrics,

dyeing/printing, …) takes long times (upto 90

days)

(28)

(29)

Hong

Kong

Seattle

Denver

(30)

The SO Supply Chain

Shell Fabric

Others

Cut/Sew

Subcontractors

Lining Fabric

Insulation mat.

Snaps

Zippers

Distr Ctr

Retailers

(31)

O’Neill’s Hammer 3/2 wetsuit

(32)

Hammer 3/2 timeline and economics

Nov Dec Jan

Feb

Mar Apr May Jun

Jul

Aug

Generate forecast

of demand and

submit an order

to TEC

• Discounted suits

sell for

v

= $90

• The “too much/too little problem”:

–

Order too much and inventory is left over at the end of the season

–

Order too little and sales are lost.

(33)

Newsvendor model

implementation steps

• Gather economic inputs:

–

Selling price, production/procurement cost, salvage value

of inventory

• Generate a demand model:

–

Use empirical demand distribution or choose a standard

distribution function to represent demand, e.g. the normal

distribution, the Poisson distribution.

• Choose an objective:

–

e.g. maximize expected profit or satisfy a fill rate

constraint.

• Choose a quantity to order.

(34)

The Newsvendor Model:

Develop a Forecast

(35)

Historical forecast performance at O’Neill

0 1000

2000

3000

4000

5000

6000

7000

Forecast

Forecasts and actual demand for surf wet-suits from the previous season

(36)

Empirical distribution of forecast accuracy

Empirical distribution function for the historical A/F ratios.

0%

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75 A/F ratio

Product description

Forecast

Actual demand

Error* A/F Ratio**

JR ZEN FL 3/2

90

140 -50

1.56 * Error = Forecast - Actual demand

(37)

Normal distribution tutorial

• All normal distributions are characterized by two parameters, mean =

m

and standard

deviation =



• All normal distributions are related to the standard normal that has mean = 0 and

standard deviation = 1.

• For example:

–

Let

Q

be the order quantity, and (

m

,



) the parameters of the normal demand

forecast.

–

Prob

{demand is

Q

or lower} =

Prob

{the outcome of a standard normal is

z

or

lower}, where

–

(The above are two ways to write the same equation, the first allows you to

calculate

z

from

Q

and the second lets you calculate

Q

from

z

.)

–

Look up

Prob

{the outcome of a standard normal is

z

or lower} in the Standard

Normal Distribution Function Table.

or

Q

z

m

Q

m

z







  

(38)

-Converting between Normal distributions

Start with

m

= 100,



= 25,

Q

= 125

Center the

distribution over 0

by subtracting the

mean

(39)

• Start with an initial forecast generated from hunches, guesses, etc.

–

O’Neill’s initial forecast for the Hammer 3/2 = 3200 units.

• Evaluate the A/F ratios of the historical data:

• Set the mean of the normal distribution to

• Set the standard deviation of the normal distribution to

Using historical A/F ratios to choose a Normal

distribution for the demand forecast

Forecast

1. Why not just order/buy 3200 units? It is

the most likely outcome!

2. Forecasts always are biased, so order

less than 3200

(40)

Empirical distribution of forecast accuracy

Empirical distribution function for the historical A/F ratios.

0%

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75 A/F ratio

Product description

Forecast

Actual demand

Error* A/F Ratio**

JR ZEN FL 3/2

90

140 -50

1.56 * Error = Forecast - Actual demand

(41)

Table 11.2

Product description

Forecast

Actual demand A/F Ratio* Rank

Percentile**

ZEN-ZIP 2MM FULL

470

116

0.25

1 3.0%

* A/F Ratio = Actual demand divided by Forecast

(42)

If the coming year is a similar to the last year,

i.e., the forecasting errors are similar, then,

• There is a 3% chance that demand will be

800 units or fewer (0.25*3200)

• There is a 90.9% chance demand is 150%

(43)

O’Neill’s Hammer 3/2 normal distribution forecast

• O’Neill should choose a normal distribution with mean 3192 and standard

deviation 1181 to represent demand for the Hammer 3/2 during the

Spring season.

Product description

Forecast Actual demand

Error

A/F Ratio

JR ZEN FL 3/2

90

140 -50

1.5556

EPIC 5/3 W/HD

120

83

37 0.6917

(44)

Empirical vs normal demand distribution

0 1000

2000

3000

4000

5000

6000

Quantity

(45)

The Newsvendor Model:

The order quantity that maximizes

expected profit

(46)

“Too much” and “too little” costs

• C

_o

= overage cost

–

The cost of ordering one more unit than what you would have ordered

had you known demand.

–

In other words, suppose you had left over inventory (i.e., you over

ordered).

C

_o

is the increase in profit you would have enjoyed had you

ordered one fewer unit.

–

For the Hammer 3/2

C

_o

=

Cost

–

Salvage value

=

c

–

v =

110 –

90 = 20

• C

_u

= underage cost

–

The cost of ordering one fewer unit than what you would have

ordered had you known demand.

–

In other words, suppose you had lost sales (i.e., you under ordered).

C

_u

is the increase in profit you would have enjoyed had you ordered one

more unit.

(47)

Balancing the risk and benefit of ordering a unit

• Ordering one more unit increases the chance of overage …

–

Expected loss on the

Q

th

₍₊₁₎

_{unit =}

_C

o

x

F

(

Q

)

–

F

(

Q

) = Distribution function of demand =

Prob

{

Demand

<=

Q

)

• … but the benefit/gain of ordering one more unit is the reduction in the

chance of underage:

–

Expected gain on the

Q

th

₍₊₁₎

_{unit =}

_C

0

800 1600

2400

3200

4000

4800

5600

6400

Q

th

unit ordered



As more units are ordered,

the expected benefit from

ordering one unit decreases

while the expected loss of

ordering one more unit

increases.

11-50

(48)

Newsvendor expected profit

maximizing order quantity

• To maximize expected profit order

Q

units so that the

expected loss on the

Q

th

unit equals the expected gain on the

Q

th

unit:

• Rearrange terms in the above equation ->

• The ratio

C

_u

/ (

C

_o

+

C

_u

) is called the

critical ratio

.

• Hence, to maximize profit, choose Q such that we don’t have

lost sales (i.e., demand is Q or lower) with a probability that

equals the critical ratio

(49)

Product description

Forecast

Actual demand

A/F Ratio Rank

Percentile

Finding the Hammer 3/2’s expected profit maximizing order

quantity with the empirical distribution function

• Inputs:

–

Empirical distribution function table;

p

= 180;

c

= 110;

v

= 90;

C

_u

= 180-110 =

70;

C

_o

= 110-90 =20

• Evaluate the critical ratio:

• Lookup 0.7778 in the empirical distribution function table

–

If the critical ratio falls between two values in the table, choose the one that