Inventory Management :
MODEL PERSEDIAAN

TUJUAN
Mengetahui model-model pengelolaan
persediaan
MODEL PERSEDIAAN

Tujuan

Ukuran persediaan berhubungan dengan
ukuran pesanan, frekuensi pesan

1.
2.
menentukan ukuran persediaan
Item dengan permintaan atau kebutuhan
yang relatif stabil dalam jangka panjang,
ukuran pesanan berdampak pada
frekuensi pesan
rata-rata persediaan.
TRADE OFF
Menentukan ukuran pesanan
Makin besar ukuran pesanan :
 frekuensi pesan lebih kecil
 rata-rata persediaan besar
 biaya pesan kecil
 biaya simpan besar
Sebaliknya untuk ukuran pesan kecil.
Model
Pengelolaan Persediaan
Item dengan pasokan relatif stabil :
 dapat menggunakan model EOQ untuk
menentukan ukuran pesanan yang ekonomis.
 Ketidakpastian diakomodasi dengan
menentukan reorder point dan safety stock
Model Persediaan
Item bersifat musiman :
 Penting mempertimbangkan trade off antara
biaya kelebihan dan kekurangan persediaan.
 Resiko kelebihan dapat dikurangi dengan
(1) mengurangi harga jual di musim jual,
(2) mengurangi lead time sehingga responsif
terhadap pasar
VENDOR MANAGED INVENTORY
Vendor Managed Inventory (VMI)
 Model pengelolaan persediaan dimana
keputusan waktu dan ukuran pengiriman
ditentukan supplier.

Pembeli memberikan informasi yang up to
date tentang kondisi persediaan dan
kebutuhan
•Biaya pesan dan simpan
•Demand is known and constant D units
per time.
•No stock-outs!
•Leadtime=0!
Costs:
K: order cost
c: Unit variable cost
h: inventory holding cost
Q : order size (decision var.)
Inventory
Q
-D
Time
T
Deriving EOQ




Total cost at every cycle:
C(Q)=K+cQ
Average inventory holding cost in a cycle: Q/2
Cycle time T =Q/D
G(Q)=(K+cQ)/T + hQ/2 = KD/Q + Dc + hQ/2
Q* 
2 KD
h
EOQ: Costs
G(Q)
Ordering Cost
Holding cost
Total cost
G(Q)
hQ
2
KD
Q
Q
Q*
Stochastic Demand

Usually the demand has a variable component
D=Dconstant+Dvariable
Inventory Policy
C ontinuous P eriodic
T ype A
(s,S)
(R ,s,S)
T yp e B
(s,Q )
(R ,S)
Continuous review,
reorder policy
m – demand rate
L – replenishment lead time
S: inventory reorder level; Q: reorder size
inventory
+Q
+Q
S
dL=mL
Safety stock: S-dL
L
place
order
order arrives
time
Periodic Review, Orderup-to Policy
Define:
Inventory Position = Quantity
on hand
+
Quantity
on order
S - Base stock level/Order-up-to Point
R- Review period
L- Replenishment lead time
m - Demand per unit time
Q - Order quantity
ss - Safety stock
Ordering Rule:
Place an order every R periods so as to bring your
inventory position to the Base Stock Level, S.
Periodic review with no
demand variability
Inventory position
Inventory Level
On-hand inventory
m(R+L)
mR
mL
0
R
L
2R
R+L
3R
2R+L
4R
3R+L
time
Periodic review with no
demand variability
Order Quantity, Q = mR
Average Cycle stock = Q/2 = mR / 2
Pipeline stock = m L
Order-up-to point, S = m (R+L)
Periodic review with
variable demand
Order-up-to point (S) = m (R+L) + Safety Stock (ss)
Average Order Quantity (Q) = mR
Average Pipeline stock = m L
Average Cycle stock = Q/2 = mR / 2
Average Safety Stock = ss = ?
Determination of the
Safety Stock
Inventory Level
Inventory position
On-hand inventory
mR+mL+ss
mR+ss
mL+ss
ss
0
R
L
2R
R+L
3R
2R+L
4R
3R+L
time
Inventory Level
Freq
Inventory
On-hand
X
Place
order
Lead Time
Receive
order
Time
Inventory Level
Freq
Inventory
On-hand
X
m ( R  L ) + SS  z  R  L
=S
Safety Stock (SS)
Place
order
Lead Time
Receive
order
Time
Given R, L, m, and :
Safety Stock (ss) =
z R  L
Expected standard
loss (shortage)
Demand variability
over R + L units time
Choose z such that:
Fill Rate (p) = 1 
L( z) 
RL
mR
Average demand filled
per period
So:
L ( z )  1  p 
where L(z) is the standard loss function
Base Stock Level (S) =m R  m L  z 
RL
mR

RL
Example #1
Given:
Solve:
L  z   1 
R = 2 weeks
L= 1 week
m = 150 units per week
 = 10 units per week
Target fill rate, p=99%
p
mR

R L
Safety stock = ss  z 
 . 01 
150  2
10
2 1
 0 . 173
so from table, z = 0.58
R  L  0 . 58  10 3  10
Base stock level = S  m R  m L  z 
R  L  150  2  150  1  10  460
Example #2
Given:
R = 2 weeks
L= 1 week
m = 150 units per week
 = 10 units per week
Target fill rate, p=95%
Solve:
L  z   1  p 
mR

R L
Safety stock = ss  z 
Base stock level =
 . 05 
150  2
10
2 1
 0 . 866
so from table, z = -0.73
R  L   0 . 73  10 3   12
S  m L  m R  z
R  L  150  2  150  1  12  438